Problems and tasks of LC reliability. The basic concepts of the problem and the problem of vehicle reliability are also valid for laser complexes of the LK. Experimental determination of LC reliability indicators is many times more complicated than measurement or determination of most technical parameters. The science of reliability studies the change in the quality indicators of products under the influence of those reasons that lead to absolute changes in their properties.

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Lecture 1. Introduction to the reliability of technical systems (TS). Problems and tasks of LC reliability.

Technical systems (TS) include technical objects (products, machines, technical complexes) for military and civil purposes. The basic concepts, problems and tasks of vehicle reliability are also valid for laser systems (LC).

According to the modern theory of reliabilitythe reliability of the LC is the property to maintain its operability over time, that is, the state in which the complex is able to perform the specified functions, keeping the values ​​of the specified parameters (technical characteristics) within the limits established by the regulatory and technical documentation.

An event that consists in a malfunction, i.e. the transition of the LC to an inoperative state is called a failure. The failure of the LC is not only the immediate termination of functioning, but also an unacceptable decrease in technical characteristics that determine the effectiveness of the task..

Various failures also have different consequences: from minor deviations in work to emergency situations.

The areas of operability of the LC are subdivided into a valid area, which determines the required performance of the product, and a designated area, which is dictated by the requirements of the technical specifications for individual parameters.

The performance depends on the operating time - the amount of work, which can be estimated in calendar hours, the number of cycles, the number of impulses, kilometers traveled, storage time, etc..

Measurement of time in calendar hours is typical for such reasons of malfunctioning of the product as corrosion, the effect of external temperature factors and radiation.

Run-to-Failure Time is a random variable.

If the duration of the product's operation is regulated and is a deterministic value, then it is called the established resource.

The resource is the operating time to the limiting state specified in the technical documentation.

The service life is the calendar duration of the LC operation up to the limiting state, taking into account the breaks for maintenance and repair.

Reliability, being one of the main properties that characterize the quality of the complex operation, is itself also characterized by a number of properties, the main of which are reliability, durability, maintainability and preservation.

Reliability - the property to continuously maintain an operable state for a certain operating time without taking into account forced interruptions.

Durability - the property of the paintwork to maintain performance up to the limit state with the necessary breaks for maintenance and repairs.

The limiting state is a state in which further use of the drug for its intended purpose is unacceptable due to safety requirements or low efficiency, including economic.

It should be noted that durability and reliability are not identical concepts; they define different sides of one phenomenon. LK can have high reliability and at the same time have low durability.

Maintainability - a property of the LC, which consists in its adaptability to the prevention, detection and elimination of failures and malfunctions by carrying out maintenance and repairs.

The goal of preventive maintenance is to prevent malfunction or abnormal operating conditions from occurring through preventive measures such as tweaking or adjusting, lubricating, cleaning, and some corrections. Preventive maintenance can also include replacing items or items that are at their limits.

Persistence is the property of the LC to maintain an operable state during its storage.

Thus, the reliability of LC is a very specific property, depending on a large number of different variable factors, many of which are random and difficult to assess with a single numerical indicator. Experimental determination of LC reliability indicators is many times more complicated than measurement or determination of most technical parameters.

Reliability, which characterizes the change in quality indicators over time, is, as it were, "quality dynamics",its sweep in time. Hence, reliability is the property of a product to maintain the required quality indicators throughout the entire period of its use.

The science of reliability studies the change in the quality indicators of products under the influence of those reasons that lead to absolute changes in their properties.

Product reliability is one of the main indicators of its quality..

Striving to provide a high level of quality and reliability is the main driving force in the creation of new and the operation of existing products..

The main properties of reliability (reliability, durability, maintainability and preservation) must be ensured at all stages of the LC life cycle.

When designingLK establishes and substantiates the necessary requirements for reliability, which must be ensured through the adopted rational circuit and design solutions. At this stage, methods of protection against various harmful influences are developed, the possibilities are considered to automatically restore the lost operability, and the suitability for repair and maintenance is assessed.

When making(production), the reliability of the LC is ensured and monitored, depending on the quality of manufacturing of parts, methods of control of manufactured products, the ability to control the course of the technological process, on the quality of assembly, methods of testing and debugging and other indicators of the technological process.

During operationLK realizes its reliability. At the same time, it depends on the modes and conditions of operation, the adopted repair system, maintenance technology and other operational factors.

Methods for improving the quality and reliability of a vehicle, having a general orientation for all technical systems, have, as a rule, certain specific features depending on the design, purpose and technical requirements that apply to a specific sample.

Table 1.1 shows the classification of technical systems (machines) according to their purpose. It contains the basic requirements for the technical characteristics of vehicles for various purposes.

Table 1.1.

The level of reliability should be such that when using the vehicle in any situations stipulated by the technical conditions (TS), failures do not occur, i.e. performance was not impaired. In addition, in many cases it is desirable that there is a safety margin to increase resistance to extreme influences when the technical system falls into conditions not provided for by the technical specifications.

In addition, a safety margin is necessary to ensure operability under conditions of wear, which leads to a gradual deterioration in technical characteristics. Therefore, the higher the safety margin, the longer, ceteris paribus, the vehicle will be in an operable state.

An insufficient level of reliability of the vehicle (both new and "worn out") can lead to various consequences in the event of a violation of its performance, the main of which are:

1.- catastrophic failureassociated with the death of people (as a result of aircraft or other accidents), failure of military equipment at crucial moments, irreversible destruction of the environment. Suffice it to recall such tragic events as the accident at the Chernobyl nuclear power plant or the destruction of the Challenger spacecraft. Numerous accidents and disasters constantly occur in the world.

For example, statistics show that about 1200 major ship accidents occur in the world every year. There are more than 50 nuclear warheads and more than 10 nuclear reactors at the bottom of the world's oceans after accidents.

2. - failure, due to which the vehicle ceases to function as a result of the failure of one or another unit (element), which leads to significant economic losses;

3.- decrease in work efficiency when the vehicle is capable of functioning, but with lower efficiency, productivity, power, accuracy and other technical characteristics that were achieved for a new product.

The behavior of the vehicle from the standpoint of reliability is associated with the change in time of those "output" parameters that characterize the purpose and quality.

Assessment of the parametric reliability of the vehicle and analysis of the causes and consequences of changes in its technical characteristics during long-term operation are the foundation of the entire reliability problem.

Huge funds are spent in the world to keep the machine park in working order. The creation of repair enterprises and factories for the production of spare parts, the use of multipurpose services for the repair and maintenance of machines, including information, transportation and supply systems - all this is a consequence of the fact that machines lose their performance due to the processes of wear, corrosion, fatigue destruction and other processes leading to the "aging" of the machine.

According to various sources, 5-10 times more money is spent on the repair and maintenance of machines for the entire period of their operation than on the manufacture of new ones.

In industrialized countries, approximately 4.5 gross national income is spent on friction, wear, and corrosion of the movable joints of technical products. This results in the loss of raw materials and energy at a total cost of several hundred billion dollars annually worldwide.

Losses from insufficient reliability of unique machines are especially great. If they fail due to unforeseen circumstances, there is a great danger of tragic consequences for people and the environment.

Therefore, more and more attention is paid all over the world to the issues of operation and repair of industrial products.

The forecast for the development of the leading industries shows that in the XX I century in most industries in the field of operation and repair will employ up to 80 ... 90% of all labor resources.

An insufficient level of product reliability leads to large economic losses.

The safety of functioning of the vehicle is a complex problem that includes issues related to human activities, the organization of labor, the socio-political situation (for example, the possibility of sabotage), the training of personnel, and their discipline. The reliability of the vehicle, including its behavior in extreme situations, is one of the main factors in the problem of safety.

The malfunction and failure of many vehicles are associated not only with safety issues and economic costs, but also have a direct impact on the environment and the ecological situation on our planet.

The operation of machines when their characteristics (for example, efficiency, composition of exhaust gases, tightness, dynamic loads, temperature, etc.) go beyond the permissible limits, when repair and maintenance of machines is carried out, especially under unforeseen circumstances or during the elimination of the consequences of an accident, lead to harmful, often destructive effects on the biosphere, on inanimate nature, on the atmosphere, on the entire mechanism of interaction in the world around us.

In the problem of creating competitive products and finding the most effective ways of selling them, the level of reliability of the machines supplied to the consumer plays a significant role.

Refusal of a vehicle during use, even if this does not lead to serious consequences, causes serious moral damage to the manufacturer and undermines its credibility.

In the event of vehicle failures during their operation or storage, manufacturers or special organizations are forced to create an extensive network of maintenance and emergency repairs with an appropriate information system, achieving maximum satisfaction of various consumer requests. The higher the level of reliability of the vehicle guaranteed by the manufacturer, the more competitive it will have, all other things being equal.

Decision-making on the need to increase the achieved level of vehicle reliability should be based on economic analysis. The modern level of development of technology allows you to achieve almost any quality and reliability indicators of the product. It's all about the cost to achieve the goal.

Thus, it is advisable to create a highly reliable vehicle not only in terms of reliability and prestige requirements, but also from the standpoint of economic efficiency.

With an increase in the cost of manufacturing a new vehicle, it is necessary to decide how much of these funds should be used to improve technical characteristics and how much to increase reliability.

In the context of the intensive development of mechanical engineering, practice, with its various requests in the field of design, production and operation, poses new problems for the science of reliability, associated with forecasting, with methods of testing for reliability, with optimization of the design according to the criteria of quality and reliability.

At the same time, no matter how varied the TS and the conditions of their operation, the formation of reliability indicators occurs according to general laws, obeys a single logic of events, and the disclosure of these connections is the basis for assessing, calculating and predicting reliability, as well as for building rational production systems, testing and operation.

The science of reliability studies the patterns of changes in the quality indicators of products over time, and on the basis of this, methods are developed that provide the necessary duration and reliability of the vehicle with the least cost of time and money.

It should be emphasized that the issues of achieving a certain level of quality indicators of machines - their accuracy, power, efficiency, productivity and others - are considered, as a rule, by industry sciences, and "reliability" is considered the process of changing these indicators over time.

Currently, the methodological approach, based on the development of parametric reliability models, in which the process of changes in the TS performance over time is formalized, is gaining ground. The probabilistic characteristics of this process can be predicted in the early stages of their creation.

That's why The main features of the scientific aspect of the vehicle reliability problem are:

• taking into account the time factor, since the change in the initial characteristics of the vehicle is assessed during its operation;

• combination of probabilistic methods with the laws of physical processes;

• forecasting a possible change in the state of an object during its operation;

• establishing a connection between the reliability of the vehicle and the indicators of its quality and performance.

The main tasks of reliability include:

• At the design stage- calculation of the service life of the main elements of the vehicle (in terms of wear, fatigue strength), predicting reliability based on its output parameters, analyzing options and choosing a rational design in terms of reliability, evaluating optimal operating modes and areas of application, taking into account a given period of serviceability.

• At the manufacturing stagea new sample - the creation of a quality and reliability management system, ensuring the reliability of the technological process of manufacturing parts and assemblies of the vehicle, developing methods for testing samples in terms of quality and reliability.

• During the operation phase- development of a rational system of technical maintenance and repair of the vehicle, the creation of methods and tools for diagnosing the state of the vehicle during operation, the creation of an information database on the reliability of the system and its elements.

When solving various problems of reliability, it is necessary, first of all, to establish how the vehicle will behave when performing its functions and in interaction with the environment, as a result of what reasons its technical characteristics will gradually change.

The general methodological approach for solving these problems is presented in Fig. 1.1 in the form of a physical-probabilistic model for assessing parametric reliability.

Rice. 1.1. Scheme of a physical-probabilistic model for assessing parametric reliability.

This diagram reveals the main cause-and-effect relationships that lead to a change (degradation) in time of the output parameters.

Degradation of the state of the vehicle (machine) occurs because during operation all types of energy - mechanical, thermal, chemical, electromagnetic - act on it and cause reversible and irreversible processes in it that change its initial characteristics.

You can specify the following main sources of energy impact on the machine:

• the effect of the energy of the environment in which the vehicle is located during operation, including the person performing the functions of the operator;

• internal energy sources associated both with the working processes taking place in the vehicle and with the operation of its individual units;

• potential energy that is accumulated in the materials and parts of the vehicle during their manufacture (internal stresses in the casting, assembly stresses);

• impact on the vehicle during repair work and maintenance.

The main types of energy that affect the performance of the vehicle include:

• Mechanical energy, which is not only transmitted through all links of the vehicle during operation, but also affects it in the form of static and dynamic loads from interaction with the external environment.

The forces arising in the vehicle are determined by the nature of the working process, inertia of moving parts, friction in kinematic pairs. These forces are random functions of time, since the nature of their occurrence is associated with complex physical phenomena and with variable modes of operation of the vehicle. For example, the loads in dynamic systems, the torque of engines, the forces on the working bodies of agricultural, construction, textile and other machines, the friction forces in kinematic pairs, etc. change within a fairly wide range.

Mechanical energy in a vehicle can also manifest itself as a result of those energy costs that took place in the manufacture of its parts and were stored in them in a potential form. For example, deformation of parts during redistribution of internal stresses after assembly of a subassembly or after heat treatment of a part.

• Thermal energy acting on the vehicle and its parts during ambient temperature fluctuations, during the implementation of the working process (especially strong thermal effects occur during the operation of engines and a number of technological machines), during the operation of drive mechanisms, electrical and hydraulic devices.
• Chemical energy that affects the operation of the vehicle, for example, through the corrosion of individual components in air, which contains moisture and aggressive components.

If the vehicle operates in corrosive environments (equipment of the chemical industry, ships, many machines of the textile industry, etc.), then chemical influences cause processes that lead to the destruction of individual elements and assemblies.

• Nuclear (atomic) energy generated in the process of nuclear reactions and affecting materials (especially in space), changing their properties.
• Electromagnetic energy in the form of radio waves (electromagnetic oscillations) that penetrate the entire space around the vehicle and have a negative impact on the operation of electronic equipment, which is increasingly used in modern systems.
• Biological factors can also affect the performance of the vehicle and cause biological damage, for example, in the form of biocorrosion of a metal, when microorganisms (so-called hydrogen bacteria) develop on its surface. These processes are especially intense in tropical countries, where there are microorganisms that not only destroy some types of plastics, but can also affect the metal.

All types of energy acting on the vehicle and its units cause a number of undesirable processes in it, create conditions for the deterioration of its technical characteristics.

Some of the processes occurring in the vehicle are reversible. Reversible processes temporarily change the parameters of parts, assemblies and the entire system within certain limits, without a tendency of progressive deterioration. The most typical examples of such processes are elastic deformation of machine units and parts, which occurs under the action of external and internal forces, and thermal deformation of structures.

Irreversible processes lead to a progressive deterioration of the technical characteristics of the vehicle over time and therefore they are called aging processes.

The most typical irreversible processes are wear, corrosion, fatigue, redistribution of internal stresses and warpage of parts over time.

The processes that change the initial characteristics of the vehicle proceed at different rates and can be divided into three main categories.

Fast flowing processesarise immediately as soon as the vehicle begins to function. These processes have a frequency of change, usually measured in fractions of a second. They end within the cycle of the vehicle and reappear during the next cycle.

This includes unit vibrations, changes in frictional forces in movable joints, fluctuations in working loads and other processes that affect the relative position of the vehicle units at each moment of time and distort the cycle of its operation.

Medium speed processesassociated with the period of continuous operation of the vehicle, their duration is usually measured in minutes or hours. They lead to a monotonic change in the initial parameters. This category includes both reversible processes (for example, a change in the temperature of the vehicle itself and the environment) and irreversible (for example, the process of wear of a cutting tool, which occurs many times more intensively than the wear of parts and assemblies of a metal-cutting machine).

Slow processesappear during the entire period of operation of the vehicle. They last for days and months. These processes include wear of basic elements, creep of metals, contamination of friction surfaces, corrosion, and seasonal temperature changes.

These processes also affect the accuracy, power, efficiency and other parameters of the vehicle, but their changes are very slow. The usual methods of dealing with these processes are repairs and preventive measures, which are carried out at regular intervals.

It should be emphasized that all processes are random functions characterized by scattering of values. For many vehicles, the wear process plays the most important role.

When considering the influence of various processes on the output parameters of the vehicle, one should also take into account the feedback that exists between them and the state of the vehicle itself. For example, the wear of individual machine mechanisms can not only reduce the accuracy of its operation, but also lead to an increase in dynamic loads, which, in turn, intensify the wear process. Thermal deformations of individual links can not only distort the position of the machine units and thus affect the quality of its operation, but also lead to increased loads and, as a consequence, to increased heat generation in the mechanisms.

The general scheme of a physical-probabilistic model for assessing parametric reliability (Fig. 1.1) shows that one of the main reasons for an irreversible change in the state of a vehicle is the course of various aging processes in the materials from which it is made. This significantly affects the operational state of the vehicle. The assessment of the probability of the vehicle technical characteristics going beyond the permissible limits is essentially an assessment of the level of the parametric reliability of the machine. The distribution law describing this probabilistic process in differential or integral form is called the law of reliability.

Lecture 2. Indicators of vehicle reliability. Types of failures.

To solve the problems of assessing and analyzing the reliability of vehicles, which include both military and civilian aircraft, it is necessary first of all to establish the main indicators, the numerical values ​​of which determine the level of reliability of the vehicle (products, machines, devices, etc.).

The main indicators of reliability that can quantitatively assess the level of reliability, durability, preservation and maintainability of the vehicle include:

Reliability indicators.

1.Probability of uptimeis the main indicator of the vehicle reliability, which shows the probability that a system failure will not occur in a given time interval (or within a given operating time).

Uptime probability can be appliedto assess the level of reliability of both recoverable and non-recoverable systems and devices. The value ‚as any probability can be within the limits.

For example, if the probability of no-failure operation of the vehicle during the period equals 0.95, this means that out of a large number of systems, on average, 5% will lose their operability earlier than through work.

The indicator is applicable to assess the reliability of a single product. In this case, it determines the ability of the product to work without failures for a given period of time. The probability of failure-free operation and the probability of failure form a complete group of events, therefore

The value characterizes the degree of danger of failure and, therefore, the lower its value, the more reliable the product will operate, all other things being equal. For example, for critical products of aviation technology, the permissible values ​​of the probability of failure-free operation reach and higher.

If the consequences of failure are associated with insignificant economic losses, the admissible value is usually taken within the limits.

The value of the probability of failure-free operation of a given product can be determined if the law of distribution of the operating time to failure is known, which is also called the law of reliability.

In fig. 2.1 shows a diagram of the formation of the law of reliability in differential (probability density) and integral forms.

The reason for the failure is a random process of changing the output parameter of the product over time from the initial to the maximum permissible value. Due to the randomness of the process, it can proceed with different intensities. Therefore, the operating time to the limit state, i.e. operating time to failure appear as a random variable.

Rice. 2.1. Scheme of the formation of the law of reliability.

The distribution law can be expressed in analytical form or in the form of a histogram obtained on the basis of statistical data.

If for a given output parameter the law of distribution of operating time to failure is known, then the probability of failure-free operation can be determined for any given value by the dependence

Numerically, the values ​​and are equal, respectively, to the area under the distribution curve before and after the value (Fig. 2.1, b).

It should be borne in mind that the use of the indicator without specifying the period of time during which the operation of the product is considered does not make sense.

The lower the reliability requirements, the longer the duration of the product can be tolerated.

1. With high requirements for the reliability of the product, they are set by an acceptable value and determine the operating time of the product corresponding to the given regulated probability of no-failure operation. The value is called the gamma-percentage resource (non-random value) and its value is used to judge the greater or lesser reliability of the products. With γ = 50%, we get the value of the average resource Tav.r.

1. With the usual requirements for reliability, if the failure does not lead to serious consequences, it is possible to set the set resource of the product t = Tv.p, (or the service life t = Tcl). In this case, the reliability of the product is judged directly by the value of P (t) corresponding to the established resource.

2.Failure flow parameter ω.

,

where:

Ω (t) is the average number of failures in a given time interval from 0 to t (so

called the leading function);

T m - MTBF;

The failure flow parameter ω is the average number of product failures per unit time.

This parameter is used for recoverable vehicles in the event of failures that are easily eliminated and do not lead to any significant consequences (for example, tool replacement when working on a metal-cutting machine).

3.Safety margin K n which represents the ratio X max to such a value of the parameter X γ, at which the parameter does not go beyond the given limits with the probability γ, i.e.

.

The period of time during which the fulfillment of the condition (Кн≥1) is ensured is called the guaranteed period of no-failure operation of the product Tr.

4 bounce rate(λ-characteristic).

This is the conditional density of the probability of a product failure, determined for the considered point in time, provided that no failure has occurred before this point in time.

The failure rate in the general case is a function of time λ (t) and is related to other characteristics of the reliability law by the dependence

.

The failure rate is statistically assessed by the dependence

1.14.

where:

The number of all products participating in the experiment;

The number of remaining serviceable products at the point in time

In the practice of calculating the reliability of vehicles of the LK type, the use of the failure rate is advisable during the period of normal operation, for which the valueλ-characteristicand is assumed to be constant (λ = const).

The qualitative dependence of the failure rate on time is shown in Fig. 2.2.

Rice. 2.2. Time dependence of the failure rate.

As follows from the figure, we can conventionally distinguish three time intervals, in which the behavior of λ (t)> 0 is significantly different.

An interval with a duration from 0 to t 1 - running-in interval.

On it, the failure rate monotonically decreases, reaching a certain stationary rate by the time instant. The very name of the interval indicates that device failures on it are mainly due to poor quality assembly, installation, violation of technology, defects in components, etc. At the beginning of the running-in interval, devices with latent defects are more likely to fail. The failure rate decreases towards the end of the running-in interval.

This is followed by an interval of normal operation of duration

t n = t 2 - t 1.

In this interval, device failures are mainly caused by random factors acting during operation and hidden defects. The failure rate λ can be considered constant (λ = const) throughout the entire interval of normal operation.It is this failure rate λ, especially in electronics, that is given in the reliability reference books.

In this case, the probability of failure-free operation in the interval of normal operation is determined by the dependence

The interval of normal operation is followed by an aging interval at which the failure rate monotonically increases.

In this interval, fatigue stresses in the structural elements of the vehicle, the degradation of individual functional blocks and components begin to affect more and more significantly.

Indicators of durability.

The main indicators of durability include technical resource, average resource, gamma-percentage resource and service life.

5.Technical resource- the operating time of the object from the beginning of its operation or its resumption after repair until the transition to the limiting state.

For non-repairable (non-recoverable) objects, it coincides with the operating time to failure.

6.Average resource - mathematical expectation of a technical resource.

7.Gamma Percentage Resource- operating time, during which the object does not reach the limit state with a probabilityγ expressed as a percentage.

8.Service life - calendar duration from the start of operation of the facility to the transition to the limit state.

For vehicles being repaired, a distinction is made between pre-overhaul, overhaul, post-overhaul and full (before retirement) service life. Service life is measured in units of calendar time.

The considered reliability indicators do not characterize integrally the reliability of the restored system. For this purpose, complex reliability indicators are used.

Complex indicators of reliability.

These include the availability factor, the operational readiness factor,efficiency retention rateand the coefficient of technical utilization.

9. Coefficient of availability Kg- the probability that the system will be in an operational state at an arbitrary point in time, except for the planned periods during which the system is not intended to be used for its intended purpose. In general, Kg (t) is a function of time.

For large time intervals, it is determined by the formula

It can be seen from this formula that the availability factor simultaneously characterizes two different properties of the system: reliability and maintainability (recoverability). T 0 Is the mean time between failures. TV - average recovery time.

10. The coefficient of operational readinesscharacterizes the reliability of systems, the need for the use of which arises at an arbitrary moment in time and which must work for a certain time with a given probability of failure-free operation:

where

Tp is the required uptime after the start of operational use of the vehicle.

Until the moment of operational use, the vehicle can be on duty (at full or light loads, but without performing the specified working functions) or in the application mode - to perform other working functions. In both modes, failures and restoration of system performance are possible.

11.Efficiency preservation ratioIs the ratio of the real value of the efficiency indicator of the vehicle use for its intended purpose for a certain period of operation to the nominal value of the efficiency indicator, calculated provided that the vehicle does not fail during this period.

In practice, as a rule, they are limited to calculating the operational readiness factor.

12. Coefficient of technical use KtiIs the ratio of the mathematical expectation of the time interval of the object's stay in a working state for a certain period of operation to the duration of this period. The coefficient of technical use (Kty) characterizes the proportion of the time that the object is in a working condition for a given period of operation, including all types of maintenance and repairs, and is determined by the dependence

where Trab is the total time of the machine's useful work when it is used for its intended purpose for a given period of operation;

ΣTirem is the total downtime of the machine due to its repair and maintenance over the same period.

The coefficient of technical utilization is a dimensionless value (0≤Kti≤1), and the higher its value, the more adapted the machine is for long-term operation. The coefficient Кti is numerically equal to the probability that at a given, arbitrarily taken moment in time, the vehicle is operating, and not being repaired or undergoing maintenance.

At the design and development stages of the vehicle and devices, these indicators are evaluated by calculation, at the stages of production and operation are determined based on the test results.

The main types and classification of failures.

When calculating reliability indicators, the type and nature of emerging or possible failures is of great importance.

The main features that determine various types of failures are the nature of the occurrence and course of processes leading to failure, the consequences of failures and methods of their elimination.

From this point of view, there are the following main types of failures:

1. Gradual and sudden failures

Gradual failures occur as a result of an aging process that degrades the initial parameters of the product..

The main sign of gradual failure is that the probability of its occurrence within a given period of time from to, depends on the duration of the previous operation of the product. t 1 ... The longer the product has been used, the higher the probability of a failure occurring, i.e. , if. Most failures belong to this type. They are associated with wear, corrosion, fatigue, creep and other aging processes of the materials from which the products are made.

Sudden failures are those caused by processes that have arisen as a result of a combination of adverse factors and random external influences that exceed the product's ability to perceive them..

The main symptom of a sudden failure is that the probability of its occurrence within a given period of time does not depend on the duration of the previous operation of the product.

Examples of such failures include thermal cracks in a part due to an interruption in the lubricant supply; part breakdowns due to improper operating methods of the machine or the occurrence of overloads; deformation or breakage of parts that have fallen into unforeseen working conditions.

In this case, the failure occurs, as a rule, suddenly, without previous symptoms of destruction and does not depend on the degree of wear and tear.

For example, the cause of failure of a car tire can be both tread wear as a result of long-term use of the machine, and a puncture caused by driving on a bad road and an unfavorable combination of random factors.

An old tire is many times more likely to fail due to tread wear than a new one. In contrast, a puncture - a sudden failure - is not related to the length of time the tire has been in operation prior to the event. The likelihood of its occurrence is the same for both new and worn tires.

The division into gradual and sudden failures is determined by the nature of their occurrence.

For a gradual failure, the process of loss of performance begins immediately during the operation of the product.

For a sudden failure, the time of its occurrence is a random value. The rate of occurrence is very fast.

There may be a third type of failure, which includes the features of the previous two and is called a complex failure. Here, the time of the onset of the failure is a random variable that does not depend on the state of the product, and the speed of the process of losing the performance of the product depends on the physics of the aging process. For example, external shock to a machine from foreign objects (a rare random event) can be a source of fatigue cracks due to primary damage to the surface of the part.

2. Failures of functioning and parametric failures.

Failure to functionleads to the fact that the product cannot perform the functions assigned to it. For example, as a result of a failure, the gearbox does not transmit movement, the internal combustion engine does not start, the pump does not supply oil, etc. Often, the failure of functioning is associated with breakdowns or seizure of individual elements of the product.

Parametric failure, which is most typical for modern machines and products, arises when the parameters (characteristics) of the product go beyond the permissible limits. Here the product becomes inoperative in terms of the requirements set by the technical specifications.

Continued use of a product with a parametric failure can lead to very serious economic and other consequences. For example, to the release of low-quality products, which can be the cause of operational failures in the sphere of its operation, to the failure of the product to fulfill the assigned tasks, to large additional costs of time and money. But the role of parametric failures is also important because in complex systems, parametric failures of elements can lead to failure of functioning.

Therefore, parametric failures are one of the main objects of consideration in the theory of reliability of vehicles and machines.

3. Actual and potential failures.

During the operation of the product, sooner or later its first and then subsequent failures will occur. If these failures are prevented by the early implementation of repairs and adjustments, then they are not perceived as actual, but as potential events.We will call such refusals potential.

Manufacturers and operators are constantly striving to avoid any malfunctions in the operation of the machine. This can be achieved not only due to the perfection of the machine design, but also by preventing possible failures with the correct organization of the repair and maintenance system, strict adherence to the operating rules.

However, the absence of actual failures does not yet indicate a high reliability of the machine. The machine may not have any failures during operation, nevertheless, the level of its reliability will not satisfy developers and consumers if this is achieved due to a large amount of preventive and repair work. Statistical information from the field of operation, when only actual failures are taken into account, often gives a wrong idea of ​​the level of reliability of the vehicle and the machine.

4. Acceptable and unacceptable refusals.

All failures that occur during the operation of the vehicle and machines can be divided into those that are inevitable, since the product has limited capabilities to perceive various influences, and failures that are the result of violation of the methods and rules of design, manufacture and operation of the machine and which are possible and necessary to avoid.

Acceptable refusalsare usually associated with aging processes that cannot be prevented and which lead to a gradual deterioration in the output parameters of the product. This should also include sudden failures that are caused by an unfavorable combination of factors, if the latter are within the limits specified in the technical conditions. The designer can deliberately allow some (usually small) probability of failure in order to facilitate and reduce the cost of the design.This, of course, is permissible only in cases where the failure will not cause catastrophic consequences.... For example, even in aircraft structures, fatigue cracks can develop in some wing members and panels.

Unacceptable refusalsassociated with violation of production and operating conditions and unaccounted for factors.

Firstly, these are failures due to violation of technical conditions during the manufacture and assembly of products. Secondly, failures can occur when the rules and conditions of operation and repair are violated - exceeding the operating modes of the machine above permissible, violation of the repair rules, mistakes of people operating the machine, etc. In addition, there are hidden reasons for the occurrence of unacceptable failures - these are parameters that have not been taken into account in technical conditions and standards that affect reliability. The product can be made in strict accordance with the technical specifications (TU), however, the TU themselves do not take into account all those objectively existing factors that affect the reliability and appear during operation. The analysis of the belonging of each failure to a particular classification category allows you to choose reliability indicators and a calculation model that correctly reflect the real situation in which the product is used.

Standardization of reliability indicators

When creating a new vehicle or machine, it is necessary to assign reliability indicators so that during the operation of the machine safety and high work efficiency are guaranteed.

Usually, depending on the requirements for the efficiency of the product and on the requirements for its reliability, a compromise is reached between them.

The normalization is primarily subject to the probability of failure-free operation of the product with an estimate of the duration of the period during which it is assessed, and for highly reliable systems, in which the safety margin and value should be established.

In this case, the admissible value of the probability of failure-free operation is a measure for assessing the consequences of failure, which can be very diverse - from insignificant material damage to catastrophic. These consequences are associated with the nature of the failure itself, with the category of failure and with such factors as the time required to eliminate the failure, the type of repair, the duration of the failure (the possibility of self-healing of the product's performance), the impact of this failure on the likelihood of other failures, etc.

All features of a failure and its consequences should be characterized by the admissible probability of failure-free operation, which accumulates and numerically estimates the danger of failure consequences.

So, if a failure exists for a short time, and then the machine's performance is self-healing and no irreversible processes occur during this time, then a lower probability of failure-free operation will be allowed than with a "complete" failure and more dangerous consequences. When assessing the reliability of complex products, not only the machine as a whole, but also its individual components and assemblies should be characterized by an acceptable probability of failure-free operation. When standardizing reliability indicators, it is necessary to take into account the specifics of the design and the purpose of this machine.

Usually, six reliability classes are used, depending on the permissible values ​​(Table 2.2).

Table 2.2.

The zero class includes unimportant parts and assemblies, the failure of which remains practically without consequences. For them, a good indicator of reliability can be the average service life, MTBF, or the parameter of the failure flow.

Classes 1-4 are characterized by increased reliability requirements (the class number corresponds to the number of nines after the decimal point in the value.

To the fifth grade includes highly reliable products, the failure of which

in the given period is invalid.

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0

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

FEDERAL STATE AUTONOMOUS EDUCATIONAL INSTITUTION

HIGHER EDUCATION

"National Research Nuclear University" MEPhI "

Obninsk Institute of Atomic Energy -

branch of the federal state autonomous educational institution "National Research Nuclear University" MEPhI "

(IATE NRNU MEPhI)

Technical school IATE NRNU MEPhI

Course design

in the discipline "Theoretical foundations of ensuring the reliability of automation systems and modules of mechatronic systems"

on the topic "Reliability of technical systems"

Introduction. 3

1 General part. 6

1.1 Theory of reliability. 6

1.2 Indicators for assessing reliability. nine

1.3 Indicators for assessing maintainability. eleven

1.4 Indicators for assessing durability. eleven

1.5 Indicators for assessing persistence. 12

2 Selection and justification of calculation methods 12

2.1 Reliability calculation. 12

3 Calculated part. fourteen

3.1 Calculation of system reliability .. 14

3.2 Event tree. twenty

3.3 Fault tree. twenty

4 System reliability ... 21

4.1 Ways to Improve System Reliability .. 21

4.2 Construction of a circuit with increased reliability. 23

5 Conclusion. 24

6 Conclusion. 25

List of used literature .. 26

Introduction

More and more attention is paid to the issues of reliability of technical systems every year. The importance of the problem of the reliability of technical systems is due to their ubiquity in virtually all industries.

In our country, the theory of reliability began to develop intensively since the 50s, and by now it has formed into an independent discipline, the main tasks of which are:

• Establishing the types of indicators of the reliability of those. systems;
• Development of analytical methods for assessing reliability;
• Simplification of the assessment of the reliability of technical systems;
• Optimization of reliability at the stage of system operation.

Reliability - the property of the system to keep in time and within the established limits the values ​​of all parameters characterizing the ability of the system to perform the required functions in the specified modes and operating conditions. Reliability is the most important indicator of product quality, which must be ensured at all stages of the product life cycle (design - manufacture - operation). Reliability depends on such key indicators as quality, efficiency and safety. Technique can only work well if it is sufficiently reliable.

Reliability is, in essence, a characteristic of the efficiency of a system. If, to assess the quality of an automatic system, it is sufficient to characterize it by the reliability of the system performing functions in various states, then the reliability coincides with the efficiency of the system.

The reliability of technical equipment depends on its design and manufacture. To create a reliable technical system, you need to correctly calculate its reliability at the time of design, know the methods and programs for calculating and ensuring high reliability. It is also necessary to prove in practice that the indicators of the obtained reliability of the technical system are not lower than the specified indicators.

Intuitively, the reliability of objects is associated with the inadmissibility of failures in work. This is an understanding of reliability in the "narrow" sense - the property of an object to maintain an efficient state for some time or some operating time. In other words, the reliability of an object lies in the absence of unforeseen unacceptable changes in its quality during operation and storage. Reliability in the "broad" sense is a complex property, which, depending on the purpose of the object and the conditions of its operation, may include the properties of reliability, durability, maintainability and preservation, as well as a certain combination of these properties.

The relevance of this course work is the importance of calculating the reliability, in which various methods and means can be used, and the achievement of the required reliability. In the course work, methods for calculating the reliability of technical systems, types of failures, methods of increasing reliability, as well as the reasons causing failures are considered.

The object of research in this course work is electrical circuits.

The main purpose of this course work is to analyze the parameters of a given system and the requirements for it, the selection of the necessary methods for calculating the reliability of the system, as well as the justification of these methods.

To achieve this goal, it is necessary to solve a number of tasks:

• Consider the given system, as well as the parameters, description and requirements;
• Select and justify calculation methods;
• Deal with the computational part: directly calculate the reliability of the system, build a fault tree and an event tree;
• Find methods to improve reliability for a given system.

This course work will consist of the following parts:

1) Introduction, which describes the purpose and objectives of the work

2) The theoretical part, which sets out the basic concepts, requirements and methods for calculating reliability.

3) The practical part, where the reliability of the given system is calculated.

4) Conclusion, which contains conclusions on this work

The degree of importance of the reliability of various technical systems in the modern world is very high, since modern technical facilities must be as reliable and safe as possible.

1 General

1.1 Reliability theory

Reliability - this property of the object to keep in time within the established limits the values ​​of the parameters characterizing the ability to perform the required functions in the specified modes and conditions of application of maintenance, repairs, storage and transportation. Reliability is a complex property, which, depending on the purpose of the object and the conditions of its use, consists of a combination of safety and maintainability.

For the vast majority of year-round technical devices, when assessing their reliability, three properties are most important: reliability, durability and maintainability.

Reliability - property of an object to continuously maintain an efficient state for some time or operating time.

Durability - the property of an object to maintain an operational state until the onset of a limiting state with an installed maintenance and repair system.

Maintainability - property of an object, which consists in its adaptability to maintaining and restoring an operable state through maintenance and repair.

Persistence - the property of an object to keep within the specified limits the values ​​of the parameters characterizing the ability of the object to perform the required functions during and after storage and (or) transportation.

Resource (technical) - operating time of the product until it reaches the limiting state, agreed in the technical documentation. The resource can be expressed in years, hours, kilometers, hectares, number of inclusions. Distinguish between resource: full - for the entire service life until the end of operation; pre-repair - from the start of operation to overhaul of the restored product; used - from the beginning of operation or from the previous overhaul of the product to the considered moment in time; residual - from the considered moment of time to the failure of a non-recoverable product or its overhaul, overhaul.

Running time - the duration of the functioning of the product or the amount of work performed by it for a certain period of time. It is measured in cycles, units of time, volume, run length, etc. Distinguish between daily operating time, monthly operating time, operating time to first failure.

MTBF - reliability criterion, which is a static value, the average value of the operating time of a repaired product between failures. If the operating time is measured in units of time, then the mean time between failures is understood as the mean time between failures.

The listed properties of reliability (reliability, durability, maintainability and preservation) have their own quantitative indicators.

So reliability is characterized by six indicators, including such important as uptime probability... This indicator is widely used in the national economy to assess various types of technical means: electronic equipment, aircraft, parts, components and assemblies, vehicles, heating elements. The calculation of these indicators is carried out on the basis of state standards.

Refusal - one of the main definitions of reliability, consisting in a malfunction of the product (one or more parameters of the product are outside the permissible limits).

Failures are classified according to the following criteria:

1) by the nature of the manifestation:

• Sudden (characterized by a sharp change in one or more specified parameters of the product);
• Gradual (characterized by a gradual change in one or more set parameters of the machine);
• Intermittent (occur repeatedly and last for a short time).

2) failures as random events can be:

• Independent (when the failure of any element does not lead to the failure of other elements);
• Dependent (appear as a result of failure of other elements);

3) by the presence of external signs:

• Obvious (explicit);
• Hidden (implicit);

4) refusals by volume:

• Full (in case of an accident);
• Partial;

5) refusals for reasons of occurrence:

• Constructive (arising from insufficient reliability, unsuccessful assembly design, etc.);
• Technological (arising from the use of low-quality materials or violation of technological processes during manufacturing);
• Operational (arising from a violation of operating modes, wear of mating parts from friction).

All objects are divided into repairable (recoverable) and non-repairable (non-recoverable), depending on the method of eliminating the failure.

Failure rate - the conditional density of the probability of a failure of a non-recoverable object is determined under the condition that a failure has not occurred before the considered moment of time.

Probability of uptime - the possibility that, within a given operating time, an object's failure does not occur.

Durability is also characterized by six indicators representing different types of resource and service life. From the point of view of safety, the most interesting is the gamma-percentage resource - the operating time during which the object does not reach the limit state with the probability g, expressed as a percentage

An indicator of the quality of an object is its reliability. Therefore, the higher the reliability, the higher the quality of the object. During operation, the facility may be in one of the following technical states (Figure 1.1):

1) Serviceable condition - the condition of an object in which it meets all the requirements of the normative and technical documentation.

2) Defective state - a state of an object in which it does not meet at least one of the requirements of the normative and technical documentation.

3) Serviceable state - the state of an object in which the values ​​of all parameters characterizing the ability to perform the specified functions comply with the requirements of the normative and technical documentation.

4) Inoperative state - the state of an object in which the value of at least one parameter characterizing the ability to perform certain functions does not meet the requirements of the normative and technical documentation.

5) Limit state - a state in which further operation of an object is unacceptable or impractical, or restoration of an operable state is impossible or impractical.

1.2 Indicators for assessing reliability

To assess the reliability, such indicators are used as:

1) Probability of failure-free operation - the probability that within the specified operating time no object failure occurs. The probability of no-failure operation varies from 0 to 1 and is calculated by the formula:

where is the number of operable objects at the initial moment of time, and is the number of objects that have failed at the moment t from the start of testing or operation.

2) MTBF (or MTBF) and MTBF. Mean time between failures is the mathematical expectation of an object's operating time before the first failure:

where is the operating time to failure of the th object, and is the number of objects.

3) The density of the probability of failure (or the frequency of failures) is the ratio of the number of failed products per unit time to the initial number under observation:

where is the number of failures in the considered operating time interval;

- the total number of items under supervision;

- the value of the considered operating time interval.

4) Failure rate - the conditional density of the probability of the object's failure, determined under the condition that the failure did not occur before the considered moment of time:

where is the failure rate;

Probability of no-failure operation;

The number of failed products from to;

The considered operating time interval;

The average number of trouble-free working products, which is determined by the following formula:

where is the number of trouble-free working products at the beginning of the considered operating time interval;

- the number of trouble-free working products at the end of the operating time interval.

1.3 Indicators for assessing maintainability

To assess maintainability, such indicators are used:

1) Average recovery time - the mathematical expectation of the recovery time of an object, which is determined by the formula:

where is the recovery time of the th object failure;

The number of failures during a given test or operation period.

2) Probability of restoration of the operational state - the probability that the restoration time of the operational state of the object will not exceed the specified value. For a larger number of mechanical engineering objects, the recovery probability is determined by the exponential distribution law:

where is the failure rate (constant value).

1.4 Indicators for assessing durability

The property of durability can be realized both during a certain operating time (then they talk about a resource), and during a calendar time (then they talk about a service life). Some key indicators of resource and service life:

1) Average resource - the mathematical expectation of the resource.

2) Gamma-percent resource - the total operating time during which the object will not reach the limit state with a given probability.

3) Average service life - mathematical expectation of service life.

4) Gamma-percent service life - the calendar duration of operation, during which the object does not reach the limit state with probability.

5) Assigned resource - the total operating time, upon reaching which the operation of the facility should be terminated, regardless of its technical condition.

6) Unassigned service life - the calendar duration of operation, upon reaching which the operation of the facility must be terminated regardless of its technical condition.

1.5 Indicators for assessing persistence

From the standpoint of the theory of reliability, it is natural to assume that the object is put into storage or begins to be transported in good condition.

The persistence property is also realized for some time, which is called the persistence period.

1) Storage life - the calendar duration of storage and / or transportation of an object, during which the values ​​of the parameters that characterize the ability of the object to perform the specified functions are maintained within the specified limits.

2) Average shelf life - the mathematical expectation of the shelf life of an object.

3) Gamma-percentage shelf life - the calendar duration of storage and / or transportation of the object, during which the indicators of reliability, maintainability and durability of the object will not go beyond the established limits with probability.

1. Selection and justification of calculation methods

2.1 Reliability calculation.

The study of the reliability of technical systems is carried out on the basis of methods with data on failures and restorations obtained as a result of the use of systems and their elements. In the course of work, analytical methods for calculating reliability are usually used. Most often, these are logical - probabilistic methods, as well as methods based on the theory of random processes.

The recovery time for system elements is usually much shorter than the time between failures. This fact makes it possible to use asymptotic methods for calculating reliability. But the study of reliability using these methods is a difficult task, since the formulas for describing reliability are not always possible to obtain, and they are difficult for practical use.

However, other methods are used to analyze and calculate the reliability of systems. These are logical - probabilistic, graph, heuristic, analytical - static and machine modeling.

The logical - probabilistic methods are based on the direct application of theorems and probability theories for the analysis and calculation of the reliability of technical systems.

The graph method is more general for describing a technical system. It takes into account the influence of any factors affecting the system. But the disadvantage of this method is the complexity of data entry and determination of reliability characteristics.

The essence of the heuristic method for assessing and calculating reliability is to combine groups of system elements into one common element. Thus, there is a decrease in the number of elements in the system. This method is used only for highly reliable elements without computational errors.

Machine modeling methods are universal and allow considering systems with a large number of elements. But the use of this method as a reliability study is advisable only when it is impossible to obtain an analytical solution.
When analyzing systems with high reliability, problems arise associated with large expenditures of computer time. To increase the speed of calculations, an analytical-static method is used. But this method does not allow to fully determine the reliability of the system, given the large number of factors that affect its correct functioning.

The calculation of the given system is based on the method exponential distribution.

The method of exponential distribution was chosen, because it is determined by one parameter λ. This feature of the exponential distribution indicates its advantage over distributions that depend on a larger number of parameters. Usually the parameters are unknown and one has to find approximate values. It is easier to estimate one parameter than two or three, etc.

3 Calculated part

3.1 Calculation of system reliability

1. Objective 1:

Block diagram of task 1:

Rice. 1 - Block diagram of task 1

Failure rate:

Mean time to failure:

Uptime probability:

FBG systems with serial connection of elements:

1. Objective 2:

Block diagram of task 2:

Rice. 2 - Block diagram of the task

Table 1 - Failure rate and mean time to failure:

λ i, x10 -6 1 / h

λ i, x10 -6 1 / h

Formula for calculating the probability of failure-free operation of an individual element:

Probability of failure-free operation of each circuit element:

Calculation of the reliability of the electrical circuit:

3.2 Event tree

Rice. 3 - Event tree

3.3 Fault tree

Rice. 4 - Fault tree

4 System reliability

4.1 Ways to Improve System Reliability

Among the methods of increasing the reliability of equipment, the main ones can be distinguished:
... reducing the failure rate of system elements;
... reservation;
... reducing the time of continuous work;
... reduction in recovery time;
... selection of a rational frequency and scope of systems control.
These methods are used in the design, manufacture and operation of equipment.
As already mentioned, the reliability of systems is based on design, construction and manufacture. It depends on the work of the designer and constructor how the equipment will work under certain operating conditions. The organization of the operation process also affects the reliability of the facility. During operation, maintenance personnel can significantly change the reliability of systems, both downward and upward.
Constructive ways to improve reliability include:
- the use of highly reliable elements and optimization of their operating modes;
- ensuring maintainability;
- creation of optimal conditions for the work of service personnel, etc .;
- rational choice of a set of controlled parameters;
- rational choice of tolerances for changing the basic parameters of elements and systems;
- protection of elements from vibrations and shocks;
- unification of elements and systems;
- development of operational documentation, taking into account the experience of using such equipment;
- ensuring the operational manufacturability of the structure;
- the use of built-in control devices, automation of control and indication of malfunctions;
- Convenience of approaches for maintenance and repair.
In the production of equipment, such methods of increasing reliability are used as:
- improvement of technology and organization of production, its automation;
- the use of instrumental methods of product quality control with statistically valid samples;
- training of elements and systems.
The named methods of increasing the reliability should be applied taking into account the influence of each of them on the performance of the system.
To increase the reliability of systems during their operation, methods based on the study of operating experience are used. The qualifications of the operating personnel are also of great importance for improving reliability.

The state of the system is determined by the state of its elements and depends on its structure. To increase the reliability of systems and elements, redundancy is used: Redundancy is a method of ensuring the reliability of an object through the use of additional funds and (or) capabilities that are redundant in relation to the minimum necessary to perform the required functions. Reserve - a set of additional funds and (or) opportunities used for redundancy.

There are three ways to enable the reserve:

• constant - in which the elements function on an equal basis with the main ones;
• redundancy by replacement - in which a reserve element is introduced into the system after the failure of the main one, such a redundancy is called active and it requires the use of switching devices;
• sliding redundancy - replacement redundancy, in which a group of the main elements of the system is backed up by one or more redundant elements, each of which can replace any failed main element in this group.

4.2 Building a circuit with increased reliability

The structural diagram that is given to us:

Rice. 5 - Block diagram

Elements 1 and 18 are the most unreliable, since if one of them fails, the entire system will fail.

Block diagram of increased reliability with the use of redundancy by replacement:

Rice. 6 - Block diagram with increased reliability

5 Conclusion

Reservation by replacement is a more convenient form of increasing the reliability of the system.

Its advantages:

1. Significantly increase the likelihood of system uptime
2. Few spare parts
3. Improving maintainability (since it is known exactly which element has failed).

The disadvantages of this type of reservation are that:

1. If an error is detected, it is necessary to interrupt the operation of the main software to detect the faulty element and exclude it from operation.
2. The software becomes more complicated, due to the fact that a special program for detecting faulty elements is required
3. The system cannot detect an error when the primary and backup elements fail at the same time.

6 Conclusion

In this course work, the probability of failure-free operation of a complex system was calculated. On the basis of the structural diagram, a fault tree and an event tree were built. Methods for increasing reliability were also considered, and on the basis of redundancy, a structural diagram with increased reliability was built, an analysis of the advantages and disadvantages of the selected method of increasing reliability was carried out.

List of used literature

1. Polovko, A.M. Fundamentals of the theory of reliability / A.M. Polovko, S.V. Gurov - SPb .: BHV - Petersburg, 2006.- S.
2. Reliability of technical systems: a reference book / Yu.K. Bilyaev; V.A. Bogatyrev
3. Reliability of technical systems [Electronic resource]: electronic tutorial. - Access mode: http://www.kmtt43.ru/pages/technical/files/pedsostav/krs/Nadejnost"%20tehnicheskih%20sistem.pdf
4. GOST 27.301 - 95 Reliability in technology. Reliability calculation. Basic Provisions
5. Basic concepts of the theory of reliability [Electronic resource]: electronic tutorial. - Access mode: http: //www. obzh. ru / nad/4-1. html(Date of treatment February 13, 2017)
6. GOST R 27.002-2009 Reliability in technology. Terms and Definitions.

Download: You do not have access to download files from our server.

Reliability indicators are the quantitative characteristics of one or more properties of an object that make up its reliability. Such characteristics include, for example, time concepts - operating time, operating time to failure, operating time between failures, resource, service life, recovery time. The values ​​of these indicators are obtained from the results of tests or operation.

According to the recoverability of products, reliability indicators are divided into while-recoverable products and indicators of non-recoverable products.

Apply also complex indicators. The reliability of products, depending on their purpose, can be assessed using either part of the reliability indicators or all indicators.

Reliability indicators :

uptime probability - the probability that an object does not fail within a given operating time;

mean time to failure - the mathematical expectation of the operating time of the object before the first failure;

mean time between failures - the ratio of the total operating time of the restored object to the mathematical expectation of the number of its failures during this operating time;

failure rate - the conditional density of the probability of the object's failure, determined under the condition that the failure did not occur before the considered moment of time. This indicator refers to non-recoverable products.

Indicators of durability.

Quantitative indicators of the durability of the restored products are divided into 2 groups.

1. Indicators related to the service life of the product:

life time - the calendar duration of operation from the beginning of the object's operation or its resumption after repair to the transition to the limiting state;

average service life - mathematical expectation of service life;

service life until the first overhaul of the unit or unit- this is the duration of operation before repairs performed to restore serviceability and complete or close to complete restoration of the product's resource with the replacement or restoration of any of its parts, including basic ones;

service life between overhauls, which depends mainly on the quality of the repair, i.e. on the extent to which their resource has been restored;

total service life- is the calendar duration of the technical system from the start of operation to rejection, taking into account the time of operation after repair;

gamma percentage service life - calendar duration of operation, during which the object will not reach the limit state with the probability γ, expressed as a percentage.

Indicators of durability, expressed in the calendar time of work, allow them to be directly used in planning the timing of the organization of repairs, the supply of spare parts, the timing of equipment replacement. The disadvantage of these indicators is that they do not allow the intensity of equipment use to be taken into account.

2. Indicators associated with the resource of the product:

resource - the total operating time of the object from the beginning of its operation or its renewal after repair until the transition to the limit state.

average resource - mathematical expectation of the resource; for technical systems, a technical resource is used as a criterion of durability;

assigned resource- total operating time, upon reaching which the operation of the facility should be terminated regardless of its technical condition;

gamma percent resource - total operating time during which the object will not reach the limit state with a given probability γ, expressed as a percentage.

The units for measuring the resource are chosen for each industry and for each class of machines, assemblies and structures separately. As a measure of the duration of operation, any non-decreasing parameter can be chosen that characterizes the duration of the object's operation (for airplanes and aircraft engines, the natural measure of the resource is the flight time in hours, for cars - the mileage in kilometers, for rolling mills - the mass of rolled metal in tons If the operating time is measured by the number of production cycles, then the resource will take discrete values.

Complex indicators of reliability.

The indicator that determines the durability of a system, object, machine, can serve as the coefficient of technical use.

Technical utilization factor - the ratio of the mathematical expectation of the total residence time of the object in an operational state for a certain period of operation to the mathematical expectation of the total residence time of the object in an operational state and all downtime for repair and maintenance:

The technical utilization factor, taken for the period between scheduled repairs and maintenance, is called the availability factor, which

who assesses unanticipated machine stops and that scheduled repairs and maintenance activities do not fully fulfill their role.

Availability factor - the probability that the object will be in a workable state at an arbitrary point in time, except for the planned periods during which the use of the object for its intended purpose is not provided. The physical meaning of the availability factor is the probability that the product will be in good working order at the predicted point in time, i.e. it will not be under unscheduled repairs.

The operational readiness factor - the probability that the object will be in a working state at an arbitrary moment of time, except for the planned periods during which the use of the object for its intended purpose is not provided, and, starting from this moment, it will work flawlessly for a given time interval.

Classification of indicators . Depending on the method of obtaining, the indicators are divided into calculated, obtained by calculation methods; experimental, determined by test data; operational, obtained from the operation data.

Depending on the area of ​​use, there are standard and estimated reliability indicators.

Regulatory are called reliability indicators, regulated in the normative-technical or design documentation.

TO evaluative refer to the actual values ​​of the reliability indicators of prototypes and serial products obtained from the results of tests or operation.

7. Structural and logical analysis of technical systems. Structural - logical diagrams of the reliability of technical systems.

8. Structural and logical analysis of technical systems. Analysis of the structural reliability of technical systems. Sequence of operations.

9. Calculations of the structural reliability of systems. General characteristics.

10. Calculations of the structural reliability of systems. Systems with series connection of elements.

11. Calculations of the structural reliability of systems. Systems with parallel connection of elements.

13. Almost the same as at 12

14. Calculations of the structural reliability of systems. Bridge systems. Direct enumeration method.

15. Calculations of the structural reliability of systems. Bridge systems. Minimum section method.

16. Calculations of the structural reliability of systems. Bridge systems. Minimal Paths Method.

17. Calculations of the structural reliability of systems. Bridge systems. Decomposition method for a particular element.

18. Calculations of the structural reliability of systems. Combined systems.

19. Improving the reliability of technical systems. Reliability Improvement Techniques

23. Improving the reliability of technical systems. Calculation of the reliability of systems with lightweight and sliding redundancy.

26 The main properties of the object of technical diagnostics. Maintainability.

27 The main properties of the object of technical diagnostics. Reliability. Reliability indicators.

28. The main properties of the object of technical diagnostics. Durability.

29. The main properties of the object of technical diagnostics. Persistence.

32. Methods for predicting failures of elements (statistical and instrumental).

33. Methods for increasing reliability. Development. Manufacturing. Operation.

44. The current state of the issue of diagnostics of machining processes and mechatronic machine tool systems.

45. Diagnostics and pattern recognition. Basic concepts of pattern recognition.

46. ​​Purpose and main tasks of technical diagnostics. Applied questions of technical diagnostics.

39 Diagnostics of digital devices. Truth table method.

47. The main problems arising in the development of systems

48. Pre-processing of images and selection of features.

52. A brief overview of foreign and domestic

53. Machine-tool systems as an object of diagnostics.

55. Automated control and diagnostics of the tool in the process of machining. Tasks of automated control and diagnostics of the tool.

1. Reliability of automated technical systems. Reliability concept. The main problems of reliability.

Reliability is the property of an object to keep in time within the established limits the values ​​of all parameters characterizing the ability to perform the required functions in specified modes and conditions of use, maintenance, repairs, storage and transportation. Expansion of operating conditions, increased responsibility of functions performed by radio electronic means (RES), their complication leads to increased requirements for the reliability of products.

Reliability is a complex property, and is formed by such components as reliability, durability, recoverability and preservation. The main thing here is the reliability property - the ability of the product to continuously maintain an operable state over time. Therefore, the most important thing in ensuring the reliability of RES is to increase their reliability.

A feature of the reliability problem is its connection with all stages of the “life cycle” of the electronic equipment, from the inception of the idea of ​​creation to write-off: when calculating and designing a product, its reliability is incorporated into the project; during manufacturing, reliability is ensured, and during operation, it is implemented. Therefore, the problem of reliability is a complex problem and it must be solved at all stages and by different means. At the design stage of the product, its structure is determined, the selection or development of the element base is made, therefore, there are the greatest opportunities to ensure the required level of reliability of the electronic equipment. The main method for solving this problem is reliability calculations (first of all, reliability), depending on the structure of the object and the characteristics of its constituent parts, followed by the necessary correction of the project.

2. Quantitative characteristics of reliability. MTBF.

Reliability (and other components of the reliability properties) of the RES is manifested through random values, operating time to the next failure and the number of failures in a given time. the quantitative characteristics of the property here are probabilistic variables.

Running time there is the duration or amount of work of the object. for RES, it is natural to calculate the operating time in units of time, while for other technical means, other means of measurement may be more convenient (for example, the operating time of a car - in kilometers). For non-recoverable and recoverable products, the concept of operating time is different, in the first case it means the operating time to the first failure (which is also the last failure), in the second - between two adjacent failures in time (after each failure, the operating state is restored). The mathematical expectation of a random operating time T

(1.1) is a failure-free characteristic and is called mean time between failures (between failures). In (1.1) through t denotes the current value of the operating time, and f ( t) the probability density of its distribution.

Probability of uptimet object failure does not occur:

. (1.2)

probability of failure q(t) = Ver (T£ t) =1 – p(t) = F(t). (1.3)

In (1.2) and (1.3) F ( tt failure rate:

. (1.4) From (1.4) it is obvious that it characterizes the rate of decrease in the probability of failure-free operation in time.

The failure rate is the conditional density of the probability of a product failure, provided that by the time t no refusal occurred:
. (1.5)

The functions f ( t) and l ( t) are measured in h -1.

. (1.6)

t

(1.7)

The flow of failures at l ( t) = const is called the simplest

t

T 0 = 1 / l, (1.8) i.e. at the simplest flow of failures, the average operating time T 0 t= T 0 , the probability of failure-free operation of the product is 1 / e. A characteristic called g is often used - percentage operating time

. (1.9)

3.Probability of uptime - the probability that within the specified operating time t object failure does not occur:

. (1.2)

The probability of the opposite event is called probability of failure and complements the probability of failure-free operation to unity:

q(t) = Ver (T£ t) =1 – p(t) = F(t). (1.3)

In (1.2) and (1.3) F ( t) is the integral function of the distribution of the random operating time t. Probability density f ( t) is also an indicator of reliability called failure rate:

It is obvious from (1.4) that it characterizes the rate of decrease in the probability of no-failure operation over time.

4. Failure rate is called the conditional density of the probability of a product failure, provided that by the time t no refusal occurred:

. (1.5)

The functions f ( t) and l ( t) are measured in h -1.

By integrating (1.5), it is easy to obtain:

. (1.6)

This expression, called the basic law of reliability, allows you to establish a temporary change in the probability of failure-free operation for any nature of the change in the failure rate over time. In the particular case of a constant failure rate l ( t) = l = const (1.6) turns into the exponential distribution known in the theory of probability:

(1.7)

The flow of failures at l ( t) = const is called the simplest and it is precisely this that is realized for most of the RES during the period of normal operation from the end of running-in to the beginning of aging and wear.

Substituting the expression for the probability density f ( t) of the exponential distribution (1.7) in (1.1), we obtain:

T 0 = 1 / l, (1.8)

those. at the simplest flow of failures, the average operating time T 0 the inverse of the failure rate l. Using (1.7), it can be shown that during the average operating time, t= T 0 , the probability of failure-free operation of the product is 1 / e.

5. Often they use a characteristic calledg - percentage operating time - time during which the failure does not occur with probability g (%):

. (1.9)

The choice of a parameter for quantitative assessment of reliability is determined by the purpose, operating modes of the product, and ease of use in calculations at the design stage.

"

LECTURE 1

The purpose of the lecture: Acquaintance with the basic concepts of the theory of reliability. Introduction to the theory of reliability. Basic terms and definitions of the theory of reliability.

1.1 Introduction. Basic concepts and definitions of the theory of reliability.

Reliability theory– a scientific discipline in which methods of ensuring the efficiency of objects (devices, systems) during operation are studied.

Reliability theory (TS) appeared in the mid 40s of the 20th century and was used for the necessary calculations of the reliability of control systems and various types of communication.

Gradually, it found application in many areas of human activity (mechanical engineering, transport, construction, energy, control systems).

The technical means and their working conditions are becoming more and more complex. The number of elements in certain types of devices is estimated at hundreds of thousands. If you do not take special measures to ensure reliability, then any modern complex device will practically be inoperative.

The science of reliability is developing in close cooperation with other sciences. First of all, it is closely related to the design of information systems and issues of ensuring their security.

Among the mathematical disciplines, first of all, the most widely used are: the theory of probability; some elements of discrete mathematics; differential equations and integral calculus.

At present, the theory of reliability is an independent scientific discipline.

Its main tasks: establishing the types of quantitative indicators of reliability; development of methods for analytical assessment of reliability; development of methods for assessing reliability based on test results; optimization of reliability at the stages of development and operation of technical systems.

1.2 Basic terms and definitions.

Reliability- the property of an object (system) to keep in time within the established limits the values ​​of all parameters characterizing the ability to perform the required functions in the specified modes and operating conditions.

Technical system- a set of elements interacting with each other in the process of performing specified functions.

System element- an integral part of any system, which is considered without further division as a whole; the internal structure of the element is not a subject of research.

The concepts "system" and "system element" are expressed one through the other and are often conditional: what is a system for solving some problems is accepted by an element for others, depending on the objectives of the study, the required accuracy, the level of knowledge about reliability, etc.

From the point of view of reliability, all technical systems are divided into two types:

1) Non-recoverable elements and systems, those. not repairable during operation (radioelements, integrated circuits, part of instruments, aircraft equipment, etc.)

2) Recoverable elements and systems, which can be repaired immediately after a failure at a given time.

The very concept of "restoration" should be understood not only as an adjustment, adjustment, soldering or other repair work in relation to certain technical means, but also as a replacement for these means.

The vast majority of systems used to automate technological processes, as a rule, are subject to recovery after failure, after which they continue to work again.

Operability- such a state of the product in which it meets all the requirements for its main parameters. The main parameters of technical systems include: performance; load characteristic; stability and accuracy of operations.

A set of other indicators of a technical system: weight, dimensions, ease of maintenance, etc. may change over time. These changes have permissible values, exceeding them can lead to a failure state (partial or complete).

The states of a technical system can also be divided into: serviceable in which the system fully complies with all the requirements of regulatory and technical documentation and design documentation;

faulty– when the system has at least one non-compliance with these requirements.

An event consisting in a malfunction of the system, i.e. in its transition from a workable state to an inoperative state, is called rejection.

An event consisting in the transition of the system from a working state to a faulty (but working) state is called damage.

Limit state- arises under the condition that further use of the technical system or equipment is impossible or impractical.

After reaching the limiting state, repairs (major or medium) can follow, as a result of which the serviceable state is restored, or the system finally ceases to be used for its intended purpose (physical and moral aging, wear).

Figure 1 - Scheme of the main states and events of the restored system

LECTURE 2

The purpose of the lecture: Familiarization with the main stages of the calculation and indicators of the reliability of non-recoverable systems.

Normal distribution

In contrast to the exponential distribution, the normal is used to describe such systems and especially their elements that are subject to wear. In this case, the function and distribution density of the operating time to failure must be taken into account. T, t- mean time to failure.

The parameters of the normal distribution are: m is the mathematical expectation of a random variable, T- MTBF (or uptime); σ - standard deviation of mean time to failure T according to the test results of the systems.

The normal distribution describes the behavior of random variables in the range (- ∞, ∞), but since mean time to failure is not a negative value, in order to take this into account, instead of the normal one, in principle, a truncated normal distribution should be used.

The range of possible values ​​of a random variable can be from 0 to ∞ (0 at t = 0). The truncated normal distribution is applied if m< 3σ, в противном случае использование более простого нормального (не усеченного) распределения дает достаточную точность.

Reliability indices of normal distribution:

P (t)

f (t)

l (t) P (t) f (t)

Figure 3.2 - Graphs of changes in reliability indicators with a normal distribution

Lecture 4

The purpose of the lecture: teaching methods of calculating the reliability indicators of restored systems.

Lecture 5

The purpose of the lecture: Study of methods for calculating the reliability of non-recoverable systems with various complexities of the structural scheme for calculating the reliability.

5.1 Methods for calculating the reliability of non-recoverable systems

When calculating the probability of no-failure operation, the mean time to first failure, system elements are considered as non-recoverable. In this case, with the main (serial) connection of elements (Figure 5.1), the probability of failure-free operation is calculated as the product of the probabilities of all elements:

P c (t) = R 1 (t) R 2 (t)....R n -1 ( t) R n ( t)= (5.1)

Figure 5.1 - Block diagram of reliability calculation, serial connection of elements

With a backup (parallel) connection of elements (Figure 5.2) and provided that the operation of one of the elements connected in parallel is sufficient for the operation of the system, the failure of the system is a joint event that occurs when all the elements connected in parallel fail. If elements are connected in parallel and the probability of failure of each, then the probability of failure of this system:

Q c (t) = Q 1 (t) Q 2 (t).... Q m-1 ( t) Q m ( t)= (5.2)

Figure 5.2 - Block diagram of reliability calculation, parallel connection of elements

If the structural diagram of reliability consists of a series-parallel connection, then the reliability calculation uses formulas (5.1) and (5.2). For example, Figure 5.3 shows a diagram, and Equation 5.3 shows the calculation of the reliability function for this design.

Figure 5.3 - Block diagram of reliability calculation, mixed

connection of elements

Pc (t) = P1 (t) * P2 (t) * P3456 (t) = P1 (t) * P2 (t) * (1-) (5.3)

However, not all structural schemes for calculating reliability can be reduced to a series-parallel connection. Figure 5.4 shows a single bridge design for calculating reliability.

Figure 5.4 - Bridge connection diagram of elements

For all circuit elements, the probabilities of failure-free operation P1, P2, P3, P4, P5 and the corresponding failure probabilities of the "break" type q1, q2, q3, q4, q5 are known. It is necessary to determine the probability of the presence of a circuit between points a and b of scheme 5.4.

State enumeration method

The calculation of the reliability of any system, regardless of the method used, is preceded by the determination of two disjoint sets of states of elements corresponding to the operable and inoperative states of the system. Each of these states is characterized by a set of elements that are in operable and inoperative states.

Since in case of independent failures the probability of each of the states is determined by the product of the probabilities of finding elements in the corresponding states, then for the number of states equal to m, the probability of an operational state of the system is determined by the expression:

P = ; (5.1)

Probability of failure: Q = 1- (5.2)

where m- the total number of operational states, in each j-th of which the number of operational elements is equal to those that are out of order - kj.

With a relatively simple structure of the system, the application of the method of enumerating states is associated with cumbersome calculations. For example, for the circuit in Figure 5.4, we will compose a table of states, transferring first one, then two, three elements to an inoperative state, preserving the operable state of the system.

Table 5.1

State No.	Item status	Probability of states
	+	+	+	+	+	P1, P2, P3, P4, P5
	-	+	+	+	+	q1, P2, P3, P4, P5 q1, q2, q3, q4, q5
	+	-	+	+	+	P1, q2, P3, P4, P5
	+	+	-	+	+	P1, P2, q3, P4, P5
	+	+	+	-	+	P1, P2, P3, q4, P5
	+	+	+	+	-	P1, P2, P3, P4, q5
	-	+	-	+	+	q1, P2, q3, P4, P5
	-	+	+	-	+	q1, P2, P3, q4, P5
	-	+	+	+	-	q1, P2, P3, P4, q5
	+	-	-	+	+	P1, q2, q3, P4, P5
	+	-	+	-	+	P1, q2, P3, q4, P5
	+	-	+	+	-	P1, q2, P3, P4, q5
	+	+	-	+	-	Р1, Р2, q3, Р4, q5
	+	+	+	-	-	P1, P2, P3, P4, P5
	-	+	-	+	-	q1, P2, q3, P4, q5
	+	-	+	-	-	Р1, q2, Р3, q4, q5

If all elements of the system are equally reliable, then the probability of failure-free operation of the system at p i = 0.9:

P c = = p 5 + 5p 4 q + 8p 3 q 2 + 2p 2 q 3 = 0.978

Lecture 6

The purpose of the lecture: Study of the main ways to improve reliability through redundancy.

Reservation types

To increase the reliability of systems and elements, redundancy is used , based on the use of one or another type of redundancy.

Redundancy determines the following types of redundancy: functional, temporary, informational, structural.

In this case, if different systems or devices perform similar functions, functional redundancy. This redundancy is often used for multifunctional systems. For example, the value of the steam temperature at the outlet of the boiler unit can be determined by the readings of the potentiometer, which, together with the thermoelectric converter, carries out individual control of the critical parameter, and by calling this parameter to the electronic display of the information-measuring system that calculates the technical, economic and other indicators.

Temporary reservation is that it is allowed to interrupt the functioning of the system or device due to the failure of the element. In many cases, temporary redundancy, ensuring the continuity of the technological process, is carried out through the introduction of storage tanks, warehouses for raw materials and semi-finished products. For example, a short interruption in the fuel supply will not lead to the termination of steam generation due to the accumulation of heat on the heating surfaces of the boiler unit.

Information reservation associated with the possibility of compensating for the loss of information on one channel with information on another channel.

On most technological objects, due to internal connections, information redundancy takes place, which is often used to assess the reliability of information.

For example, the average steam consumption at the boiler outlet corresponds to the average water consumption at its outlet, the gas consumption at the boiler determines the air consumption with a fixed composition of flue gases.

For local systems, the most typical structural redundancy. With this type of redundancy, increased reliability is achieved by introducing additional elements into the system structure.

Structural redundancy

Structural redundancy is divided into general and item-by-item (separate). With general redundancy, the system or device is reserved as a whole; with element-by-element redundancy, individual elements or their groups are reserved.

If the redundant elements function on a par with the main elements, then there is a permanent redundancy that is passive. If the reserve is introduced into the system after the failure of the main element and is accompanied by switching operations, then there is redundancy by replacement - active redundancy.

Schemes of general constant (a) and general redundancy by replacement (b) are shown in Figure 6.1.

Figure 6.1 - Schemes of general redundancy

With the element-by-element method of redundancy (Figure 6.2 a - permanent, b - replacement), the reserve elements can be in a loaded, lightweight and unloaded state.

With a loaded (hot) reserve, the failure rate of the main o and backup n elements is the same, o = n. For a light (warm) reserve, the failure rate of reserve elements is lower than that of the main workers, o> vol.

With an unloaded (cold) reserve, the probability of failures of elements in the reserve state can be neglected, x = 0.

Figure 6.2 - Schemes of element-by-element redundancy

When making a reservation by replacement, the same reserve can be used to replace any of a number of elements of the same type. This method of redundancy is called sliding or with ambiguous match.

All the considered redundancy methods are widely used in the subsystems of automated control systems. In local systems, element-by-element (Figure 6.2, b) reservation by replacement with an unloaded reserve is mainly used.

Failed primary and secondary devices, regulating units and control units, actuators are replaced with serviceable ones (from the warehouse).

To characterize the ratio between the total number of elements of the same type n and the number r necessary for the functioning of the system of working elements, the concept of redundancy multiplicity is introduced

k = (n - r) / r.(6.1)

Meaning k can be whole if r = 1, and fractional if r> 1... In this case, the fraction cannot be canceled.

Sliding reservation is a variation fractional redundancy. Structural redundancy is associated with additional costs for redundant elements, then they should pay off by increasing the reliability of the system and reducing losses from its failures.

The simplest indicators of the effectiveness of redundancy is the following expression:

In τ = τ p / τ; B p = P p / P; В Q = Q / Q р (6.2)

where In τ- gain by increasing the mean time to failure of the redundant system τ p in comparison with the operating time of the non-redundant system τ; In p and In Q- similar indicators to increase the likelihood of failure-free operation and reduce the likelihood of failure.

Reservation is effective if the value of the indicators In p, In Q and In τ more than one.

Lecture 7

The purpose of the lecture: teaching methods of calculating the reliability of non-recoverable systems with a constant reserve

Item-by-item reservation

The reliability of a system containing groups of elements or individual elements with element-by-element redundancy (Figure 7.3, b) is calculated using the formulas for total constant redundancy (5.1) and (5.2). So, if the system consists of n sections with element-by-element redundancy of integer multiplicity k i, then the probability of failure-free operation of the system is:

where q ij is the probability of failure of the j-th element included in the i-th section of redundancy. To compare the efficiency of general and element-by-element redundancy, let us compare the probability of failure of two systems that include the same n (k + 1) number of equally reliable elements. Common Redundancy System Failure Probability:

Assuming that the probability of failure of each of the elements q<<1 (1-q) n ≈1-nq, Q op =n k +1 q k +1 . Для раздельного резервирования, используя (7.3) и считая q<<1, получаем: Q пр =1-(1-q k +1) n ≈nq k +1 .

The efficiency of the element-by-element reservation in comparison with the total Q op / Q pr will be n k. With an increase in the depth n and the multiplicity k of the reservation, its efficiency increases. The use of element-by-element redundancy is associated with the introduction of additional connecting elements with limited reliability. In this regard, there is an optimal reservation depth n opt; for n> n opt, the effectiveness of the reservation decreases.

Lecture 8

The purpose of the lecture: Teaching the basic methods of calculating the reliability of recoverable systems during operation.

Lecture 9

The purpose of the lecture: Teaching the basic practical methods of assessing reliability based on test results.

Definitive tests

Definitive tests can be exposed to automated control systems as a whole, their subsystems, functions, technical means and any other elements of systems.

Before the start of definitive tests, a test plan... A test plan refers to the rules governing the sample size, the order in which the tests are carried out, and the criteria for their termination. Let's consider the most common plans for definitive tests. The name of the plan is usually denoted by three letters (numbers): the first of them denotes the number of tested systems, the second - the presence of R or the absence of U restorations during the tests in case of failure, the third - the test termination criterion.

Plan corresponds to the simultaneous testing of systems. These systems are not restored after failure (or they are restored, but the data on their behavior after the first failure are not considered in the tests). The tests are terminated at the expiration of the operating time of each failed system. In Figure 9.1, a “x” indicates the presence of a failure; t i- operating time to failure i-Th system. This plan is usually used to determine the probability of system uptime in a time Ť.

Figure 9.1 - Test plans

The tests are terminated at the expiration of the operating time of each failed system. This plan is usually used to determine the likelihood of system uptime in a specified time Ť.

Plan- corresponds to tests of N of the same non-recoverable systems, however, unlike the plan, the test is stopped when the number of failed systems reaches r. In Figure 9.1, b, the r-th failure occurs in the i-th system. If r = N, go to plan , when testing is terminated after failure of all systems.

The plan is usually used to determine the mean time to failure in the case of an exponential distribution, and the plan in the case of a normal distribution. Planned testing requires a significant amount of time and the number of systems tested, but provides the ability to fully determine the empirical distribution function. Plans allow you to determine the empirical distribution function only for a certain time interval, give less information, but allow you to finish tests faster.

Plan - describes the tests of N systems, whereby the systems that failed during the tests are replaced with a new one or restored. The tests are terminated after the expiration of the operating time. Ť each of the positions (by position we mean a certain place on the stand or object, in relation to which the operating time is calculated regardless of the replacements or restorations that have occurred at this position - Figure 9.1, c)

Plan - corresponds to testing v N systems, when systems that failed during testing are replaced with new ones or restored. The test is stopped when the total number of failed systems for all positions reaches r (Figure 9.1, d).

The planning tasks are to determine the minimum volume of observations - the choice of the number of tested systems N, as well as the duration of observations Ť for plans and or the number of failures r for plans and.

The results of definitive tests should be point and interval estimates of reliability indicators.

Point estimate is a mathematical statistics concept. Let there be the results of k observations t 1, t 2,… .t k over some random variable T with the distribution function F (t, υ), and the parameter υ of this distribution is unknown. It is necessary to find such a function ῦ = g (t 1, t 2,… .t k) of observation results t 1,… .t k, which could be considered as an estimate of the parameter υ. With this choice of finctions g, each population (t 1, ... .t k) will correspond to a point ῦ on the number axis, which is called a point estimate for the parameter υ.

The statistical definitions of reliability indicators given in Lecture 2 are their point estimates. At the same time, the estimate of the mean time to failure corresponds to the plan, since here the completed (not interrupted in tests) operating time to failure of each of the tested systems is considered.

where S is the total operating time of all systems during testing; n S is the total number of failures of all systems during the tests.

For example, with the plan

With the plan, the estimate of the parameter of the flow of failures coincides with the estimate of the failure rate:

With a normal distribution and plan:

(9.7)

(9.8)

To consider the accuracy of the estimate, the concept of a confidence interval is introduced. Interval estimates is to determine the confidence interval. Let us assume that there are results of k observations t 1, t 2 ..., t k over a random variable T with a distribution function F (t, V), where the parameter V is unknown. It is necessary to find such a function V n = g n (t 1, t 2 ..., t k) of observation results so that the interval (V n, ∞) covers the unknown parameter V with a given probability γ 1:

The value V H is called the lower confidence limit of the parameter V with a one-sided confidence probability γ 1.

For a given probability γ 2, from the same set of observations, a function V bp = g bp (t 1, t 2 ..., t k) can be found such that the interval (0, V bp) covers the parameter V with probability γ 2:

(9.9)

The value V BP is called the upper confidence limit of the parameter V at a one-sided confidence probability γ 2.

The lower and upper confidence limits form the confidence interval, which with probability γ covers the unknown value of the parameter V on the number axis. For γ 1> 0.5 and γ 2> 0.5 8) according to (9.8) and (9.9):

where γ = γ 1 + γ 2 -1; It is usually assumed that γ 1 = γ 2, then γ = 2 γ 1 - 1.

The value of the confidence interval is the less. The greater the number of observations (for example, the greater the number of test failures) and the smaller the γ value of the confidence level.

Determining the boundaries of the confidence interval is as follows. Since the estimate of the unknown parameter V is a random variable, we find the law of its distribution. Then we determine the interval (V N, V ​​BP), in which the random variable falls with probability γ.

Control tests

Control tests usually exposed subsystems, hardware and their elements. For technical means, control tests for reliability are mandatory.

Tests for maintainability, preservation and durability are carried out in cases where it is provided for by standards, technical specifications or specifications for a specific device (means).

The frequency of proof tests for reliability is usually at least once every three years.

To carry out control tests from a set (batch) of homogeneous devices, a certain sample is drawn up and tests are carried out for the reliability of the devices included in this batch.

Based on the results of the sample test, a judgment is made on the compliance of the entire batch with the requirements.

The mathematical apparatus for solving the problem is the methods of testing statistical hypotheses studied in mathematical statistics.

As a testable (or, as they say, null) hypothesis, the assumption is accepted that the batch meets the reliability requirements, as the opposite (alternative) - that the batch does not meet these requirements.

According to the test results, one of the following four situations occurs:

1. The party meets the requirements; according to the test results, the null hypothesis was confirmed and a decision was made to accept the batch. This decision is correct.

2. The batch satisfies the requirements, but the test results did not confirm the null hypothesis. This was because the random sample contained a higher number of failed devices than the population. An alternative hypothesis is accepted; this solution is wrong and disadvantageous for the instrument manufacturer. At the same time, an error occurred, the probability of which is called the risk of the supplier (manufacturer) α.

3. The batch does not meet the requirements, according to the test results, the null hypothesis was not confirmed. An alternative hypothesis is accepted, i.e. decision not to accept the party. This decision is correct.

4. The batch does not meet the requirements, but the test results confirmed the null hypothesis of compliance with the reliability requirements, since the sample contained an increased number of non-failing devices compared to the entire batch. A decision was made, but it is not profitable, in contrast to item 2, not for the manufacturer, but for the consumer - the customer of these devices. An error has occurred, the probability of which is called consumer's (customer's) risk β.

Naturally, it is desirable to reduce the values ​​of both errors, bringing them to zero. The dependence of the probability L of acceptance of the lot on the reliability indicator A (called the operational characteristic of the control plan) for such a limiting situation is given in Figure 9.2, a. Let A tr be the required value of the reliability indicator. In this situation, the null hypothesis A≥ A tr. If it is valid, then the batch is accepted with a probability equal to one, and α = 0. An alternative hypothesis is that A £ A tr. In this case, the batch is rejected with a probability equal to one, with β = 0. However, such an ideal operational characteristic is unattainable, since it requires an infinite amount of observations.

In a real situation, two levels of the controlled reliability indicator are introduced: acceptance A α and rejection A β (Figure 9.2, b).

Figure 9.2 - Ideal (a) and real (b) operational characteristics of control plans

If A ≥ A α, then the devices must be accepted with a sufficiently high probability, not less than L (A α), if A £ A β, then the devices must be rejected with a sufficiently high probability, not less than 1 - L (A β). In this case, the supplier's risk α = 1-L (A α), the consumer's risk β = 1-L (A β). Thus, we replace the verification of the null hypothesis A≥ A tr with the alternative A £ A tr with another problem - the verification of the null hypothesis A≥ A α with the alternative A £ A β. The closer A α to A β, the more testing is required to make a reliable decision on the conformity of the batch.

The value of the acceptance level A β is set taking into account the acceptance level A α, cost, duration and test conditions, etc.

The risk of supplier α and consumer β is usually taken equal to 0.1-0.2, but in principle, by agreement between the consumer and the supplier, it is possible to choose other values ​​of α and β.

Proof tests for reliability are usually carried out in one or two stages. When using the first of them, tests are performed as follows. Samples included in the sample of volume d are tested for time t and. At the end of the tests, the number of failures n is determined. If it is equal to or less than the acceptance number c, determined depending on the values ​​of А ​​α, А β, α and β, then the null hypothesis is confirmed and the batch is accepted. If n> c, then the alternative hypothesis is confirmed and the game is not accepted. The one-stage method, all other things being equal, ensures the minimum calendar duration of the tests, the two-stage method, under the same conditions, makes it possible to provide a minimum of the average volume of tests.

Lecture 10

The purpose of the lecture: Teaching the basic methods of increasing reliability at the design and operation stages.

Lecture 11

The purpose of the lecture: Teaching the basic principles of assessing the reliability of software devices and systems