The fundamentals of the theory of reliability and diagnostics are stated in relation to the most capacious component of the system man - car - road - environment. Basic information about the quality and reliability of the car as a technical system is presented. Basic terms and definitions are given, indicators of reliability of complex and dissected systems and methods for their calculation are given. Attention is paid to the physical foundations of car reliability, methods of processing information about reliability and methods of testing for reliability. The place and role of diagnostics in the system of maintenance and repair of cars in modern conditions are shown.
For university students.

The concepts of "quality" and "reliability" of machines.
A life modern society is unthinkable without the use of the most diverse in design and purpose of machines that convert energy, materials, information, change people's lives and the environment.
Despite the huge variety of all machines, in the process of their development, uniform criteria are used to assess the degree of their perfection.

In the conditions of market relations, the creation of most new machines requires compliance with the most important condition for competitiveness, namely, giving them new functions and high technical and economic indicators of their use.
For effective use machines need to be of high quality and reliability.

The international standard ISO 8402 - 86 (ISO - International Organization Standardization) gives the following definition: "Quality is a set of properties and characteristics of a product or service that gives it the ability to satisfy stipulated or implied needs."

TABLE OF CONTENTS
Foreword
Introduction
Chapter 1. Reliability is the most important property of product quality
1.1. The quality of products and services is the most important indicator of the successful operation of enterprises of the transport and road complex
1.2. The concepts of "quality" and "reliability" of machines
1.3. Reliability and universal problems
Chapter 2. Basic concepts, terms and definitions adopted in the field of reliability
2.1. Objects considered in the field of reliability
2.1.1. General concepts
2.1.2. Classification technical systems
2.2. Basic states of an object (technical system)
2.3. Transition of an object to different states. Types and characteristics of failures of technical systems
2.4. Basic concepts, terms and definitions in the field of reliability
2.5. Reliability indicators
2.6. Reliability Criteria for Non-Recoverable Systems
2.7. Reliability Criteria for Recoverable Systems
2.8. Durability indicators
2.9. Preservability indicators
2.10. Maintainability indicators
2.11. Comprehensive Reliability Indicators
Chapter 3. Collection, analysis and processing of operational data on the reliability of products
3.1. Goals and objectives of collecting information and assessing the reliability of machines
3.2. Principles of collection and systematization of operational information on the reliability of products
3.3. Construction of an empirical distribution and statistical evaluation of its parameters
3.4. The laws of distribution of time to failure, most commonly used in reliability theory
3.5. Laplace transform
3.6. Confidence interval and confidence level
Chapter 4 Reliability of Complex Systems
4.1. Complex system and its characteristics
4.2. Reliability of partitioned systems
Chapter 5 Mathematical models reliability of the functioning of technical elements and systems
5.1. General model of reliability of a technical element
5.2. General model of system reliability in terms of integral equations
5.2.1. Basic designations and assumptions
5.2.2. State Matrix
5.2.3. Transition matrix
5.3. Reliability Models for Unrecoverable Systems
Chapter 6. The life cycle of a technical system and the role of scientific and technical preparation of production to ensure its quality requirements
6.1. The structure of the life cycle of a technical system
6.2. Comprehensive Product Quality Assurance System
6.3. Quality assessment and reliability management
6.3.1. International quality standards ISO 9000-2000 series
6.3.2. Quality control and its methods
6.3.3. Methods of quality control, analysis of defects and their causes
6.4. Technical and economic management of product reliability
6.5. Seven simple statistical methods quality assessments applied in ISO 9000 standards
6.5.1. Classification of statistical methods of quality control
6.5.2. Data stratification
6.5.3. Graphical representation of data
6.5.4. Pareto chart
6.5.5. cause and effect diagram
6.5.6. Scatterplot
6.5.7. Control sheet
6.5.8. control card
Chapter 7
7.1. Causes of loss of efficiency and types of damage to machine elements
7.2. Physical and chemical processes of destruction of materials
7.2.1. Classification of physical and chemical processes
7.2.2. Processes of mechanical destruction of solids
7.2.3. Material aging
7.3. Failures by strength parameters
7.4. tribological failures
7.5. Types of wear of car parts
7.6. Failures based on corrosion parameters
7.7. Wear diagram and methods for measuring the wear of car parts
7.8. Methods for determining the wear of machine parts
7.8.1. Periodic wear measurement
7.8.2. Continuous wear measurement
7.9. Influence of residual deformations and aging of materials on the wear of parts
7.10. Assessment of the reliability of elements and technical systems of vehicles during their design
7.11. The most common methods and methods for ensuring and predicting reliability used in the creation of machines
Chapter 8. The system of maintenance and repair of machines
8.1. Systems of maintenance and repair of machines, their essence, content and principles of construction
8.2. Requirements for the system of maintenance and repair, and methods for determining the frequency of their implementation
8.3. Operation of the machine in extreme situations
Chapter 9
9.1. General information about diagnostics
9.2. Basic concepts and terminology of technical diagnostics
9.3. Significance of diagnostics
9.4. Diagnostic parameters, determination of limit and allowable values ​​of technical condition parameters
9.5. Principles of car diagnostics
9.6. Organization of car diagnostics in the system of maintenance and repair
9.7. Types of car diagnostics
9.8. Diagnostics of car units during repair
9.9. Diagnostics of the state of the cylinder-piston group
9.10. The concept of diagnosing equipment in modern conditions
9.11. Technical diagnostics is an important element of technological certification of services of service enterprises
9.12. Management of reliability, technical condition of machines based on the results of diagnostics
9.13. Vehicle diagnostics and safety
9.14. Brake system diagnostics
9.15. Diagnostics of headlights
9.16. Suspension and steering diagnostics
Conclusion
Bibliography.

I. Fundamentals of the theory of reliability and diagnostics.

1. Systems for maintaining the working condition of cars. The essence of the planned preventive system is that preventive actions are carried out forcibly without agreeing on the actual need, and malfunctions and failures are eliminated when they occur. During the PPR, runs are planned from the 1st impact to another of the same type.

The PPR system has the following types of preventive actions: EO: washing (cosmetic and in-depth), refueling Zh., polishing, installing spikes, sanitizing vans and ambulance car interiors. TO-1: is standardized strictly after 4-5 thousand kilometers, including work: fastening - periodic tightening of threaded connections; lubricants, including changing the oil in the crankcase; simple low-volume adjustment work (fan belt tension). TO-2: incl. all works related to TO-1 + necessary adjustment work. CO: 2 times a year. It is planned to replace seasonal oils, tires, batteries, gaps in candles. The work is determined by the "Regulations on MOT and TR".

Pluses: 1) It is necessary at low education; 2) You can pre-determine the amount of work, distribute them by day of the week. Cons: 1) recommendations are developed based on the average results of observation; 2) the system requires to perform work sometimes without their need.

2. Calculation of the reliability of a car with serial and parallel connection of elements. A complex system is understood as an object that performs specified functions, which can be divided into elements, each of which also performs certain functions and interacts with other elements. Elements can have a variety of output parameters, which, from the standpoint of reliability, can be divided into three groups (types): XI - parameters, the change of which, with going beyond the established levels of indicators, leads to a loss of operability of the element and the system; X2 - parameters involved in the formation of the output parameters of the entire system, by which it is difficult to judge the failure of the element; HZ - parameters affecting the performance of other elements in the same way as changing the external conditions of the system. For greater clarity of possible types of output parameters, a system of two elements (for example, an engine) can be represented by a block diagram B shown in Fig. 18 diagram for the power system XI- this is the throughput of the fuel jet (if the jet is clogged and no fuel is supplied, then the power system fails and the engine fails), X2 - this is the wear of the fuel jet (fuel efficiency of the car is deteriorating), HZ - a rich mixture will cause the engine to overheat and hinder the operation of the cooling system. In turn, the poor performance of the cooling system leads to engine overheating and the formation of vapor locks in the power system - this HZ for element #2, poor thermostat operation delays the warm-up of the engine, which leads to a decrease in the fuel efficiency of the car - this x2, a broken belt leads to cooling system failure and vehicle failure - this is XI for element #2. In real complex systems, elements can have either all three types of outputs or less (one or two). This largely depends on the degree of dismemberment of the system into elements. In the considered example, the power supply system and the cooling system are themselves complex systems. A car is a very complex system that can be broken down into a large number of elements. When analyzing the reliability of such a complex system, it is useful to divide its elements into groups; 1. Elements, the failure of which practically does not affect the performance of the car (damage to the upholstery, corrosion of the wing). The failure of such elements is usually considered in isolation from the system. 2. Elements, the performance of which practically does not change over the considered period of time or operating time (for a car sent for harvesting, it does not make sense to take into account the change in the state of the gearbox housing). 3. Elements, the recovery of which does not require a significant investment of time and, in practice, does not reduce the performance of the vehicle (fan belt tension). 4. Elements, the failures of which lead to the failure of the car and regulate its reliability. Due to the fact that the functioning of the car is associated with the performance of various tasks in unequal operating conditions, the allocation of elements to these groups can be problematic (wiper failure in good dry weather does not lead to car failure, and in rain and slush - leads to failure). Depending on the nature of the impact on the reliability of a complex system, its elements can be considered connected in series or in parallel (by analogy with the inclusion of light bulbs in a garland). In this case, the real structural diagram of the system should be represented by a structural diagram of reliability. Let us give an example of a block diagram of a bearing assembly, consisting of the following elements; 1 - shaft, 2 - bearing, 3 - bearing housing, 4 - screws securing the bearing cover (4 pcs.), 5 bearing cover. If the failure of the element leads to the failure of the system, then we can assume that the element is connected in series. If the system continues to function when the element fails, then the element is connected in parallel. In accordance with this, the block diagram of the bearing assembly will have the first element, however, with an increase in operating time to a value of 2, the probability of failure of the second element may increase significantly. The third element at the considered values ​​of operating time remains practically trouble-free. Thus, in order to increase the reliability of a system consisting of elements connected in series, it is necessary first of all to increase the reliability of the “weakest” elements. Equally increase the average resource of all elements of the system is inappropriate.

3. Basic concepts, definitions, properties and indicators of reliability. During the operation of the car, its quality usually deteriorates due to changes in performance. Reliability is a property of quality, since it only manifests itself over a long period of time. Reliability is expressed by four parameters: a) failure-free operation - the property of an object to continuously maintain a working state for some time, the indicators are the mean time between failures; b) durability - the property of the object to maintain operability to the limit state with the necessary interruptions for maintenance, the indicators are the average service life, average resource; c) maintainability - the property of the object, which consists in its adaptability to the detection, elimination of failures and malfunctions, the indicators are the frequency of maintenance, specific labor intensity, the number of tools used; d) persistence - the property of an object to maintain the established quality indicators during storage, transportation, the indicators are the average and gamma percentage shelf life. The main terms and concepts are: a) failure - a change in one or more indicators of the specified parameters of an object, leading it to an inoperable state; b) malfunction - a state when an object does not meet at least one of the requirements of regulatory and technical documentation; c) failure - a self-recovering failure. By origin or causes of occurrence, failures and malfunctions are divided into three types: a) structural, production, and operational.

4. Processes of changing the properties of structural materials that affect the reliability of the car. A wide variety of materials are used in the construction of a car: various metals, plastics, rubber, fabrics, glass. As the car is used, the properties of structural materials also change in a very diverse way. Consider the most significant processes: Thermal softening- characteristic of metals and other materials. With an increase in temperature for different metals, their strength characteristics (yield strength) more or less decrease. For example, when the engine overheats, the bridges between the piston rings can break off at the pistons. Fatigue- softening of metals under cyclic loads, leading to the destruction of parts under stress. The sources of cyclic loads can be the conditions of the natural functioning of the part (for example, when the gear is working, the tooth takes the load, then “rests”, again takes the load, etc.), vibration loads, etc. Intergranular corrosion - this is the process of diffusion (leakage) of oxygen into the crystal lattice of the metal. This process reduces the fatigue strength of the parts. Hydrogenation - This is the process of hydrogen diffusion into the crystal lattice of metals, leading to an increase in brittleness and a decrease in the fatigue strength of the part. Hydrogen pickup can occur when the galvanic coatings of parts are violated by the regime. Intercrystalline adsorption (Rehbinder effect) This is the process of softening of parts due to the wedging action of molecules that enter cracks or notches.

The change in the properties of non-metallic materials is very diverse and should be considered separately in each specific case.

5. Processing of the results of truncated tests of the durability of parts and assemblies. The appearance of this technique is due to the protracted moments of observation of failures and the desire to get the result as soon as possible. When processing truncated tests, a failure probability curve is first built and numerical characteristics (average resource or gamma percentage resource) are found from it. Without a significant decrease in the accuracy of determining the average resource, tests of the durability of cars can be stopped (truncated) after the failure of 60 .... 70 of the number of tested cars. By arranging the test results x1 x2, x1 ... x in ascending order of resources, it is possible to calculate the failure probabilities corresponding to the obtained values ​​of random variables by dividing the serial number random variable on the number of vehicles tested. . By plotting probability points on a graph and drawing a curve through them, one can obtain the probability distribution law. With a small number of tested cars n=1, the curve shifts significantly and in order to avoid an incorrect result, the formula should be used: . The second technique that improves the accuracy of test results is the use of special probabilistic paper, when the curve of the probability distribution law is plotted on a graph with non-linear scales. . This scale can be built using a special table, or by evenly plotting the quantile values ​​with an indication of the probability corresponding to the quantile value, or directly by graphical construction. By plotting the values ​​against the corresponding values ​​on a probability paper and drawing a straight line through the obtained points, we obtain the desired probability distribution. The numerical characteristics of the resulting distribution of random variables are determined by the position of the distribution line relative to the coordinate axes on the graph. For example, for a normal law when testing durability, the average resource corresponds to a probability of 0.5.

6. Determination of durability indicators according to tests truncated on the left. Tests truncated on the left - the moment of failure is observed, and the moment the unit under test begins to work is unknown. Observing a large group of different-aged cars of the same model for a relatively short period of time or operating time, one can obtain information about the durability of their units or parts. This period of time must be large enough to allow failures, but the probability of two or more consecutive failures on one vehicle must be extremely small. Since 6 ... 8 points are enough to build the distribution law, then the value of the segment T can be chosen approximately equal to 0.25 of the expected average service life of the part.

The results of the observation are entered in the table: Dividing the possible service life into intervals, we will have a histogram (Fig.) characterizing the probability of observing failures P;, in the intervals T,. If the probability distribution is close to the normal law, then with a long service life, the failure probabilities decrease, since the main part of the parts has already failed earlier. In fact, parts of older cars fail more often than new ones. This is explained by the fact that among the failing parts there are not only the first (installed at the factory) parts, but also those installed during the repair. Thus, to construct a probability distribution law, it is necessary to exclude failures of parts installed during repairs from the observed number of failures or to correct the observed (experimental) probabilities. To derive a formula that allows us to correct the experimental probabilities, we consider a graph of possible outcomes of events for objects with different operating time or service life. On the graph, the failure state is shown by a cross, and the working state is shown by a circle, the probability of failure for the first interval - for the second - ... The probability of part failure in the first period will coincide with the experimental probability, which is determined by the results of observing a group of new cars, . Instead of the failed part during the repair of the vehicle, another part will be installed, which may also fail in the second period. The probability of two failures in a row will be expressed as the product of the probabilities of failures and will be equal to . In the second period, the failure of the part installed at the factory, the service life of which we are looking for, can most likely be observed. That. the experimental probability of part failures in the vehicle age group will be equal to P2° = P.2 + P2. Whence P2 = P2° - P,2. Similarly, for the third period, we can write . Transforming we get the expression: . Comparing the obtained expressions, we see a general trend, which is written as follows: The advantage of this method for evaluating the durability of parts is that, having come to the ATP with a large fleet of cars of different ages, an engineer already after a year of work has the opportunity to determine the average service life of all parts. Knowing the average annual mileage of a car by the average service life, it is easy to determine the average resource, which makes it possible to assess the reliability of cars and plan the consumption of spare parts.

7. Determination of the norm of spare parts, which guarantees a given probability of no downtime of cars due to lack of parts. The calculation makes it possible to determine such norms for the stock of parts that, with any predetermined probability, guarantee the absence of vehicle downtime due to a shortage of parts during the planned period. The calculation method is acceptable for any number of cars, if the resource of parts is described by an exponential law (failures are of a sudden nature), and can also be extended to large groups of cars, heterogeneous in operating time and service life, when the resource is described by any probability distribution law. In the first and second cases, when failures of normalized parts occur on different vehicles and are not related to each other, the number of failures for the planned period of time is described by Poisson's law a - the average consumption of spare parts for the planned period. With a margin of parts, the probability that the random number of failures will be less than this margin is expressed as the sum of the probabilities a = P(k = 0) + P(k = 1) + P(k = 2) + ... + P(k = Na ). Using the Poisson law, we can write for the convenience of calculation, we rewrite the formula, transferring the constant factor to the left side of the equation. Knowing the average consumption of spare parts and specifying the required probability of no downtime due to a shortage of spare parts, the left side of the equation is calculated, and then they begin to calculate the sum of the right side by sequential enumeration of the number k until the sum reaches the value of the left side of the equation. That number k at which equality will be achieved will be the required norm of spare parts Na. Based on the considered formulas, tables of relative norms of spare parts have been compiled that provide a given probability of no downtime due to a shortage of parts. Analyzing the table values, one can notice a very important pattern: the greater the average consumption of spare parts, the closer the value of ρ to unity, i.e., at high average costs, a slight excess of average stocks guarantees a high probability of no downtime due to lack of spare parts. Thus, warehouses should not be located at the input to production, but at the output of production. To ensure that there are no downtimes, ATPs with a small fleet of vehicles should have a stock of bearings several times higher than their average consumption, and there is no need to have excessive stocks in the warehouse of the bearing plant, with a slight increase in consumption, the requests of all consumers will be satisfied with a very high guarantee.

8. Determining the frequency of maintenance of parallel-connected systems that smoothly change their characteristics. Consider changing the engine oil. As the engine runs, the lubricating properties of the oil filled in
crankcase oils gradually deteriorate, which leads to an increase in the intensity of wear of parts
engine. We express the amount of wear by the formula I \u003d a-xb, where x is the oil operating time, a and b -
empirical coefficients. If you change the oil every Xto kilometers, then at each change

the nature of the increase in wear will be repeated. According to the technical and economic method for determining the frequency of maintenance, the target function of unit costs.

. Let us determine the engine resource unknown to us from the following considerations. If during the time before changing the oil the engine wears out by the amount AI = a * Xhmо, then the wear limit according to technical conditions 1pr will be reached during the operating time Substituting the value of the resource into the objective function, we obtain a formula with one required unknown - the periodicity of TO: We take the derivative o of this formula with respect to Chi and equate it to zero. From here we express the optimal frequency of oil change: The resulting formula can be simplified by entering the value of the minimum engine life without changing the oil. From the condition we express:

9. Determining the periodicity of maintenance of parallel-connected systems that discretely change their characteristics. As an example of the considered system, a full-flow oil filter can be taken, which fails when the filter element is mechanically destroyed or clogged when the oil begins to pass through the pressure reducing valve uncleaned. Consider the nature of the increase in wear of engine parts as the operating time (Fig.) With a failed filter, the wear rate is high and the engine wear limit (curve 1) can be achieved during operating time, if the filter is guaranteed to work, then the wear rate is low (curve 2) and the engine will be able to work . Filters are often made non-separable and are replaced routinely at intervals during which the filter may fail. For a particular engine, the increase in wear will be expressed by a broken line 1, and its resource will be a random variable . Let us find the optimal frequency of filter replacement using the objective function of the total unit costs: . Obviously, if , then , if (filters are not replaced), then . In addition to the periodicity of maintenance, the reliability of the filter itself on the period will also affect the engine resource, which can be represented by a reliability curve. As the car operates, the probability of the filter fail-safe operation will change from 1 to . Knowing the reliability of the filter, you can find the average engine life as the mathematical expectation of two values ​​and . Substituting the value of the resource into the objective cost function, we obtain . The optimal frequency of maintenance can be determined by the minimum cost from the condition Since it is difficult to perform an analytical solution, you can use a numerical solution, finding the average filter failure-freeness by the area under the curve on a given segment , you can find a value that will give the minimum total cost.

10. Determining the frequency of maintenance of series-connected systems.

Systems connected in series include units and systems of the car, the failure of which leads to the loss of vehicle performance without serious damage to other systems - these are devices of the power supply system, ignition, start-up, etc.

Maintenance and repair of sequentially connected systems on demand leads to high costs, including possible fines for flight disruptions, the need to tow a car to a garage, etc. The regulated maintenance of these systems in an ATP or service station is costly. Let us determine the optimal frequency of maintenance of series-connected systems using

the law of probability distribution of its time between failures. At the assigned frequency, the probability of system failure in road conditions , the probability that the failure will be prevented during scheduled maintenance, . Failure can be observed in the interval . Thus, part of the vehicle will fail and be serviced, on average, during operating time , and part - during operating time . It is possible to find the average operating time, at which sequentially connected systems will be serviced, as the mathematical expectation: . Similarly, you can find the average cost of servicing the system: If all systems are serviced in a planned manner, then if only those systems that had not previously failed and were not serviced on demand were serviced in a planned manner, then . Knowing the average maintenance costs and the average operating time at which maintenance is carried out, it is possible to write down the specific total costs, i.e., the objective function for determining the frequency of maintenance, .

The frequency of maintenance, at which unit costs are minimal, is optimal. Let us conduct a qualitative analysis of unit costs: with the probability , , at , i.e. the system will not be serviced in a planned manner, , , . The optimal frequency of maintenance can be found by a numerical solution, having the values ​​of maintenance costs in a planned manner and the average cost of eliminating system failures, as well as the curve of the system failure probability distribution law. The nature of the change in unit costs is shown in the figure.

11. The essence of the method of making a diagnosis based on a set of diagnostic parameters. Technical diagnostics is a branch of knowledge that studies the signs of vehicle malfunctions, methods, tools and algorithms for determining its technical condition without disassembly, as well as the technology and organization of the use of diagnostic systems in the processes of technical operation. Diagnostics is the process of determining the technical condition of an object without dismantling it, according to external signs, by changing the values ​​characterizing its condition and comparing them with the standards. Diagnosis is carried out according to the algorithm (a set of sequential actions) established by the technical documentation. The complex, including the object, tools and algorithms, form a diagnostic system. Diagnostic systems are divided into functional ones, when diagnostics are carried out during the operation of objects, and test ones, when the operation of an object is artificially reproduced when the diagnostic parameters change. There are universal systems, designed for several different diagnostic processes, and special ones, providing only one diagnostic process. The purpose of the diagnosis is to identify object malfunctions, determine the need for repair or maintenance, evaluate the quality of the work performed, or confirm the suitability of the diagnosed mechanism for operation before the next service. It is required to make a diagnosis based on a set of symptoms: ; ; ; - probability of diagnostic parameters - diagnosis

II. Licensing and certification in road transport.

1. Activities licensed in the field of road transport, the procedure for obtaining a license. In accordance with the law, the provision provides for the licensing of passenger transport by road vehicles equipped to carry more than eight people. Licensing of transportation of passengers by road is carried out by the Ministry of Transport of the Russian Federation, which assigned these duties to RTI. The Ministry of Transport of the Russian Federation in the field of motor transport is vested with the authority to license only three types of activities: transportation of passengers by buses, transportation of passengers by cars and transportation of goods. An appropriate license is granted for the licensed type of activity. Licensing requirements and conditions for the carriage of passengers and goods by road are: a) compliance with the requirements established by federal laws; b) compliance of vehicles declared for transportation; c) compliance of the individual entrepreneur and employees with qualification requirements; d) the presence in the staff of the legal entity of officials responsible for ensuring security traffic. A license is a document that is a permission to carry out a specific type of activity subject to the obligatory observance of license requirements. To obtain a license, the license applicant submits the following documents to the licensing authority: 1) Application indicating the legal entity, legal form, address, for individual entrepreneurs: full name, passport details, indication of the type of activity; 2) A copy of the constituent document or a copy of the IP registration certificate; 3) A copy of the certificate of registration with the tax office; 4) Copy of qualification documents; 5) A copy of the documents of a traffic safety specialist; 6) Information about vehicles; 7) Receipt of payment for licensing. The decision to issue a license must be issued within 30 days. The license is valid for no more than 5 years.

2. Technical regulations and other documents used for certification. Technical regulation - a document adopted by an international treaty of the Russian Federation, ratified in the manner prescribed by the legislation of the Russian Federation or federal law and establishes mandatory requirements for the application and implementation of requirements for objects of technical regulation (products, production processes, operation, storage, transportation). Technical regulations are adopted in purposes: a) to protect the life or health of citizens; b) property of individuals or legal entities, state or municipal property; c) protection of the environment, life or health of animals and plants; d) prevention of actions that mislead purchasers (consumers of services). Adoption of technical regulations for other purposes is not allowed. Unlike a mandatory technical regulation, a standard, as a basis for certification, is a normative document developed by consensus, approved by a recognized body, aimed at achieving the optimal degree of streamlining in a particular area. A standard is a document in which, for the purpose of voluntary reuse, product characteristics, implementation rules and characteristics of production, operation, storage, transportation, and sale processes are established.

3. Basic concepts of certification, its forms and participants. Certification in Latin means "done right". Certification is a procedure by which a third party certifies in writing that a properly identified product, process or service conforms to specified requirements. The certification system consists of: the central body; rules and procedures for certification; regulations; inspection control procedure. The objectives of certification are: a) certification of compliance of products, production processes, operation, storage, transportation with standards and terms of contracts; b) assistance to purchasers in the choice of products, works and services; c) increasing the competitiveness of products, works, services in the Russian and international markets; d) creation of conditions for ensuring the free movement of goods across the territory of the Russian Federation. Certification can be mandatory or voluntary, which is directly related to the presence or absence of adopted technical regulations. For the implementation of certification, systems are created, including: 1) a central body that manages the entire system; 2) certification bodies; 3) rules and regulations of certification; 4) normative documentation. The system is usually organized on a sectoral basis. Certification body - an individual or legal entity accredited in the prescribed manner. Functions of the certification body: a) carries out conformity assessment; b) issues a certificate; c) represents the right to use the sign of circulation on the market (if mandatory) or conformity (if voluntary); d) suspend or terminate the validity of the issued certificate. To register a voluntary certification system, it is necessary: ​​a) a certificate of state registration of a legal entity or individual entrepreneur; b) image of the mark of conformity; c) receipt of registration payment (registration takes place within 5 days). The law provides for 2 types of mandatory certification: 1) declaration of conformity; 2) conformity certification. Declaration of conformity is carried out: a) acceptance of a declaration of conformity based on own evidence; b) acceptance of a declaration of conformity based on own evidence and evidence obtained with the participation of a certification body or an accredited testing laboratory.

The assessment of the reliability indicator is the numerical values ​​of the indicators determined by the results of observations of objects under operating conditions or special tests for reliability. When determining reliability indicators, two options are possible: the type of the law of distribution of operating time is known ...

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Page 2

TEST

"Fundamentals of the theory of reliability and diagnostics"

1. The task

According to the results of testing products for reliability according to the plan [ N v z ] obtained the following initial data for assessing reliability indicators:
- 5 sample values ​​of time to failure (unit: thousand hours): 4.5; 5.1; 6.3; 7.5; 9.7.
- 5 sample values ​​of operating time before censoring (i.e., 5 products remained in working condition by the end of the tests): 4.0; 5.0; 6.0; 8.0; 10.0.

Define:

- point estimate of mean time to failure;

- with confidence probability lower confidence limits and;
- plot the following graphs to scale:

distribution function;

probability of failure-free operation;

upper confidence limit;

lower confidence limit.

1. Introduction

The calculation part of the practical work contains an assessment of the reliability indicators according to the given statistical data.

The assessment of the reliability indicator is the numerical values ​​of the indicators determined by the results of observations of objects in operating conditions or special tests for reliability.

When determining reliability indicators, two options are possible:

The form of the law of distribution of operating time is known;

The form of the operating time distribution law is not known.

In the first case, parametric evaluation methods are used, in which the parameters of the distribution law are first estimated, which are included in the calculation formula of the indicator, and then the reliability indicator is determined as a function of the estimated parameters of the distribution law.

In the second case, non-parametric methods are used, in which reliability indicators are evaluated directly from experimental data.

1. BRIEF THEORETICAL INFORMATION

Quantitative indicators of the reliability of the rolling stock can be determined from representative statistical data on failures obtained during operation or as a result of special tests, set taking into account the features of the structure, the presence or absence of repairs and other factors.

The initial set of objects of observation is called the general population. According to the coverage of the population, 2 types of statistical observations are distinguished: continuous and selective. Continuous observation, when each element of the population is studied, is associated with significant expenditures of money and time, and sometimes it is not physically feasible at all. In such cases, they resort to selective observation, which is based on the selection from the general population of some of its representative part - a sample population, which is also called a sample. Based on the results of studying the trait in the sample population, a conclusion is made about the properties of the trait in the general population.

The sampling method can be used in two ways:

Simple random selection;

Random selection by typical groups.

Dividing the sample population into typical groups (for example, by models of gondola cars, by years of construction, etc.) gives a gain in accuracy when estimating the characteristics of the entire population.

No matter how detailed the sample observation is, the number of objects is always finite, and therefore the volume of experimental (statistical) data is always limited. With a limited amount of statistical material, only some estimates of reliability indicators can be obtained. Despite the fact that the true values ​​of reliability indicators are not random, their estimates are always random (stochastic), which is associated with the randomness of the selection of objects from the general population.

When calculating an estimate, one usually tries to choose such a way that it is consistent, unbiased and efficient. Consistent is called an estimate, which, with an increase in the number of objects of observation, converges in probability to the true value of the indicator (condition 1).

An estimate is called unbiased, the mathematical expectation of which is equal to the true value of the reliability indicator (condition 2).

An estimate is called effective if its variance is the smallest in comparison with the variances of all other estimates (condition 3).

If conditions (2) and (3) are satisfied only for N tending to zero, then such estimates are said to be asymptotically unbiased and asymptotically efficient, respectively.

Consistency, unbiasedness and efficiency are qualitative characteristics of estimates. Conditions (1)-(3) allow for a finite number of objects N observations write only an approximate equality

a~â(N )

Thus, the estimate of the reliability indicator â( N ), calculated from a sample set of volume objects N is used as an approximate value of the reliability indicator for the entire population. Such an estimate is called a point estimate.

Considering the probabilistic nature of reliability indicators and a significant spread of statistical data on failures, when using point estimates of indicators instead of their true values, it is important to know what are the limits of a possible error and what is its probability, that is, it is important to determine the accuracy and reliability of the estimates used. It is known that the quality of a point estimate is the higher, the more statistical material it is obtained on. Meanwhile, a point estimate by itself does not carry any information about the amount of data on which it was obtained. This determines the need for interval estimates of reliability indicators.

The initial data for assessing the reliability indicators are determined by the observation plan. The initial data for the plan ( N V Z ) are:

Selective values ​​of time to failure;

Selected values ​​of operating hours of machines that remained operational during the observation period.

The operating time of machines (products) that remained operational during the tests is called the operating time before censoring.

Censoring (cutoff) on the right is an event that leads to the termination of tests or operational observations of an object before a failure (limiting state) occurs.

Reasons for censorship are:

Variation in the beginning and (or) end of testing or operation of products;

Withdrawal from testing or operation of some products for organizational reasons or due to failures of components, the reliability of which is not being investigated;

Transfer of products from one application mode to another during testing or operation;

The need to assess the reliability before failure of all the products under study.

Operating time before censoring is the operating time of the object from the start of testing to the onset of censoring. A sample whose elements are the values ​​of time to failure and before censoring is called a censored sample.

A singly censored sample is a censored sample in which the values ​​of all operating times before censoring are equal and not less than the maximum time to failure. If the values ​​of time before censoring in the sample are not equal to each other, then such a sample is repeatedly censored.

1. Evaluation of reliability indicators by NON-PARAMETRIC METHOD

1 . The time to failure and time to censoring are arranged in a general variational series in non-decreasing order of time (time to censoring is marked *): 4,0*; 4,5; 5,0*; 5,1; 6,0*; 6,3; 7,5; 8,0*; 9,7; 10,0*.

2 . We calculate point estimates of the distribution function for operating time according to the formula:

where is the number of workable products j th failure in the variation series.

3. We calculate a point estimate of the mean time to failure using the formula:

where;

Thousand hour.

4. The point estimate of uptime for operating hours, thousand hours, is determined by the formula:

where;

5. We calculate point estimates using the formula:

6. Based on the calculated values ​​and we build graphs of the distribution functions of the operating time and the reliability function.

7. The lower confidence limit for the mean time to failure is calculated by the formula:

Where is the quantile of the normal distribution corresponding to the probability. Accepted according to the table depending on the confidence level.

According to the condition of the assignment, the confidence probability. We select the corresponding value from the table.

Thousand hour.

8 .The values ​​of the upper confidence limit for the distribution function will be calculated by the formula:

where is the chi-squared quantile of the distribution with the number of degrees of freedom. Accepted according to the table depending on the confidence level q .

Curly brackets in the last formula mean taking the integer part of the number enclosed in these brackets.

For;
for;
for;
for;
for.

9. The values ​​of the lower confidence limit of the probability of failure-free operation are determined by the formula:

10. The lower confidence limit of the probability of failure-free operation for a given operating time thousand hours is determined by the formula:

where; .

Respectively

11. Based on the calculated values ​​and we construct graphs of the functions of the upper confidence limit and the lower confidence limit, which are the same as the previously constructed models of point estimates and

1. CONCLUSION ON THE WORK DONE

When studying the results of testing products for reliability according to the plan [ N v z ] the values ​​of the following reliability indicators were obtained:

Point estimate of mean time to failure thousand hours;
- a point estimate of the probability of no-failure operation for operating time thousand hours;
- with confidence probability lower confidence limits thousand hours and;

Based on the found values ​​of the distribution function, the probability of failure-free operation, the upper confidence limit and the lower confidence limit, graphs are constructed.

Based on the calculations performed, it is possible to solve similar problems that engineers face in production (for example, when operating cars on a railway).

1. Bibliography
2. Chetyrkin E. M., Kalikhman I. L. Probability and statistics. M.: Finance and statistics, 2012. - 320 p.
3. Reliability of technical systems: Handbook / Ed. I. A. Ushakova. - M.: Radio and communication, 2005. - 608 p.
4. Reliability of engineering products. A practical guide to rationing, validation and assurance. M.: Publishing house of standards, 2012 . – 328 p.
5. Methodical instructions. Reliability in technology. Methods for assessing reliability indicators based on experimental data. RD 50-690-89. Introduction S. 01.01.91, Moscow: Publishing House of Standards, 2009. - 134 p. Group T51.
6. Bolyshev L. N., Smirnov N. V. Tables mathematical statistics. M.: Nauka, 1983. - 416 p.
7. Kiselev S.N., Savoskin A.N., Ustich P.A., Zainetdinov R.I., Burchak G.P. Reliability of mechanical systems railway transport. Tutorial. Moscow: MIIT, 2008 -119 p.

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Professor T.P. Resurrection

INTRODUCTION The Importance of Reliability Theory

in modern technology.

The modern period of development of technology is characterized by the development and implementation of complex technical systems and complexes.

The basic concepts that are used in this discipline are the concepts of a complex dynamic system and a technical device (TD) or an element that is part of the system. Difficulty is usually understood as complexity systems of individual elements, while considering not just the sum of the elements, but their interaction. The interaction of elements and their properties change over time. The complexity of the interaction of elements and their number are two aspects of the concept of a complex dynamic system. The complexity of the system is determined not so much by the number of elements, but by the number of connections between the elements themselves and between the system and the environment.

Complex dynamic systems are systems oversaturated with internal connections of elements and external connections with the environment.

Let us define a complex dynamic system as the formation of elements of a different nature, which have certain functions and properties that are absent from each of the elements, and are able to function, statically correlated in a certain range with environment, and thanks to this, maintain its structure in the course of continuous change of interacting elements according to complex dynamic laws.

Complex dynamical systems are essentially nonlinear systems, the mathematical description of which is present stage not always possible.

Any complex dynamic system is created to solve a specific theoretical or production problem. Due to the deterioration of the properties of the system during operation, there is a need for periodic maintenance, the purpose of which is to maintain the ability of the system to perform its functions. Therefore, fundamental to complex dynamic systems have information processes. The cyclicity of information processes is provided by the feedback mechanism. On the basis of information about the behavior of the system, the management of its state is organized, taking into account the results of which the subsequent management of the system is adjusted.

When designing technical systems, it is necessary to provide for maintenance issues during the intended operation. Among other problems of design and creation of the complex:

Compliance with specified technical requirements;

Cost-effectiveness of the complex, taking into account the tests and conditions of the intended operation;

Development of technical means for servicing the complex and mathematical support for them;

Ensure the suitability of the complex for work in the link "man - machine", etc.

Thus, already when designing the complex, attention should be focused on all the noted, interconnected issues as a whole, and not on each individual of them.

It is possible to design a complex that meets the given technical requirements, but does not meet the economic requirements, the requirements for maintenance and the functioning of the complex in the “man-machine” link. Therefore, the problem of creating a complex must be solved from the standpoint of a systematic approach. The essence of this approach can be demonstrated in simple example. Suppose that we have selected one car of each of the brands available for sale. Then we turn to a group of experts with a request to study them and choose the best carburetor, then choose the best engine, distributor, transmission, etc., until we collect all the car parts from different cars. We are unlikely to be able to assemble a car from these parts, and if we can, it is unlikely to work well. The reason is that the individual parts will not fit together. Hence the conclusion: it is better when the parts of the system fit together well, even if individually they do not work perfectly, than when the parts that work perfectly do not fit together. This is the essence of the systems approach.

Sometimes the improvement of one part of the complex leads to a deterioration specifications another, so that the improvement is meaningless. A systematic approach to the analysis of the phenomena under consideration involves the use of a complex of various mathematical methods, modeling methods and experiments.

The proposed course deals with the solution of particular problems of servicing complex systems and their elements. analytical method and the features of solving more complex problems of operation by the method of statistical modeling are noted. In practice, the implementation of the obtained methods will lead to the analysis of the complex from the standpoint of a systematic approach.

The main features of a complex system or technical device (TD) are as follows:

Having a certain unity of purpose and contributing to the development of optimal outputs from the existing set of inputs; the optimality of outputs should be evaluated according to a previously developed optimality criterion;

Performing a large number of different functions that are carried out by many parts of the system;

Complexity of functioning, i.e. a change in one variable entails a change in many variables and, as a rule, in a non-linear manner;

High degree of automation;

Possibility of describing the perturbation entering the system in a quantitative measure.

The operation of a complex TS is a continuous process that includes a number of activities that require a planned, continuous impact on the TS in order to maintain it in working order. Such activities include: scheduled maintenance, recovery after a failure, storage, preparation for operation, etc. The above definition of operation does not cover all those activities that make up the operation of complex systems. Therefore, operation in a broad sense should be understood as the process of using the technical equipment for its intended purpose and maintaining it in a technically sound condition.

The state of technical specifications is determined by the totality of values ​​of its technical characteristics. During operation, the technical characteristics of the device change continuously. For the organization of operation, it is important to distinguish between the states of technical specifications that correspond to extreme or permissible (boundary) values ​​of technical characteristics, which correspond to the operating state, failure, maintenance state, storage, restoration, etc. For example, an engine is in working condition if it provides the necessary thrust, provided that the values ​​of all other characteristics are within the limits established in the technical documentation. The engine must be in a maintenance state if its performance values ​​have reached the appropriate limits. In this case, its immediate use for its intended purpose is impossible.

The main task of the theory of operation is to scientifically predict the states of complex systems or technical specifications and develop, using special models and mathematical methods for the analysis and synthesis of these models, recommendations for organizing their operation. When solving the main problem of operation, a probabilistic-statistical approach is used to predict and control the states of complex systems and to model operational processes.

Some issues of the theory of operation, such as predicting the reliability of technical specifications in operating conditions, organizing the restoration of technical specifications during the execution of a task, diagnosing failures in complex systems, determining the required number of spare elements, etc., have received sufficient development in reliability theory, restoration theory and queuing theory , in technical diagnostics and the theory of inventory management.

1. Basic concepts and definitions

reliability theory.

Reliability theory is the science of methods for ensuring and maintaining reliability in the design, manufacture and operation of systems.

The ability of any product or system to maintain its original technical characteristics during operation is determined by its reliability. The physical meaning of reliability is the ability of technical specifications to maintain their characteristics over time.

Operational characteristics are also readiness for use, recoverability, maintenance parameters. Reliability can be determined both as an independent operational characteristic of technical specifications, and as a component of other operational characteristics.

Under reliability is understood as the property of technical specifications to perform specified functions, maintaining their performance within specified limits for the required period of time or the required operating time under certain operating conditions.

As follows from the definition, reliability depends on what functions the product performs over time, during which the performance of these functions must be ensured, and on operating conditions.

Any product has many performance indicators and it is necessary to strictly stipulate in each case when the technical parameters or property of the specification should be taken into account when determining its reliability.

In this regard, the concept performance , which is defined as the state of the TS, in which it is able to perform the specified functions with the parameters established by the requirements of the technical documentation. The introduction of the concept of operability is necessary to determine the technical parameters and properties of technical specifications that determine the performance of the specified functions and the permissible limits for their change.

It also follows from the definition of reliability that reliability consists in the ability of a technical specification to maintain its initial technical characteristics over time. However, even the most reliable technical specifications cannot maintain their initial technical characteristics for an unlimited time. Therefore, it is meaningless to talk about reliability without defining a specific period of time during which these characteristics should be provided. In addition, the actual reliability of each TU largely depends on the operating conditions. Any predetermined value of reliability is valid only for specific operating conditions, including the modes of use of specifications.

In the theory of reliability, the concepts of an element and a system are introduced. The difference between them is purely conditional and lies in the fact that when determining the reliability, the element is considered indivisible, and the system is presented as a set of separate parts, the reliability of each of which is determined separately.

The concepts of element and system are relative. For example, one cannot assume that an aircraft is always a system, and one of its engines is an element. An engine can be considered an element if, when determining reliability, it is considered as a whole. If it is divided into its constituent parts (combustion chamber, turbine, compressor, etc.), each of which has its own reliability value, then the engine is a system.

It is much more difficult to quantify or measure the reliability of a technical specification than it is to measure any of its technical characteristics. As a rule, only the reliability of the elements is measured, for which special, sometimes quite complex and lengthy tests are carried out, or the results of observations of their behavior in operation are used.

The reliability of systems is calculated based on the data on the reliability of the elements. As starting data, when determining the quantitative values ​​of reliability, events are used that consist in a violation of the operability of the technical specifications and are called failures.

Under refusal an event is understood, after which the TS ceases to perform (partially or completely) its functions. The concept of failure is fundamental in the theory of reliability and the correct understanding of its physical essence is the most important condition for the successful solution of issues of ensuring reliability.

In some cases, the system continues to perform the specified functions, but violations of technical characteristics appear with some elements. This state of the element is called a failure.

Malfunction - the state of the element in which it is in this moment does not meet at least one of their requirements, established both in relation to the main and secondary parameters.

Let's consider some other concepts that characterize the operational qualities of technical specifications. In some cases, it is required that the technical equipment not only work flawlessly for a certain period of time, but, despite the presence of failures during breaks in operation, would generally retain the ability to perform the specified functions for a long time.

The property of technical specifications to remain operational with the necessary interruptions for maintenance and repairs up to the limit state specified in the technical documentation is called durability . The limit states of technical specifications can be: breakdown, wear limit, drop in power or productivity, decrease in accuracy, etc.

Tu can lose its performance not only during operation, but also during long-term storage, as a result of aging. In order to emphasize the property of TS to maintain operability during storage, the concept of persistence is introduced, which makes sense of the reliability of TS under storage conditions.

Persistence the property of technical specifications to have conditional performance indicators during and after the period of storage and transportation established in the technical documentation is called.

Importance when determining the operational characteristics, technical specifications have the concepts of service life, operating time and resource.

Service life called the calendar duration of operation of the technical specifications until the occurrence of the limit state specified in the technical documentation. Under operating time is understood as the duration (in hours or cycles) or the amount of work of the technical specifications (in liters, kilograms, t-km, etc.) until a failure occurs . resource is the total operating time of technical specifications up to the limit state specified in the technical documentation.

2. A quantitative measure of the reliability of complex systems

To select rational measures aimed at ensuring reliability, it is very important to know the quantitative indicators of the reliability of elements and systems. A feature of the quantitative characteristics of reliability is their probabilistic-statistical nature. From this follows the features of their definition and use. As practice shows, the same type of technical specifications coming into operation, for example, cars, even being manufactured at the same plant, show different ability to maintain their performance. During operation, technical equipment failures occur at the most unexpected, unforeseen moments. The question arises, are there any patterns in the appearance of failures? Exist. Only to establish them, it is necessary to monitor not one, but many technical equipment in operation, and to process the results of observations, apply the methods of mathematical statistics and probability theory.

The use of quantitative estimates of reliability is necessary when solving the following problems:

Scientific substantiation of requirements for newly created systems and products;

Improving the quality of design;

Creation scientific methods testing and control of the level of reliability;

Substantiation of ways to reduce economic costs and reduce the time for product development;

Improving the quality and stability of production;

Development of the most efficient methods of operation;

Objective assessment of the technical condition of the equipment in operation;

Currently, in the development of reliability theory, there are two main directions :

Progress in technology and improvement in the technology of manufacturing elements and systems;

Rational use of elements in the design of systems - synthesis of systems by reliability.

3. Quantitative indicators of reliability

elements and systems.

The quantitative indicators of the reliability of elements and systems include:

Reliability factor R G ;

Probability of failure-free operation for a certain time P ( t ) ;

Mean time to first failure T cf for non-recoverable systems;

MTBF t Wed for recoverable systems:

Failure rate λ( t ) ;

Average recovery time τ cf ;

μ( t ) ;

Reliability function R G ( t ).

Definitions of named quantities:

R G – probability of finding the product in working condition.

P ( t ) is the probability that in a given period of time ( t ) the system will not fail.

T cf is the mathematical expectation of the system operation time until the first failure.

t Wed is the mathematical expectation of the system operation time between successive failures.

λ( t ) – mathematical expectation of the number of failures per unit of time; for a simple bounce stream:

λ( t )= 1/ t Wed .

τ cf is the mathematical expectation of the system recovery time.

μ( t ) - mathematical expectation of the number of restorations per unit of time:

μ( t ) = 1/ τ cf.

R G ( t ) – change in system reliability over time.

4. Classification of systems for the purposes of reliability calculation.

Systems for the purposes of reliability calculation are classified according to several criteria.

1. According to the features of functioning during the period of application:

Single use systems; these are systems whose reuse is impossible or impractical for some reason;

Reusable systems; these are systems whose reuse is possible and can be carried out after the system has performed the functions assigned to it for the previous application cycle.

2. By adaptability to recovery after the appearance of failures:

Recoverable, if their performance, lost in case of failure, can be restored during operation;

Non-recoverable, if their performance, lost in the event of a failure, cannot be restored.

3. On the implementation of maintenance:

Unattended - systems, the technical condition of which is not controlled during operation and no measures are taken to ensure their reliability;

Maintained - systems, the technical condition of which is monitored during operation and appropriate measures are taken to ensure their reliability.

4. By type of maintenance performed:

With periodic maintenance - systems in which measures to ensure reliability are implemented only during scheduled maintenance and preventive maintenance at predetermined intervals That ;

With a random maintenance period - systems in which measures to ensure reliability are implemented at random intervals corresponding to the appearance of failures or the achievement of the limiting state by the system;

With combined maintenance - systems in which, in the presence of scheduled maintenance and repair, maintenance elements with a random period take place.

5. Classification of systems by structure.

The reliability indicators of systems depend not only on the reliability indicators of the elements, but also on the methods of “connecting” the elements into the system. Depending on the method of "connecting" the elements into the system, block diagrams are distinguished: a. serial (main connection); b. parallel (redundant connection); in. combined (in the block diagram there is both a main and a redundant connection of elements); see fig. one.

Rice. 1. Structures of systems for the purposes of reliability calculation.

Classification of the system structure as the main or redundant one does not depend on the physical relative placement of elements in the system, it depends only on the influence of element failures on the reliability of the entire system.

The main structures of the system are characterized by the fact that the failure of one element causes the failure of the entire system.

Redundant system structures are those in which failure occurs when all or a certain number of elements that make up the system fail.

Redundant structures can be with general redundancy, redundancy by groups of elements and with element-by-element redundancy (see Fig. 2, a., b., c.).

Figure 2. System redundancy options.

The classification affiliation of the system by structure is not constant, but depends on the purpose of the calculation. The same system can be primary and redundant; for example, what "connection" do the engines of a four-engine aircraft have? The answer is twofold.

If we consider the system from the point of view of a technician servicing the aircraft, then the engines are "connected" in series, because the aircraft cannot be released for flight if at least one engine is out of order; thus, the failure of one element (engine) means the failure of the entire system.

If we consider the same system in flight, then from the point of view of pilots, it will be redundant, because. the system will fail completely if all engines fail.

6. Classification of failures and malfunctions of systems and elements.

Failures have a different nature and are classified according to several criteria. The main ones are the following:

- impact of failure on job safety : dangerous, safe;

- effect of failure on the operation of the main mechanism : leading to downtime; reducing the performance of the main mechanism; not leading to downtime of the main mechanism;

- fault recovery nature : urgent; not urgent; compatible with the operation of the main mechanism; incompatible with the operation of the main mechanism;

- outward manifestation of failure : explicit (obvious); implicit (hidden);

- failure recovery time : short-term; long;

- the nature of the failure : sudden; gradual; dependent; independent;

- reason for failure : structural; manufacturing; operational; erroneous; natural;

- failure time : during storage and transportation; during the launch period; before the first overhaul; after overhaul.

All listed types of failures are of a physical nature and are considered technical.

In addition to them, in systems consisting of autonomous elements (machines, mechanisms, devices), technological failures can occur.

Technological - these are failures associated with the performance of individual elements of auxiliary operations that require stopping the operation of the main mechanism of the system.

Technological failures occur in the following cases:

Performing operations preceding the cycle of operation of the main mechanism of the system;

Execution of operations following the cycle of the main mechanism, but not compatible with the execution of a new cycle;

The cycle of working out the main mechanism of the system is less than the cycle of working out an auxiliary element in technological process;

The technological operation performed by any element is incompatible with the operation of the main mechanism of the system;

Transition of the system to a new state;

Non-compliance of the operating conditions of the system with the conditions specified in the passport characteristics of the mechanisms of the system.

7. Basic quantitative dependencies in the calculation of systems for reliability.

7.1. Statistical analysis of the operation of elements and systems.

Qualitative and quantitative characteristics of the reliability of the system are obtained as a result of the analysis of statistical data on the operation of elements and systems.

When determining the type of distribution law of a random variable, which includes intervals of failure-free operation and recovery time, calculations are performed in the sequence:

Preparation of experimental data; this operation consists in the fact that primary sources about the operation of systems and elements are analyzed to identify clearly erroneous data; the statistical rad is represented as a variational rad, i.e. placed as the random variable increases or decreases;

Construction of a histogram of a random variable;

Approximation of experimental distribution by theoretical dependence; verification of the correctness of the approximation of the experimental distribution by the theoretical one using the fit criteria (Kolmogorov, Pearson, omega-square, etc.).

As observations made in various fields of technology show, the flow of failures and recovery is the simplest, i.e. has ordinary, stationary and no aftereffect.

The reliability of complex systems is subject, as a rule, to an exponential law, which is characterized by dependencies:

Probability of failure-free operation:

Uptime distribution function:

Density of uptime distribution:

	f(t)

These dependencies correspond to the simplest failure flow and are characterized by constants:

Failure rate λ( t ) = const ;

Recovery intensity μ( t ) = const ;

MTBF t Wed = 1/λ( t ) = const ;

Recovery time τ cf = 1/μ( t ) = const .

Parameters λ( t ), t Wed ; μ( t ) And τ cf - obtained as a result of processing a variational series by chronometric observation of the operation of elements and systems.

7.2. Calculation of the coefficient of reliability of elements.

The reliability coefficient of the element is determined according to the data of statistical processing of variation series according to the formulas:

or (1)

as well as in terms of failure and recovery rates λ( t ) And μ( t ) :

. (2)

In industrial transport systems, one should distinguish between technical and technological failures. Accordingly, the characteristics of the reliability of elements in technical and technological terms are the coefficients of technical r T i and technological rci element reliability. The reliability of the element as a whole is determined by the dependence:

r G i = r T i · rci . (3)

7.3. Calculation of the technical reliability of the system.

The reliability of the main system (a system of series-connected elements) is determined in the presence of only technical failures by the dependence:

with equally reliable elements:

where n is the number of series-connected elements in the system;

When calculating the quantitative indicators of redundant and combined structures of systems, it is necessary to know not only their reliability, but also the unreliability of the element; because reliability r i and unreliability q i element constitute the total sum of probabilities equal to one, then:

q i =(1 - r i ) . (6)

The unreliability of a redundant system (with parallel connection of elements) is defined as the probability that all elements of the system have failed, i.e.:

(7)

Reliability, respectively, is determined by the dependence:

(8)

Or, with equally reliable elements

, (9)

where m - the number of spare elements.

Degree ( m + 1) when calculating the reliability of the system, it is explained by the fact that in the system one element is mandatory, and the number of reserve elements can vary from 1 to m .

As already noted, redundancy in combined systems can be element-by-element, group of elements and element-by-element. The system reliability indicators depend on the type of redundancy in the combined system. Consider these options for different ways of developing the system.

The reliability of combined redundant systems with general redundancy (system redundancy) is determined by the dependence:

(10)

with equally reliable elements (hence, subsystems):

(11)

The reliability of combined systems with redundancy by groups of elements is determined sequentially; first, the reliability of the redundant subsystems is determined, then the reliability of the system of series-connected subsystems.

The reliability of combined systems with element-by-element (separate) redundancy is determined sequentially; first, the reliability of block elements is determined (an element reserved by one, two, etc. up to m elements), then - the reliability of the system of series-connected block-elements.

The reliability of a block element is equal to:

; (12)

R to j for element-by-element redundancy is:

; (13)

or with equally reliable elements:

(14)

Consider example calculating the reliability of a system without redundancy and with various forms of its development (redundancy).

Given a system consisting of four elements (see Fig. 1.):

	r 1 = 0,95		r 2 = 0,82		r 3 = 0,91		r 4 = 0,79

Figure 1. Block diagram of the (basic) system.

Reliability of the main system:

0.95 0.82 0.91 0.79 = 0.560.

The reliability of the combined system with total (system) redundancy will be (see Fig. 2):

r 1 = 0,95

r 2 = 0,82

r 3 = 0,91

r 4 = 0,79

r 1 = 0,95

r 2 = 0,82

r 3 = 0,91

r 4 = 0,79

Figure 2. Block diagram of a combined system with system redundancy.

1- (1- 0,560) 2 = 1 – 0,194 = 0,806.

The reliability of a combined system when redundant by groups of elements will depend on how the elements are grouped; in our example, we group the elements as follows (see Fig. 3):

r 1 = 0,95

r 2 = 0,82

r 3 = 0,91

r 4 = 0,79

r 1 = 0,95

r 2 = 0,82

r 3 = 0,91

r 4 = 0,79

Figure 3. Block diagram of a combined system when redundant by groups of elements.

Reliability of the first subgroup R o1 from the 1st and 2nd series-connected elements will be equal to:

0.95 0.82 = 0.779;

Reliability of the block element of the first subgroup:

= 1- (1- 0,779) 2 = 0,951.

Reliability of the second subgroup R oP of the 3rd and 4th series-connected elements will be equal to:

0.91 0.79 = 0.719.

Reliability of the block element of the second subgroup:

= 1 – (1 – 0,719) 2 = 0,921.

System Reliability R ks of two series-connected subsystems will be equal to:

0.951 0.921 = 0.876.

Combined System Reliability R to j with element-by-element redundancy, it is equal to the product of the reliability of block-elements, each consisting of one element of the system (see Fig. 4)

r 1 = 0,95

r 2 = 0,82

r 3 = 0,91

r 4 = 0,79

r 1 = 0,95

r 2 = 0,82

r 3 = 0,91

r 4 = 0,79

Figure 4. Block diagram of a combined system with element-by-element redundancy.

The reliability of a block element is determined by the formula:

;

For the first element: rj 1 = 1 – (1 – 0,95) 2 = 0,997;

For the second element: rj 2 = 1 – (1 – 0,82) 2 = 0,968;

For the third element: rj 3 = 1 – (1 – 0,91) 2 = 0, 992;

For the fourth element: rj 4 = 1 – (1 – 0,79) 2 = 0,956.

For a system of series-connected block elements:

0.997 0.968 0.992 0.956 = 0.915.

As the calculation example shows, the more connections between the elements of the system, the higher its reliability.

7.4. Calculation of the technical readiness of the system.

The system readiness parameters in the presence of technical and technological failures are determined by the formula:

.

where r G i – technical reliability of the element;

rci – technological reliability of the element;

r G i - generalized reliability of the element.

When reserving elements, the change in technical and technological reliability occurs in different ways: technical - according to a multiplicative scheme, technological - according to an additive scheme, while the maximum technological reliability can be equal to one.

Hence, with a double redundancy of the element, we obtain its reliability of the block element:

With an arbitrary number of reserve elements m:

where m is the number of reserve elements.

The readiness of combined systems is determined similarly to the definition of reliability in the presence of only technical failures, i.e. the readiness of block elements is determined, and according to their indicators, the readiness of the entire system.

7. Formation of the optimal structure of the system.

As the results of calculations show, with the development of the structure of the system, its reliability asymptotically approaches unity, while the cost of forming the system increases linearly. Since the operational performance of the system is the product of its reliability by the nominal (passport) performance, the outpacing increase in the costs of forming the system with a slowing growth in its reliability will lead to the fact that the costs per unit of performance will increase and further development of the system structure will become economically unfeasible. Thus, the solution of the question of the expedient reliability of the system is an optimization problem.

The objective function of system optimization has the form:

where is the total cost of the system; - achieved on the basis of these costs, the availability factor of the combined system.

EXAMPLE Initial conditions: the main view system is set (see figure):

Figure 5. Structure of the main system, reliability indicators

elements and conditional values ​​of elements.

It is required to determine the optimal multiplicity of redundancy of the third element of the system (other elements are not redundant).

Solution:

1. Determine the reliability of the main system:

0.80 0.70 0.65 0.90 = 0.328.

2. Determine the cost of the main system:

C o \u003d\u003d 20 + 30 + 12 + 50 \u003d 112 c.u.

3. We determine the unit costs for achieving this availability factor of the main system:

Ministry of Education and Science of the Russian Federation

State educational institution

higher professional education

"Omsk State Technical University"

A. V. Fedotov, N. G. Skabkin

Fundamentals of the theory of reliability and technical diagnostics

Lecture notes

Publishing house OmSTU

UDC 62-192+681.518.54

BBC 30.14 + 30.82

Reviewers: n. S. Galdin, Dr. Sci. Sciences, prof. PttMiG SibAdi; Yu. P. Kotelevsky, Ph.D. Tech. Science, Gen. Director of OOO "adl-Omsk"

Fedotov, A. V.

F34 Fundamentals of the theory of reliability and technical diagnostics: lecture notes / A. V. Fedotov, N. G. Skabkin. - Omsk: Publishing House of OmGTU, 2010. - 64 p.

The basic concepts of the theory of reliability, qualitative and quantitative characteristics of reliability are considered. The mathematical foundations of the theory of reliability, calculations of reliability indicators, basic concepts, definitions and tasks of technical diagnostics are considered.

The abstract can be used both for the practical consolidation of theoretical material in the course "Diagnostics and reliability of automated systems" for students daily form training, and in the self-training of students of correspondence and distance learning.

Published by decision of the editorial and publishing council

Omsk State Technical University

UDC 62-192+681.518.54

BBC 30.14 + 30.82

© GOU VPO "Omsk State

Technical University", 2010

1. General characteristics of reliability as a science

The emergence of technology and its widespread use in production processes has made the question of its effectiveness relevant. The efficiency of the use of machines is related to their ability to continuously and efficiently perform the functions assigned to them. However, due to breakdowns or malfunctions, the quality of the operation of machines decreases, there are forced downtime in their work, there is a need for repairs to restore the working capacity and the required technical characteristics of the machines.

These circumstances led to the emergence of the concept of reliability of machines and other technical means. The concept of reliability is associated with the ability of a technical tool to perform the functions assigned to it within the required time and with the required quality. From the first steps in the development of technology, the task was to make a technical device such that it worked reliably. With the development and complication of technology, the problem of its reliability became more complicated and developed. To solve it, it was necessary to develop the scientific foundations of a new scientific direction - the science of reliability.

Reliability characterizes the quality of the technical means. Quality is a set of properties that determine the suitability of a product for its intended use and its consumer properties. Reliability is a complex property of a technical object, which consists in its ability to perform specified functions, while maintaining its main characteristics within the established limits. The concept of reliability includes non-failure operation, durability, maintainability and safety.

The study of reliability as a qualitative indicator characterizing a technical device led to the emergence of the science "Reliability". The subject of science research is the study of the causes that cause failures of objects, the determination of the patterns that they obey, the development of methods for quantitative measurement of reliability, methods of calculation and testing, the development of ways and means to improve reliability.

Distinguish between the general theory of reliability and applied theories of reliability. The general theory of reliability has three components:

1. Mathematical theory of reliability. Defines the mathematical laws that govern failures and methods for quantitative measurement of reliability, as well as engineering calculations of reliability indicators.

2. Statistical theory of reliability. Processing of statistical information about reliability. Statistical characteristics of reliability and failure patterns.

3. Physical theory of reliability. Study of physical and chemical processes, physical causes of failures, the effect of aging and strength of materials on reliability.

Applied theories of reliability are developed in a specific field of technology in relation to the objects of this field. For example, there is a theory of reliability of control systems, a theory of reliability of electronic devices, a theory of reliability of machines, etc.

Reliability is related to the efficiency (eg cost-effectiveness) of the technique. Insufficient reliability of the technical means results in:

reduced productivity due to downtime due to breakdowns;

decrease in the quality of the results of using the technical means due to the deterioration of its technical characteristics due to malfunctions;

the cost of repairs of technical equipment;

loss of the regularity of obtaining the result (for example, a decrease in the regularity of transportation for vehicles);

decrease in the level of safety in the use of technical means.

Diagnostics is directly related to reliability. Diagnostics - the doctrine of the methods and principles of disease recognition and diagnosis. Technical diagnostics considers issues related to the assessment of the actual state of technical systems. The task of diagnostics is to identify and prevent emerging failures of technical means in order to increase their overall reliability.

The process of technical diagnostics provides for the presence of a diagnostic object, diagnostic tools and a human operator. In the process of diagnostics, measuring, control and logical operations are performed. These operations are performed by the operator using diagnostic tools in order to determine the actual state of the technical tool. The evaluation results are used to decide on the further use of the technical means.