Basic concepts and definitions of reliability theory. Basic concepts and definitions of reliability theory Basics of reliability theory

A term such as “Refusal” requires special consideration. This is a key concept in reliability theory. The transition from a serviceable state to a faulty but functional state occurs due to damage. The transition of an object to an inoperative state occurs through a failure. Failure is an event consisting in malfunction object. It was the occurrence of failures during the operation of equipment that stimulated the emergence and development of reliability theory. Therefore, failure is rightfully considered a key concept in reliability theory. And it is no coincidence that the main property that makes up reliability is failure-free operation. In practice, the main activity of people servicing equipment is to eliminate failures and restore the operational state of objects. And, of course, maintenance personnel are always interested in knowing about the forecast in terms of the occurrence of failures; it is interesting to know the expected uptime. This makes it possible to evaluate the effectiveness of technical systems in performing their inherent tasks, and to calculate the required number of spare parts to replace failed ones. Carrying out maintenance and establishing the frequency of preventative maintenance is also based on taking into account possible failures. In short, starting from such a concept as “failure,” a theory of reliability was developed.

To distinguish between failures, they are classified. There are mathematical (probabilistic) classifications of failures and engineering (physical) classifications.

For reasons of occurrence, failures can be structural, production, operational and degradation.

Constructive failure arises due to imperfection or violation of established rules and regulations of design and construction. It is obvious that the perfection of the design of technical objects largely depends on the human factor, namely, on the talent of the designers and developers. They are designed to ensure the absence of “weak links” in the design of the equipment being developed.

Manufacturing failure occurs due to imperfection or violation of the established manufacturing or repair process. A good design can be ruined by what is commonly called low “production culture.”

Operational failure occurs due to a violation of established rules and operating conditions. Any piece of equipment has a set of operational documentation developed taking into account the recommendations of reliability theory. The task of the operating personnel is to strictly follow the operating instructions. When this is not done, operational failure may occur. Often such failures occur due to failure to perform or poor quality of any maintenance measures that prevent failures.

Degradative failure is caused by the natural processes of aging, wear, corrosion and fatigue, subject to compliance with all established rules and regulations for design, manufacture and operation. Each piece of equipment has a very specific limited resource. Of course, the size of this resource depends on the perfection of the design and the “production culture,” but it is always finite. Aging is characteristic not only of living beings, but also of technical objects.

Based on the nature of their manifestation, failures can also be divided into random and systematic. Random failures can be caused by overloads, defects in materials and workmanship, personnel errors, and malfunctions. Most often they appear in unfavorable operating conditions.

Systematic failures occur for reasons that cause gradual accumulation of damage (time, temperature, radiation). Expressed as wear, aging, corrosion, sticking, leakage, etc.

Failures should not be confused with defects. A defect is each individual non-compliance of an object with the requirements established by regulatory documentation. This term applies to all types of industrial and non-industrial products.

Complete failure leads to complete loss of performance. Partial failure leads to partial loss of performance.

Mathematical classification of failures:

Gradual failures- develop over time and are associated with aging, wear, fatigue strength and other factors changing the properties of the material.

Sudden failures– the probability of their occurrence is not affected by the time of previous work.

Joint failures– failures of object elements that can simultaneously appear in the amount of two or more.

Incompatible failures– failures of which no two can occur together.

Independent failures– the probabilities of their occurrence do not depend on each other.

Dependent failures– the probability of one failure occurring is related to the probability of another.

Engineering failure classification:

1. By identifying:

– before performing functions;

– during the performance of functions.

2. According to the consequences:

- without consequences;

– leads to failure to perform functions;

– leads to accidents.

3. For reasons:

– design and production errors;

– errors of operational personnel;

– external or random reasons.

4. By method of elimination:

– restoration of operability at the site of operation;

– partial repairs in repair services;

– major repairs;

– write-off of an object.

In addition to the concept of “failure”, in applied reliability theory and in practice, other concepts related to the failure of an object can be used:

Breaking– damage to an object that can be repaired by the crew or repair services, without causing loss of life.

Incident– an event associated with a disruption in the functioning of an object due to its destruction or damage.

Accident- such damage to an object in which its restoration is impractical according to economic criteria (but does not lead to loss of life).

Catastrophe– complete destruction of an object, usually leading to the death of people.

As is known, before the emergence of the theoretical foundations of reliability, the reliability of technical objects was usually discussed in qualitative terms. It sounded something like this: “this object is reliable, but that one is unreliable.” Indeed, if an object was in a non-working state more often than in a working state, it could hardly be called reliable. But as technology developed, natural questions began to arise: what should we expect during the expected period of operation of the technology; what is the prognosis for maintaining the working condition; what resource to assign to a technical object; how many spare parts are needed for the planned period of operation; How to increase the reliability of a technical system if the element base is insufficiently reliable? These and other problems led to the development of reliability theory. And the theory of reliability of technical objects is unthinkable without quantitative characteristics and, accordingly, methods for their calculation.

The study of equipment reliability began with the consideration of non-repairable technical objects, that is, objects operating until the first failure, which under given operating conditions is also the last. When we talk about restoration, we mean restoring the working condition of a technical object. It should be noted that the property of recoverability depends not so much on the design of a technical object, but on the conditions of its operation. So, for example, a failed missile in the conditions of a ship is a non-repairable object, but in the conditions of a weapons base or in the conditions of a manufacturing plant, it is certainly a repairable object.

It is obvious that complex weapons systems are recoverable systems. The activities of personnel largely consist of maintaining their working condition. At the same time, it is clear that restoration of the functionality of complex systems is carried out, as a rule, by replacing non-repairable elementary devices. For this purpose, a set of spare parts is available at the operating sites. Therefore, knowledge of the reliability characteristics of non-repairable objects and the ability to evaluate them in practice is certainly important for personnel operating the equipment. It should be emphasized that the development of the foundations of reliability theory began with the study of the characteristics of non-recoverable elements, these “bricks” from which the “building” of any technical system is built.

4.1. Basic concepts of reliability theory

Preliminary remarks.

The list is based on GOST 27.002-89 "Reliability in technology. Basic concepts. Terms and definitions", which formulates the terms and definitions used in science and technology in the field of reliability. However, not all terms are covered by the specified GOST, therefore additional terms marked with an asterisk (*) are introduced in certain paragraphs.

Object, element, system

In reliability theory, the concepts of object, element, and system are used.

An object- a technical product for a specific purpose, considered during the periods of design, production, testing and operation.

Objects can be various systems and their elements, in particular: structures, installations, technical products, devices, machines, apparatus, instruments and their parts, assemblies and individual parts.

A system element is an object representing a separate part of the system. The very concept of an element is conditional and relative, since any element, in turn, can always be considered as a collection of other elements.

The concepts system and element are expressed through each other, since one of them should be accepted as the initial one, postulated. These concepts are relative: an object considered a system in one study can be considered an element if an object on a larger scale is being studied. In addition, the very division of the system into elements depends on the nature of the consideration (functional, structural, circuit or operational elements), on the required accuracy of the research, on the level of our ideas, on the object as a whole.

Human The operator also represents one of the links in the man-machine system.

A system is an object that is a collection of elements interconnected by certain relationships and interacting in such a way as to ensure that the system performs some fairly complex function.

A sign of systematicity is the structure of the system, the interconnectedness of its constituent parts, the subordination of the organization of the entire system to a specific goal. Systems operate in space and time.

Object state

Serviceability- the state of the object in which it meets all the requirements established by the normative and technical documentation (NTD).

Malfunction- the state of the object in which it does not meet at least one of the requirements established by the normative and technical documentation.

Performance- the state of an object in which it is capable of performing specified functions, maintaining the values ​​of the main parameters within the limits established by the normative and technical documentation.

The main parameters characterize the functioning of the facility when performing assigned tasks and are established in the regulatory and technical documentation.

Inoperability- the state of an object in which the value of at least one specified parameter characterizing the ability to perform specified functions does not meet the requirements established by the normative and technical documentation.

The concept of serviceability is broader than the concept of performance. An operational object, in contrast to a serviceable one, satisfies only those requirements of the technical and technical documentation that ensure its normal functioning in performing the assigned tasks.

In general, operability and inoperability can be complete or partial. A fully operational object ensures, under certain conditions, the maximum efficiency of its use. The efficiency of using a partially operational object under the same conditions is less than the maximum possible, but the values ​​of its indicators are still within the limits established for such functioning, which is considered normal. A partially inoperative object may function, but the level of efficiency is below the acceptable level. A completely inoperative object cannot be used for its intended purpose.

The concepts of partial operability and partial inoperability are applied mainly to complex systems, which are characterized by the possibility of being in several states. These states differ in the levels of efficiency of the system. The operability and inoperability of some objects may be complete, i.e. they can only have two states.

An efficient object, in contrast to a serviceable one, must satisfy only those requirements of the technical documentation, the fulfillment of which ensures the normal use of the object for its intended purpose. However, it may not satisfy, for example, aesthetic requirements if the deterioration in the appearance of the object does not interfere with its normal (effective) functioning.

It is obvious that an operational object may be faulty, but deviations from the requirements of the technical and technical documentation are not so significant that normal functioning is disrupted.

Limit state - the state of an object in which its further use for its intended purpose must be terminated due to an irreparable violation of safety requirements or an irreparable deviation of the specified parameters beyond the established limits, an unacceptable increase in operating costs or the need for major repairs.

Signs (criteria) of a limit state are established by the normative and technical documentation for a given object.

A non-restorable object reaches a limit state when a failure occurs or when a pre-established maximum permissible value of service life or total operating time is reached, established for reasons of operational safety in connection with an irreversible decrease in efficiency of use below the permissible level or in connection with an increase in the failure rate, which is natural for objects of this type after specified period of operation.

For restored objects, the transition to a limit state is determined by the arrival of a moment when further operation is impossible or impractical due to the following reasons:

It becomes impossible to maintain its safety, reliability or effectiveness at the minimum acceptable level;

As a result of wear and (or) aging, the object has reached a state in which repairs require unacceptably high costs or do not provide the necessary degree of restoration of serviceability or resource.

For some objects being restored, the limiting state is considered to be one when the necessary restoration of serviceability can only be achieved through a major overhaul.

Regime controllability* is the property of an object to maintain a normal mode through control in order to maintain or restore the normal mode of its operation.

Transition of an object to different states

Damage- an event consisting in a violation of the serviceability of an object while maintaining its operability.

Refusal- an event consisting in a malfunction of an object.

Failure criterion is a distinctive feature or set of features according to which the fact of failure is established.

Signs (criteria) of failures are established by the normative and technical documentation for a given object.

Restoration is the process of detecting and eliminating failure (damage) in order to restore its functionality (serviceability).

Recoverable object- an object whose performance in the event of a failure is subject to restoration under the conditions under consideration.

Non-recoverable object- an object whose performance in the event of a failure cannot be restored under the conditions under consideration.

When analyzing reliability, especially when choosing indicators of the reliability of an object, the decision that must be made in the event of an object failure is of significant importance. If, in the situation under consideration, restoring the operability of a given object in the event of its failure for some reason is considered impractical or impracticable (for example, due to the impossibility of interrupting the function being performed), then such an object in this situation is unrecoverable. Thus, the same object, depending on the characteristics or stages of operation, can be considered recoverable or non-recoverable. For example, the equipment of a weather satellite during the storage stage is classified as recoverable, but during flight in space it is non-recoverable. Moreover, even the same object can be classified as one or another type depending on its purpose: a computer used for non-operational calculations is a recoverable object, since in the event of a failure any operation can be repeated, and the same computer that controls a complex technological process in chemistry, is a non-recoverable object, since failure or malfunction leads to irreparable consequences.

Accident* is an event consisting in the transition of an object from one level of performance or relative level of functioning to another, significantly lower, with a major disruption of the operating mode of the object. An accident can lead to partial or complete destruction of an object, creating dangerous conditions for people and the environment.

Temporal characteristics of an object

Operating time- duration or volume of work of the object. The object can operate continuously or intermittently. In the second case, the total operating time is taken into account. Operating time can be measured in time units, cycles, output units, and other units. During operation, a distinction is made between daily, monthly operating time, operating time until the first failure, operating time between failures, specified operating time, etc.

If the object is operated in different load modes, then, for example, the operating time in the light mode can be separated and taken into account separately from the operating time at rated load.

Technical resource- operating time of an object from the beginning of its operation until reaching the limit state.

It is usually indicated which technical resource is meant: up to medium, capital, from capital to the nearest medium, etc. If specific instructions are not contained, then the resource is meant from the start of operation until the limit state is reached after all (medium and major) repairs, i.e. until written off due to technical condition.

Life time- calendar duration of operation of the facility from its beginning or resumption after major or medium repairs until the onset of the limit state.

The operation of an object is understood as the stage of its existence at the disposal of the consumer, subject to the use of the object for its intended purpose, which may alternate with storage, transportation, maintenance and repair, if this is carried out by the consumer.

Shelf life- calendar duration of storage and (or) transportation of an object under specified conditions, during and after which the values ​​of established indicators (including reliability indicators) are maintained within specified limits.

Definition of reliability

The operation of any technical system can be characterized by its efficiency (Fig. 4.1.1), which is understood as a set of properties that determine the system’s ability to perform certain tasks during its creation.

Rice. 4.1.1. Basic properties of technical systems

In accordance with GOST 27.002-89, reliability is understood as the property of an object to maintain over time, within established limits, the values ​​of all parameters that characterize the ability to perform the required functions in given modes and conditions of use, maintenance, repairs, storage and transportation.

Thus:

1. Reliability- the property of an object to maintain over time the ability to perform required functions. For example: for an electric motor - to provide the required torque on the shaft and speed; for the power supply system - to provide power receivers with energy of the required quality.

2. The required functions must be performed with parameter values ​​within the established limits. For example: for an electric motor - to provide the required torque and speed when the engine temperature does not exceed a certain limit, the absence of a source of explosion, fire, etc.

3. The ability to perform the required functions must be maintained in specified modes (for example, in intermittent operation); under specified conditions (for example, dust, vibration, etc.).

4. The object must have the property of maintaining the ability to perform the required functions in various phases of its life: during operational operation, maintenance, repair, storage and transportation.

Reliability- an important indicator of the quality of an object. It cannot be contrasted or confused with other quality indicators. For example, information about the quality of a purification plant will be clearly insufficient if it is only known that it has a certain productivity and a certain purification coefficient, but it is unknown how consistently these characteristics are maintained during its operation. It is also useless to know that the installation stably retains its inherent characteristics, but the values ​​of these characteristics are unknown. That is why the definition of reliability includes the performance of specified functions and the preservation of this property when the object is used for its intended purpose.

Depending on the purpose of the object, it may include reliability, durability, maintainability, and storage in various combinations. For example, for a non-recoverable object not intended for storage, reliability is determined by its failure-free operation when used for its intended purpose. Information about the failure-free operation of a restored product that has been in storage and transportation for a long time does not fully determine its reliability (it is necessary to know about both maintainability and storability). In a number of cases, the ability of a product to maintain operability until the onset of a limiting state (decommissioning, transfer for medium or major repairs) becomes very important, i.e. information is needed not only about the reliability of the object, but also about its durability.

A technical characteristic that quantifies one or more properties that make up the reliability of an object is called a reliability indicator. It quantitatively characterizes the extent to which a given object or a given group of objects has certain properties that determine reliability. The reliability indicator may have a dimension (for example, mean time to recovery) or not have it (for example, the probability of failure-free operation).

Reliability in the general case is a complex property that includes such concepts as reliability, durability, maintainability, and storability. For specific objects and their operating conditions, these properties may have different relative importance.

Reliability is the property of an object to continuously remain operational for some operating time or for some time.

Maintainability is the property of an object to be adapted to prevent and detect failures and damage, to restore operability and serviceability during the process of maintenance and repair.

Durability is the property of an object to remain operational until a limit state occurs with the necessary interruption for maintenance and repairs.

Storability is the property of an object to continuously maintain a serviceable and operational state during (and after) storage and (or) transportation.

For reliability indicators, two forms of representation are used: probabilistic and statistical. The probabilistic form is usually more convenient for a priori analytical calculations of reliability, while the statistical form is more convenient for experimental studies of the reliability of technical systems. In addition, it turns out that some indicators are better interpreted in probabilistic terms, while others are better interpreted in statistical terms.

Reliability and maintainability indicators

Run-to-failure- the probability that, within a given operating time, an object failure will not occur (provided it is operational at the initial point in time).

For storage and transportation modes, the similarly defined term “probability of failure occurrence” can be used.

Mean time to failure is the mathematical expectation of the random operating time of an object before the first failure.

Average time between failures is the mathematical expectation of the random operating time of an object between failures.

Typically this indicator refers to a steady-state operating process. In principle, the average time between failures of objects consisting of elements that age over time depends on the number of the previous failure. However, as the failure number increases (i.e., with an increase in the duration of operation), this value tends to some constant, or, as they say, to its stationary value.

Mean time between failures is the ratio of the operating time of a restored object over a certain period of time to the mathematical expectation of the number of failures during this operating time.

This term can be briefly called the average time to failure and the average time between failures when both indicators coincide. For the latter to coincide, it is necessary that after each failure the object is restored to its original state.

Specified operating time- operating time during which an object must operate without failure to perform its functions.

Average downtime- mathematical expectation of the random time of forced unregulated stay of an object in a state of inoperability.

Average recovery time- mathematical expectation of the random duration of restoration of operability (repair itself).

Recovery probability is the probability that the actual duration of restoration of the object’s operability will not exceed the specified one.

Indicator of technical efficiency of operation- a measure of the quality of the actual functioning of an object or the feasibility of using an object to perform specified functions.

This indicator is quantified as the mathematical expectation of the output effect of an object, i.e. depending on the purpose of the system, it takes on a specific expression. Often the performance indicator is defined as the total probability of an object completing a task, taking into account a possible decrease in the quality of its work due to the occurrence of partial failures.

Efficiency retention rate- an indicator characterizing the influence of the degree of reliability on the maximum possible value of this indicator (i.e., the corresponding state of full operability of all elements of the object).

Non-stationary availability factor- the probability that an object will be operational at a given point in time, counted from the start of work (or from another strictly defined point in time), for which the initial state of this object is known.

Average availability factor- the value of the non-stationary availability factor averaged over a given time interval.

Stationary availability factor(availability factor) - the probability that the restored object will be operational at an arbitrarily selected point in time in the steady process of operation. (The availability factor can also be defined as the ratio of the time during which the object is in working condition to the total duration of the period under consideration. It is assumed that a steady-state operation process is being considered, the mathematical model of which is a stationary random process. The availability factor is the limiting value to which Both non-stationary and average availability factors tend to increase as the time interval under consideration increases.

Indicators that characterize a simple object are often used - the so-called downtime coefficients of the corresponding type. Each availability factor can be associated with a certain downtime factor, numerically equal to the addition of the corresponding availability factor to one. In the relevant definitions, performance should be replaced by inoperability.

Non-stationary operational readiness coefficient is the probability that an object, being in standby mode, will be operational at a given point in time, counted from the start of work (or from another strictly defined time), and from this point in time will work without failure for a given time.

Average operational readiness ratio- the value of the non-stationary operational readiness coefficient averaged over a given interval.

Stationary operational readiness ratio(operational readiness coefficient) - the probability that a restored element will be operational at an arbitrary point in time, and from this point in time will work without failure for a given time interval. It is assumed that a steady-state operation process is being considered, to which a stationary random process corresponds as a mathematical model.

Technical utilization rate- the ratio of the average operating time of an object in units of time for a certain period of operation to the sum of the average values ​​of operating time, downtime due to maintenance, and repair time for the same period of operation.

Failure Rate- conditional probability density of failure of a non-repairable object, determined for the considered moment in time, provided that the failure did not occur before this moment. The failure flow parameter is the probability density of the occurrence of a failure of a restored object, determined for the considered point in time. The failure flow parameter can be defined as the ratio of the number of failures of an object over a certain time interval to the duration of this interval with an ordinary failure flow.

Recovery intensity- conditional probability density of restoration of the object’s operability, determined for the considered moment in time, provided that the restoration was not completed until this moment.

Indicators of durability and storage

Gamma percentage resource- operating time during which the object does not reach the limit state with a given probability of 1-?.

Average resource- mathematical expectation of the resource.

Assigned resource- the total operating time of an object, upon reaching which operation must be stopped, regardless of its condition.

Average repair life- average resource between adjacent major repairs of the facility.

Average life before write-off- the average resource of an object from the start of operation until its decommissioning.

Average resource before major overhaul is the average resource from the start of operation of the facility until its first major overhaul.

Gamma percentage life- service life during which the object does not reach the limit state with probability 1-?.

Average service life- mathematical expectation of service life.

Average service life between overhauls- average service life between adjacent major repairs of the facility.

Average service life before major overhaul- average service life from the start of operation of the facility until its first major overhaul.

Average service life before decommissioning- average service life from the start of operation of the object until its decommissioning.

Gamma percentage shelf life- the duration of storage during which the object retains the established indicators with a given probability of 1-?.

Average shelf life- mathematical expectation of shelf life.

Types of reliability

The multi-purpose purpose of equipment and systems leads to the need to study certain aspects of reliability, taking into account the reasons that form the reliability properties of objects. This leads to the need to divide reliability into types.

There are:

Hardware reliability due to the condition of the devices; in turn, it can be divided into structural, circuit, production and technological reliability;

Functional reliability associated with the performance of a certain function (or set of functions) assigned to an object or system;

Operational reliability due to the quality of use and maintenance;

Software reliability due to the quality of software (programs, action algorithms, instructions, etc.);

The reliability of the “man-machine” system, depending on the quality of service of the object by the human operator.

Failure Characteristics

One of the basic concepts of reliability theory is the concept of failure (object, element, system). Failure of an object is an event in which an object completely or partially ceases to perform specified functions. With a complete loss of performance, a complete failure occurs, with a partial failure, a partial failure occurs. The concepts of complete and partial failures must be clearly formulated each time before reliability analysis, since the quantitative assessment of reliability depends on this.

According to the reasons for the occurrence of failures in a given location, they are distinguished:

failures due to design defects;

failures due to technological defects;

failures due to operational defects;

failures due to gradual aging (wear).

Failures due to design defects arise as a consequence of design imperfections due to “misses” during design. In this case, the most common are underestimation of “peak” loads, the use of materials with low consumer properties, circuit “misses”, etc. Failures of this group affect all copies of the product, object, system.

Failures due to technological defects arise as a consequence of a violation of the accepted technology for manufacturing products (for example, the departure of individual characteristics beyond the established limits). Failures in this group are typical for individual batches of products, during the manufacture of which violations of the manufacturing technology were observed.

Failures due to operational defects arise due to the non-compliance of the required operating conditions and maintenance rules with the actual ones. Failures in this group are typical for individual product units.

Failures due to gradual aging (wear) due to the accumulation of irreversible changes in materials leading to disruption of strength (mechanical, electrical) and interaction of parts of the object.

Failures based on causal patterns of occurrence are divided into the following groups:

failures with an instantaneous pattern of occurrence;

failures with a gradual pattern of occurrence;

failures with a relaxation pattern of occurrence;

failures with combined occurrence patterns.

Failures with an instantaneous occurrence pattern are characterized by the fact that the time of failure does not depend on the time of previous operation and the state of the object; the moment of failure occurs randomly, suddenly. Examples of the implementation of such a scheme can be product failures under the influence of peak loads in the electrical network, mechanical destruction by extraneous external influences, etc.

Failures with a gradual pattern of occurrence occur due to the gradual accumulation of damage due to physicochemical changes in materials. In this case, the values ​​of some “decisive” parameters go beyond the permissible limits and the object (system) is not capable of performing the specified functions. Examples of the implementation of a gradual scheme of occurrence can be failures due to a decrease in insulation resistance, electrical erosion of contacts, etc.

Failures with a relaxation pattern of occurrence are characterized by an initial gradual accumulation of damage, which creates conditions for an abrupt (sharp) change in the state of the object, after which a failure state occurs. Examples of the implementation of a relaxation scheme for the occurrence of failures can be a breakdown of cable insulation due to corrosion destruction of armor.

Failures with combined occurrence patterns are typical for situations where several causal patterns operate simultaneously. An example that implements this scheme is a motor failure as a result of a short circuit due to a decrease in the insulation resistance of the windings and overheating.

When analyzing reliability, it is necessary to identify the predominant causes of failures and only then, if necessary, take into account the influence of other causes.

Based on the time aspect and degree of predictability, failures are divided into sudden and gradual.

Based on the nature of elimination over time, a distinction is made between stable (final) and self-eliminating (short-term) failures. A short-term failure is called a crash. A characteristic sign of a failure is that restoring operability after its occurrence does not require hardware repair. An example would be short-term interference when receiving a signal, program defects, etc.

For the purposes of reliability analysis and research, causal failure patterns can be represented in the form of statistical models, which, due to the probabilistic occurrence of damage, are described by probabilistic laws.

Types of failures and causal relationships

Failures of system elements are the main subjects of study when analyzing causal relationships.

As shown in the inner ring (Fig. 4.1.2), located around the “element failure”, failures can occur as a result of:

1) primary failures;

2) secondary failures;

3) erroneous commands (initiated failures).

Failures in all of these categories can have various causes given in the outer ring. When the exact failure mode is determined and data obtained, and the final event is critical, then they are considered as initial failures.

Primary failure of an element is defined as the non-operational condition of that element, which is caused by itself, and repair work must be performed to return the element to an operational state. Primary failures occur under input influences whose value is within the design range, and failures are explained by the natural aging of elements. The rupture of a tank due to aging (fatigue) of the material is an example of primary failure.

Secondary failure is the same as primary failure, except that the element itself is not the cause of the failure. Secondary failures are explained by the effects of previous or current excess stress on the elements. The amplitude, frequency, and duration of these voltages may be outside the tolerance limits or have reverse polarity and are caused by various energy sources: thermal, mechanical, electrical, chemical, magnetic, radioactive, etc. These stresses are caused by neighboring elements or the environment, for example, meteorological (rainfall, wind load), geological conditions (landslides, soil subsidence), as well as impacts from other technical systems.

Rice. 4.1.2. Element failure characteristics

Examples of secondary failures are “triggering of a fuse against increased electric current”, “damage to storage containers during an earthquake”. It should be noted that eliminating sources of increased voltage does not guarantee the return of the element to working condition, since a previous overload could cause irreversible damage to the element, requiring repair in this case.

Triggered failures (incorrect commands). People, such as operators and maintenance personnel, are also possible sources of secondary failure if their actions cause components to fail. Erroneous commands are represented by an element being inoperative due to an incorrect control signal or interference (with only occasional repairs required to return the element to an operational state). Spontaneous control signals or interference often leave no consequences (damage), and in normal subsequent modes the elements operate in accordance with the specified requirements. Typical examples of erroneous commands are: “voltage was spontaneously applied to the relay winding”, “the switch accidentally did not open due to interference”, “interference at the input of the control device in the security system caused a false stop signal”, “the operator did not press the emergency button” (incorrect command from the emergency button).

Multiple failure (general failure) is an event in which several elements fail for the same reason. Such reasons may include the following:

Equipment design defects (defects not identified at the design stage and leading to failures due to mutual dependence between electrical and mechanical subsystems or elements of a redundant system);

Operation and maintenance errors (improper adjustment or calibration, operator negligence, improper handling, etc.);

Exposure to the environment (moisture, dust, dirt, temperature, vibration, as well as extreme conditions of normal operation);

External catastrophic impacts (natural external phenomena such as flood, earthquake, fire, hurricane);

Common manufacturer (reserved equipment or components supplied by the same manufacturer may have common design or manufacturing defects. For example, manufacturing defects may be caused by incorrect material selection, errors in installation systems, poor soldering, etc.);

Common external power supply (common power supply for main and backup equipment, redundant subsystems and elements);

Incorrect operation (incorrectly selected set of measuring instruments or poorly planned protective measures).

There are a number of examples of multiple failures: for example, some parallel-connected spring relays failed simultaneously and their failures were caused by a common cause; due to improper disengagement of the couplings during maintenance, two valves were installed in the wrong position; Due to the destruction of the steam pipeline, several failures of the switchboard occurred at once. In some cases, a common cause does not cause a complete failure of a redundant system (simultaneous failure of several nodes, i.e., an extreme case), but a less serious general decrease in reliability, which leads to an increase in the likelihood of a joint failure of system nodes. This phenomenon is observed in the case of extremely unfavorable environmental conditions, when deterioration in performance leads to failure of the backup node. The presence of general unfavorable external conditions leads to the fact that the failure of the second node depends on the failure of the first and is coupled with it.

For each common cause, it is necessary to determine all the initiating events it causes. At the same time, the scope of each common cause is determined, as well as the location of the elements and the time of the incident. Some general causes have only a limited scope. For example, a liquid leak may be limited to one room, and electrical installations and components in other rooms will not be damaged due to leaks, unless these rooms communicate with each other.

A failure is considered more critical than another if it is preferable to be considered first when developing reliability and safety issues. When comparatively assessing the criticality of failures, the consequences of failure, the probability of occurrence, the possibility of detection, localization, etc. are taken into account.

The above properties of technical objects and industrial safety are interconnected. Thus, if the reliability of an object is unsatisfactory, one can hardly expect good indicators for its safety. At the same time, the listed properties have their own independent functions. If the reliability analysis examines the ability of an object to perform specified functions (under certain operating conditions) within established limits, then when assessing industrial safety, the cause-and-effect relationships of the occurrence and development of accidents and other violations are identified with a comprehensive analysis of the consequences of these violations.

Reliability- the property of an object to maintain over time, within established limits, the values ​​of all parameters characterizing the ability to perform the required functions in given modes and conditions of use, maintenance, storage and transportation. Hereinafter, an object is understood (unless specifically stated) as an object of a specific purpose, considered during the periods of design, production, operation, research and reliability testing. Objects can be products, systems and their elements, in particular, structures, installations, devices, machines, apparatus, devices and their parts, assemblies and individual parts.

Reliability is a complex property, which, depending on the purpose of the object and the conditions of its use, may include reliability, durability, maintainability, storability, or certain combinations of these properties. In technical diagnostics, of the listed reliability components, two properties, as a rule, come to the fore - failure-free operation and maintainability of the object.

Reliability- the property of an object to continuously maintain operability for some time or operating time.

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

To determine reliability and its components, you need to know technical condition an object is a state that is characterized at a certain point in time, under certain environmental conditions, by the values ​​of the parameters established by the technical documentation for the object. Factors under the influence of which the technical condition of an object changes include the following:

· influence of climatic conditions;

· aging of object materials over time;

· adjustment and adjustment operations during manufacturing or repair;

· replacement of failed elements, nodes or blocks of an object.

Changes in the technical condition of an object are judged by the values ​​of diagnostic (monitored) parameters that make it possible to determine this state of the object without disassembling it. Reliability theory considers the following types of technical condition: serviceable, faulty, operable, inoperative and limiting.

Working condition(serviceability) - the state of an object in which it meets all the requirements of technical documentation.

Faulty condition(malfunction) - a condition of an object in which it does not meet at least one of the requirements of the technical documentation (examples: damage to the paintwork, parameter values ​​exceeding the tolerance limits, violation of signs of normal functioning of the object, etc.).

Operating state(operability) - the state of an object in which the values ​​of all parameters characterizing the ability to perform specified functions comply with the requirements of technical documentation. The operating state is characterized by a set of certain signs, such as finding the values ​​of the specified parameters of the object within the tolerances established for these parameters, a number of qualitative signs that determine its normal functioning. Unlike a serviceable object, a functional object must satisfy only those requirements of technical documentation, the fulfillment of which ensures its normal use for its intended purpose. A serviceable object may be faulty - for example, not satisfy aesthetic requirements, if the deterioration in the appearance of the object does not prevent its intended use.

Inoperative state(inoperability) - a state of an object in which the value of at least one parameter characterizing the ability to perform specified functions does not meet the requirements of technical documentation.

Limit state- the state of the object in which its further operation is unacceptable or impractical, or restoring its working condition is impossible or impractical.

The transition of an object from one state to another occurs due to the occurrence of defects in it. Defect- this is each individual non-compliance of an object with established requirements. Depending on the consequences, defects are divided into damage and failures.

Damage- an event consisting in a violation of the serviceable state of an object while maintaining the serviceable state. Damage includes deviations in the appearance of the object from the requirements of technical documentation, violations in the switching, setting and adjustment organs, as well as some mechanical damage that does not prevent the object from being used for its intended purpose, but creates inconvenience for operating personnel and leads to future failure of the object.

Damage is, for example, a violation of the paint coating, causing an object to transition from a serviceable state to a faulty state while maintaining its functionality.

Refusal- an event consisting in a violation of the operational state of an object. Signs of a failure are unacceptable changes in the signs of the operational state of the object (parameter values ​​exceeding the tolerance limits, violation of the signs of normal functioning). For a non-repairable object, the occurrence of a failure ultimately leads to its transition to a limit state and decommissioning. For an object being repaired, the consequences of a failure are eliminated by restoration and repair.

By type, failures are divided into:

· failures functioning, in which the object’s performance of basic functions ceases;

· failures parametric, in which the parameters of the object change within unacceptable limits (for example, loss of accuracy in measuring voltage with a voltmeter).

By their nature, failures can be:

· random caused by unforeseen overloads, material defects, personnel errors, control system failures, etc.;

· systematic, caused by natural phenomena that cause gradual accumulation of damage: fatigue, aging, etc.

The main features of failure classification are:

· nature of occurrence;

· cause of occurrence; consequences of failures;

· further use of the object;

· ease of detection;

· time of occurrence.

By nature of occurrence failures can be sudden, gradual and intermittent. Sudden failure is a failure manifested in a sharp (instant) change in the characteristics of an object. Gradual failure - a failure that occurs as a result of a slow, gradual deterioration of the characteristics of an object due to wear and aging of materials. Sudden failures usually manifest themselves in the form of mechanical damage to elements (breakdowns, insulation breakdowns, breaks, etc.) and are not accompanied by preliminary visible signs of their approach. Sudden failure is characterized by the independence of the moment of occurrence from the time of previous operation. Intermittent called a self-correcting failure (appearing/disappearing, for example, computer failure).

By cause of occurrence failures can be structural, production and operational. Structural failure occurs as a result of deficiencies and poor design of the object. Industrial failure is associated with errors in the manufacture of an object due to imperfection or violation of technology. Operational the failure is caused by a violation of the rules of operation of the facility.

Based on further use of the object failures can be complete or partial. Full failure excludes the possibility of the object operating until it is eliminated. Whenever partial failure object can be partially used.

Based on ease of detection failures can be obvious (explicit) and hidden (implicit).

By time of occurrence failures are divided into running-in failures that occur during the initial period of operation during normal use, wear failures caused by irreversible processes of wear of parts, aging of materials, etc.

Shutdown- transferring an object from a working state to a non-working state.

Intentional shutdown- shutdown planned and carried out by maintenance personnel.

Recovery- an event consisting of a transition from an inoperative state to an operational one.

Inclusion- transferring an object from an inoperative state to an operational one.

Aging- a process of gradual change in the physical and chemical properties of an object, caused by the action of factors independent of the operating mode of the object.

Wear- the process of gradual change in the physical and chemical properties of an object, caused by the action of factors depending on the operating mode of the object.

Service- a set of measures taken to preserve or restore the serviceability of an object.

Repair- a set of measures taken to restore the functionality of an object.

Operational shutdowns- changes in the scheme or mode of operation of the facility performed by maintenance personnel.

The diagram of the transition of an object from one state to another is shown in Fig. 2.1.

A number of important properties of an object are characterized by output parameters called threshold parameters (for example, the maximum load at which the product remains operational, the maximum permissible temperature, the minimum discernible signal amplitude, etc.). Under threshold output refers to the boundary values ​​of external parameters at which one or another specified sign of the correct functioning of the object is still fulfilled.

Requirements for output parameters, as a rule, are specified in the technical specifications (TOR). The quantities characterizing these requirements are called technical requirements (TT). They are satisfied by changing the controlled parameters X.

During the design process, only those values ​​of the controlled parameters are of interest X, which belong to the set D, formed by the intersection of sets Dx And D g :

Expressions (2.1)…(2.2) mean that the set D consists of all those vectors x = (x 1 , x 2 ,…, x n), for which systems of inequalities are simultaneously satisfied

A bunch of D called permissible range of change controlled parameters X. Any vector X, belonging to the valid region D, defines efficient(in the sense of meeting technical requirements) a variant of the designed device. In other words, the relationship between output parameters and technical requirements is called operating conditions.

By its structure, the permissible area D may turn out to be a convex or non-convex set, which, in turn, can be a simply connected or multiply connected region.

Valid area D is called multiply connected if it consists of several separate parts (convex or non-convex) that are not interconnected. Otherwise valid area D is called simply connected. In Fig. 2.2 shows examples of simply connected D and multiply connected D 1 and D 2 areas.

For a simply connected region:

For a multiply connected region consisting of two parts D 1 And D 2

Example 2.1. Technical specifications for the development of a circuit diagram of an electronic amplifier. Gain K 0 at medium frequencies must be at least 10 4 ; input impedance R input at medium frequencies - not less than 1 MOhm; output impedance R out - no more than 200 Ohm; upper limit frequency f at least 100 kHz; zero temperature drift U dr - no more than 50 µV/deg; the amplifier must function normally in the temperature range from -50 o to +60 o C; power supply voltages +5 and -5 V; maximum voltage deviations of power supplies must be no more than ±0.5%; the amplifier is operated in a stationary installation.

In this case, the output parameters are gain, input and output resistance, cutoff frequency, temperature drift, i.e. Y= .

External parameters include ambient temperature and power supply voltages.

Internal parameters are not mentioned in the technical specifications; their list and meaning are revealed after synthesizing the circuit structure. Internal parameters include the parameters of resistors, capacitors, transistors (parameters of circuit elements).

Let us denote the vector of technical requirements by TT, i.e. CT = (10 4, 1 MOhm, 200 Ohm, 100 kHz, 50 µV/deg).

In the example considered, the performance conditions take the form of the following inequalities: K 0 ≥ 10 4 , R input ≥ 1 MOhm, R out ≤ 0.2 kOhm, f at ≥ 100 kHz, U dr ≤ 50 µV/deg.

Reliability is the property of products to perform specified functions, maintain their performance characteristics within specified limits under given modes and operating conditions for the required period of time or required operating time.

From this definition it follows that reliability is an internal property of a product, an objective reality inherent in each given product sample. Thus, not only a system in which mechanical or electrical damage occurs, leading to the inoperability of the devices, is considered unreliable, but also one in which the parameters exceed the maximum permissible values.

The task of reliability theory includes solving two fundamental problems: assessing the reliability of manufactured products and assessing the reliability of products at the stage of their design.

The reliability of manufactured products is assessed as a result of their testing, i.e. for a given number of tests and the time interval during which they were carried out, the reliability of the product is determined. And assessing the reliability of a semiconductor device at the stage of its production requires a priori knowledge of the most likely types of failures and the physical processes underlying them.

The mathematical models used to quantify reliability depend on the type of reliability. Modern theory identifies three

reliability type:

1. “Instantaneous” reliability, for example the reliability of fusible

fuses.

2. Reliability with normal operational durability, for example, the reliability of computer technology. When assessing normal operational reliability, one of the main quantitative indicators is the average operating time between failures. The range recommended in practice is from 100 to 2000 hours.

3. Extremely long-term operational reliability, such as the reliability of spacecraft. If the service life requirements for devices are over 10 years, then they are classified as devices with extremely long-term operational reliability.

To characterize a specific device, use the concepts in good and working condition.

Serviceability - This is the state of the device in which it meets all the requirements of regulatory and design documentation.

Performance - This is the state of the device in which it is capable of performing specified functions with the parameters established by the regulatory, technical or design documentation.

For a more complete description of reliability, a concept such as durability.

Durability - this is the property of products to maintain their functionality (with possible breaks for maintenance or repair) until the limit state specified in the technical documentation (breakdown, reduction in power, etc.) occurs. This property covers the resource characteristics of the device and significantly complements the concept of failure-free operation.

Reliability - This is the property of a device to continuously maintain an operational state for some time or some operating time. In relation to semiconductor devices and microcircuits, reliability is understood as their ability to continuously maintain the original values ​​of parameters when used in rectifying, amplifying, switching and other modes determined by circuits and operating conditions.

Storability - This is the property of a device to maintain the values ​​of reliability and durability indicators during and after storage or transportation.

The characteristics of the device associated with its operation are operating time, representing the duration or volume of operation of the product. Operating time is measured in hours or cycles of continuous or total periodic operation of the device in electrical mode. The operating time of the device, measured in hours from the start of operation until the onset of the limit state specified in the technical documentation, is called technical resource.

Life time - this is the calendar duration of operation of the product from the start of operation until the onset of the limit state specified in the technical documentation.

Maintainability - this is a property of a product, expressed in its adaptability to maintenance and repair, i.e. to the prevention, detection and elimination of malfunctions and failures.

A fundamental concept in reliability theory is the definition refusal as an event consisting in the complete or partial loss of a product’s performance, i.e. in malfunction of the product.

Failure can occur not only due to mechanical or electrical damage to the product elements (break, short circuit), but also due to a violation of the adjustment, due to the parameters of the elements going beyond the maximum permissible values, etc. In addition, system failures may be caused by the design of parts, their manufacture or operation.

In reliability theory, there is a broad classification of failures according to various criteria.

Failure classification

1. Based on the nature of the onset, failures are divided into sudden and gradual.

Sudden(catastrophic) is a failure that occurs as a result of abrupt changes in one or more basic parameters of the system associated with internal defects of elements, violation of operating conditions, errors of maintenance personnel and other adverse effects.

Gradual(parametric) is a failure that occurs as a result of smooth changes in the specified parameters of the device, firstly, due to degradation of the physical and chemical properties of the material under the influence of operational factors and natural aging and, secondly, due to wear of system elements as a result of drift of operating parameters and their exceeding the maximum permissible values.

2. Based on the relationship between themselves, independent and dependent failures are distinguished.

Independent are called failures, the occurrence of which does not change the probability of the occurrence of other failures, for example, failures of devices that arise as a result of processes occurring in their internal structure.

Dependent are called failures, the occurrence of which changes (increases) the probability of the occurrence of other failures. For example, failure of overload protection circuit fuses and passive limiting elements leads to damage to devices.

3. Based on the signs of manifestation, obvious and hidden failures are distinguished. Explicit detected upon external inspection or switching on

equipment.

Hidden failures are detected by using special instrumentation.

4. Based on the degree of impact on the performance of the equipment, a distinction is made between complete and partial failures.

Full refers to such a failure, until the elimination of which the use of the equipment for its intended purpose is impossible.

Partial called a failure, until which is eliminated it is possible to at least partially use the equipment for its intended purpose.

5. Based on their lifetime, the following failures are distinguished: stable, failures, intermittent.

Sustainable called a failure that can only be eliminated as a result of repair or adjustment of the equipment.

Failure called a one-time self-correcting failure, the duration of which is short compared to the duration of operation of the equipment until the next failure.

Intermittent A failure is a series of fast-acting failures that occur one after another. For example, malfunctions in devices may occur due to the presence of conductive particles in the volume of a sealed housing that can create short-term short circuits between internal terminals or individual conductive paths.

When establishing the stage of the device life cycle at which the root cause of failures arose, we distinguish structural, production and operational refusals.

Constructive failures occur as a result of errors and violations of design rules and regulations during the development period.

Under production Failures mean failures that arise as a result of imperfections in the manufacturing process of devices or violations of technology.

If the capabilities of instruments are incorrectly assessed when choosing them for creating equipment, problems arise. operational refusals. As a result, devices may be subject to hardware overloads and premature failure.

The largest number of device failures occurs during the period of use of the equipment by consumers due to violations of established operating rules and adverse environmental influences.

In reliability theory, a distinction is made between the reliability of systems and elements.

System is a set of jointly operating objects that fully ensure the implementation of certain practical tasks.

element is a part of a system that has no independent meaning and performs certain functions in it.

The concepts of “system” and “element” are relative. For example, various radio components (resistors, capacitors) can be elements of systems such as an amplifier, radio receiver, etc. In turn, these systems can be considered as elements of a more complex system - a radar system, which can also be an element of, say, a satellite monitoring system, etc.

Systems can be recoverable or non-recoverable.

Recoverable(allowing multiple repairs) the system after a failure is repaired and continues to perform its functions (household, computer equipment, audio and video equipment, etc.).

Unrecoverable in the event of a failure, the system is not subject to or cannot be restored for economic or technical reasons (fuses, equipment for combat ballistic missiles).

Based on the nature of the service, a distinction is made between serviced and unserviced systems.

Serviced systems perform their tasks in the presence of maintenance personnel and are usually adapted to eliminate failures during preventive maintenance.

Maintenance-free systems perform their assigned functions without maintenance personnel, for example, equipment installed on most non-returnable space objects.

Based on the nature of the influence of failures of system elements on its output parameters and, consequently, on the efficiency of the system, it can be divided into simple and complex.

Simple If one or more elements fail, systems completely lose their functionality.

Complex systems have the ability to continue to function with reduced efficiency if elements fail.

In reliability theory, a distinction is made between serial, parallel and mixed connections of elements. These types of connections will be discussed in detail in one of the following sections.

The above terms used in the classification of failures are reflected in state standards and regulatory and technical documentation and are mandatory.

Student's coefficients Appendix 1.

Appendix 2

FUNDAMENTALS OF RELIABILITY THEORY

BASIC TERMS AND DEFINITIONS OF RELIABILITY THEORY

Reliability– the property of an object to preserve over time, within established limits, all parameters that ensure the performance of the required functions under given conditions (conditions of use, maintenance, repair, storage and transportation).

Reliability is one of the properties characterizing the quality of products. Under quality products is understood as a set of properties of products that determine its suitability to satisfy certain needs in accordance with its purpose.

Objects, considered in reliability theory:

product – unit of product produced by a given enterprise, workshop, etc.;

element – conditionally indivisible component of the system;

system - a set of jointly acting elements designed to independently perform specified functions.

Products are divided into unrecoverable, which cannot be restored by the consumer (electric lamps, etc.) and restored, which can be restored by the consumer (car, etc.).

States products characterizing its reliability:

working condition – the state of the product in which it is capable of performing the specified functions;

working condition - the state of the product in which it satisfies not only the main, but also all auxiliary requirements. A working product must be functional.

limit state – an inoperable condition of the product in which the operation or restoration of the product is impractical.

Event, characterizing the reliability of the product:

refusal - an event consisting of complete or partial loss of performance.

A failure occurs as a result of the presence of one or more defects in the product. Under defect each individual non-compliance of the product with the established requirements is understood. It should be noted that the appearance of defects does not always lead to product failure.

Refusal criterion These are the signs of an inoperable state of a product established in the regulatory, technical or design documentation.

In accordance with the nature of development and manifestation, failures are divided into sudden(breakdowns from overloads), gradual in development and sudden in manifestation(fatigue failure, lamp burnout) and gradual(wear, aging). Gradual failures consist of a smooth departure of parameters beyond the tolerance limits.

If further use of the product is possible, failures are divided into full, excluding the possibility of product operation until they are eliminated, and partial where the product may be partially used, for example at less than full power or at reduced speed.

Based on the time of occurrence, failures are divided into running-in arising during the first period of operation, on failures during normal operation(during the period before wear failures appear) and on wear and tear.

Product failures that are eliminated spontaneously, without external intervention, are called self-eliminating or interspersed(electrical contact failure) .

Based on the reasons for their occurrence, failures are divided into: structural caused by design flaws, technological caused by imperfect production technology, and operational caused by improper operation.

Reasons for failures are divided into random And systematic.

Random reasons for failures – reasons whose occurrence cannot be predicted in advance. A random cause of failure is usually an unfavorable combination of random factors.

Systematic reasons – reasons whose occurrence can be predicted in advance (the influence of temperature, friction, aggressive chemicals, etc.).

Properties of products that characterize their reliability.

Reliability – the property of continuously maintaining operability for a given operating time.

Durability – the property of maintaining operability to the limit state with an established system of maintenance and repairs. For non-repairable products, the concepts of durability and reliability coincide.

Maintainability – property of a product, which consists in its adaptability to the prevention, detection and elimination of failures and malfunctions through maintenance and repairs.

Storability – the property of a product to maintain the values ​​of reliability, durability and maintainability during storage and transportation.