1. BASIC TERMS OF RELIABILITY THEORY

BASIC CONCEPTS OF RELIABILITY THEORY



Preliminary notes

The list is based on GOST 27.002-89 "Reliability in engineering. 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 separate paragraphs.

Object, element, system

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

The object is a technical product of a specific purpose, considered during periods of design, production, testing and operation.

Objects can be various systems and their elements, in particular: structures, installations, technical products, devices, machines, devices, devices and their parts, units and individual parts.
Element of the system - an object representing a separate part of the system. The concept of an element is conditional and relative, since any element, in turn, can always be considered as a combination of other elements.

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

The human operator is also one of the links in the man-machine system.

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

A sign of consistency is the structuredness of the system, the interconnectedness of its parts, the subordination of the organization of the whole system to a specific goal. Systems function in space and time.

Condition of the object

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

Fault - the state of the object, in which it does not meet at least one of the requirements established by the NTD.

Efficiency - the state of the object, in which it is able to perform specified functions, while maintaining the values ​​of the main parameters within the limits established by the NTD.

The main parameters characterize the operation of the object when performing the tasks set and are established in the regulatory and technical documentation.

Inoperability - the state of the 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 NTD.

The concept of serviceability is broader than the concept of performance. A workable object, in contrast to a serviceable one, satisfies only those NTD requirements that ensure its normal functioning when performing assigned tasks.

The efficiency and inoperability in the general case can be complete or partial. A fully functional facility provides, under certain conditions, the maximum efficiency of its use. The efficiency of application of a partially working object in 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 inoperable object may function, but the level of efficiency is lower than allowed. Fully inoperable object can not be used as intended.
The concepts of partial operability and partial inoperability apply mainly to complex systems, which are characterized by the possibility of being in several states. These states differ in the levels of system performance. The efficiency and inoperability of some objects may be complete, i.e. they can only have two states.
A workable object, in contrast to a working one, is obliged to satisfy only those NTD requirements, the performance 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 of the appearance of the object does not interfere with its normal (effective) functioning.

It is obvious that a workable object may be faulty, but deviations from the requirements of the regulatory and technical documentation are not so significant as to disrupt normal functioning.
The limit state is the state of the facility in which its further use for its intended purpose must be terminated due to a fatal violation of safety requirements or an unrecoverable deviation of the specified parameters beyond the established limits, an unacceptable increase in operating costs or the need for capital repairs.

Signs (criteria) of the limiting state are established by the NTD for this object.

An unrecoverable object reaches the limit state when a failure occurs or when a predetermined maximum permissible value of service life or total operating time is reached, established for operational safety reasons due to an irreversible decrease in use efficiency below the allowable or due to an increase in the failure rate, which is natural for objects of this type after set period of operation.
For recoverable objects, the transition to the limit state is determined by the onset of the moment when further operation is impossible or impractical due to the following reasons:
- it becomes impossible to maintain its safety, reliability or efficiency at the minimum acceptable level;
- as a result of wear and (or) aging, the object has entered a state in which repair requires an unacceptably high cost or does not provide the necessary degree of restoration of serviceability or resource.

For some recoverable objects, the limit state is considered to be such that the necessary restoration of serviceability can be carried out only with the help of major repairs.
Mode controllability * - the property of an object to maintain normal mode by means of control in order to preserve or restore its normal mode of operation.

Transition of an object to various states

Damage - an event that impairs the health of the object while maintaining its operability.

Failure - an event consisting in the malfunction of the object.

A failure criterion is a distinctive feature or combination of signs according to which the fact of failure is established.

Signs (criteria) of failures are established by the documentation of this object.
Recovery is the process of detecting and repairing a failure (damage) in order to restore its working capacity (health).

A recoverable object is an object whose operability in the event of a failure is to be restored in the conditions considered.

Non-recoverable object - an object whose performance in the event of a failure is not recoverable in the conditions under consideration.

When analyzing reliability, especially when choosing indicators of reliability of an object, the decision that should be made in case of an object failure is essential. If, in the situation under consideration, the restoration of the performance of this object in case of its refusal for any reason is considered inexpedient or impracticable (for example, due to the impossibility of interrupting the function being performed), then such an object is not recoverable in this situation. Thus, the same object, depending on the features or stages of operation, can be considered recoverable or non-recoverable. For example, the meteorological satellite equipment at the storage stage refers to recoverable, and during flight in space - non-recoverable. Moreover, even the same object can be attributed to one or another type depending on the purpose: a computer used for non-operational calculations is an object recoverable, since in case of a failure any operation can be repeated, and the same computer controlling a complex technological process in chemistry, is an object unrecoverable, since failure or failure leads to irreparable consequences.
Accident * - an event consisting in the transition of an object from one level of working capacity or relative level of functioning to another, substantially lower, with a major violation of the mode of operation of the object. Accident can lead to partial or complete destruction of the object, creating dangerous conditions for humans and the environment.

The temporal characteristics of the object

Hours - the 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. The operating time can be measured in units of time, cycles, units of production, and other units. During operation, there are daily, monthly operating time, time to first failure, time between failures, a given time, etc.
If the object is operated in different load conditions, then, for example, the operating time in the lightweight mode can be allocated and taken into account separately from the operating time at nominal load.

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

It is usually indicated which technical resource is meant: to average, capital, from capital to the nearest average, etc. If a specific instruction is not contained, then the resource is meant from the start of operation until reaching the limit state after all (medium and major) repairs, i.e. prior to write-off due to technical condition.

Service life is the calendar duration of the facility operation from its start or resumption after major or medium repairs until the limit state.

The operation of an object is understood as the stage of its existence at the disposal of the consumer, provided that the object is used for its intended purpose, which can alternate with storage, transportation, maintenance and repair, if this is done by the consumer.

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

Determination of reliability
The operation of any technical system can be characterized by its efficiency (Fig. 4.1.1), which is understood as the combination of properties that determine the ability of the system to perform certain tasks when it is created.



Fig. 4.1.1. Main features of technical systems

In accordance with GOST 27.002-89, reliability means the property of an object to preserve, within the established limits, the values ​​of all parameters characterizing the ability to perform the required functions in specified modes and conditions of use, maintenance, repairs, storage and transportation.

In this way:
1. Reliability - the property of an object to preserve in time the ability to perform the required functions. For example: for an electric motor - to provide the required torque and speed on the shaft; for the power supply system - to provide consumers with energy of the required quality.

2. The execution of the required functions should occur at the values ​​of the parameters within the established limits. For example: for an electric motor - to provide the required moment and speed at an engine temperature not exceeding a certain limit, no source of explosion, fire, etc.

3. The ability to perform the required functions should be maintained in the specified modes (for example, in the intermittent operation mode); in specified conditions (for example, in dusty conditions, vibrations, etc.).

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

Reliability is an important indicator of the quality of an object. It can neither be opposed nor mixed with other indicators of quality. Obviously insufficient, for example, will be information about the quality of the treatment plant, if it is only known that it has a certain performance and a certain cleaning coefficient, but it is not known how stable these characteristics are maintained during its operation. Information that the installation stably retains its inherent characteristics is also useless, but the values ​​of these characteristics are unknown. That is why the definition of the concept of reliability includes the execution of specified functions and the preservation of this property when an object is used for its intended purpose.

Depending on the purpose of the object, it may include in various combinations reliability, durability, maintainability, and persistence. For example, for a non-repairable object that is not intended for storage, reliability is determined by its dependability when used as intended. Information on the reliability of the product being repaired for a long time in the state of storage and transportation does not fully determine its reliability (it is also necessary to know about maintainability and persistence). In some cases, it becomes very important for a product property to remain operable before the onset of a limiting state (decommissioning, transfer to medium or major repairs), i.e. information is needed not only about the reliability of the object, but also about its durability.

A technical characteristic that quantitatively determines one or more properties that make up an object’s reliability is referred to as a reliability indicator. It quantitatively describes the extent to which an object or a given group of objects has certain properties that determine reliability. The reliability indicator may have a dimension (for example, the average recovery time) or not (for example, the probability of failure-free operation).

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

Reliability - the property of the object to continuously maintain performance for some time or for some time.

Maintainability is the property of an object to be adapted to the prevention and detection of failures and damages, to the restoration of working capacity and serviceability during maintenance and repair.

Durability - the property of the object to maintain performance until the limit state with the necessary interruption for maintenance and repairs.

Persistence - the property of an object to continuously maintain a healthy and healthy state during (and after) storage and (or) transportation.

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

Reliability and maintainability indicators
Time to failure is the probability that, within the limits of a given time, a failure of the object will not occur (subject to working at the initial moment of time).
For the modes of storage and transportation can be used similarly defined term "probability of failure".

Mean time to failure is the expected value of a random object life before the first failure.
Mean time between failures is the expected value of a random object between failures.

Usually this indicator refers to the steady-state operation process. In principle, the average time between failures of objects consisting of elements aging in time depends on the number of the previous failure. However, with an increase in the number of failures (that is, with an increase in the duration of operation), this value tends to some constant, or, as they say, to its stationary value.
Mean time to failure - the ratio of the time the object is restored over a certain period of time to the expected number of failures during this time.

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

The specified time is the time during which the object must work smoothly to perform its functions.

The average idle time is the mathematical expectation of the random time of the forced unregulated stay of the object in a state of inoperability.

Average recovery time is the mathematical expectation of the random duration of the restoration of working capacity (the actual repair).

The probability of recovery is the probability that the actual duration of the restoration of the facility’s performance does not exceed the specified one.

Technical Performance Indicator- a measure of the quality of the actual functioning of an object or the advisability of using an object to perform specified functions.
This indicator is quantified as the expectation of the output effect of the object, i.e. depending on the purpose of the system accepts a specific expression. Often, the performance indicator is defined as the total probability that an object will perform its task, taking into account the possible reduction in the quality of its work due to partial failures.

The efficiency retention coefficient is an indicator characterizing the influence of the degree of reliability to the maximum possible value of this indicator (that is, the corresponding state of complete operability of all elements of the object).

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

The average availability factor is 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 chosen point in time in the steady-state process of operation. (The availability factor can 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 the steady-state operation process is considered, the mathematical model of which is a stationary random process. The availability factor is the limit value to which both non-stationary and average availability factors tend with increasing of the considered time interval.

Often used indicators that characterize a simple object - the so-called idle factors of the corresponding type. Each availability ratio can be assigned a certain downtime ratio, numerically equal to the addition of the corresponding availability ratio up to one. In the respective definitions, performance should be replaced with inoperability.

A non-stationary availability ratio is the probability that an object, while in standby mode, will be operational at a given point in time, counted from the start of work (or from another well-defined time), and from this point in time will run smoothly for a specified time.

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

The stationary operational readiness ratio ( operational readiness ratio) is the probability that the recoverable item will be operational at an arbitrary point in time, and from that point in time it will work flawlessly for a given time interval.
It is assumed that the steady-state operation process is considered, to which the stationary random process corresponds as a mathematical model.

Coefficient of technical use- the ratio of the average operating time of the 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 is the conditional probability density of failure of an unrecoverable object, determined for the time in question, provided that up to this point a failure has not occurred.
The failure flow parameter is the probability density of the occurrence of a failure of the object being restored, which is determined for the considered moment of time.

The failure flow parameter can be defined as the ratio of the number of object failures over a certain time interval to the duration of this interval in the case of an ordinary failure stream.

Recovery intensity- conditional probability density of the restoration of the object's performance, determined for the considered moment of time, provided that until that moment the restoration has not been completed.

Indicators of durability and persistence

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

The average resource is the expected value of the resource.

The assigned resource is the total operating time of the object, at which achievement the operation should be terminated regardless of its state.

The average repair resource is the average resource between adjacent major repairs of an object.

Average resource before write-off- The average resource of the object from the start of operation to its cancellation.

The average resource to overhaul the average resource from the start of operation of the object to its first overhaul.

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

Average service life - expectation of service life.

Average overhaul life - the average service life between adjacent major repairs of the object.

The average service life before the overhaul - the average service life from the start of operation of the object to its first overhaul.

Average service life before write-off- average service life from the start of operation of the facility to its decommissioning

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

The average shelf life is the mathematical expectation of the shelf life.

Types of reliability

Multipurpose use of equipment and systems leads to the need to investigate certain aspects of reliability, taking into account the reasons that form the reliability properties of objects. This leads to the need to subdivide reliability into species.

There are:
- instrumental reliability due to the state of the apparatus; in turn, it can be subdivided into constructive, schematic, production-technological reliability;
- functional reliability associated with the performance of a certain function (or a complex of functions) imposed on an object, system;
- operational reliability due to the quality of use and maintenance;
- software reliability due to the quality of the software (programs, algorithms of actions, instructions, etc.);
- 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 the theory of reliability is the notion of failure (object, element, system).
Object failure - an event that the object completely or partially ceases to perform specified functions. With a complete loss of working capacity, a complete failure occurs, with partial failure. The concepts of full and partial failures each time must be clearly formulated before reliability analysis, since a quantitative assessment of reliability depends on this.

For reasons of failure in this place, there are:
failures due to structural defects;
failures due to technological defects;
failures due to operational defects;
failures due to gradual aging (wear).
Failures due to structural defects arise as a result of imperfection of the design due to "misses" in the 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 instances of the product, object, system.
Failures due to technological defects arise as a result of a violation of the accepted technology of manufacturing products (for example, the output of certain characteristics beyond the established limits). Failures of this group are characteristic of individual batches of products, in the manufacture of which violations of the manufacturing technology were observed.

Failures due to operational defects occur due to non-compliance of the required operating conditions and the service rules with actual ones. Failures of this group are typical for individual copies of products.

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

Failures for 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 relaxation regimen;
failures with combined occurrence schemes.
Failures with an instantaneous pattern of occurrence are characterized by the fact that the time of the occurrence of a failure does not depend on the time of previous operation and the state of the object, the moment of failure comes by chance, suddenly. Examples of the implementation of such a scheme can serve as failures of products under the action 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 due to physicochemical changes in the damage materials. At the same time, the values ​​of some "crucial" parameters are 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 serve as failures due to reduced insulation resistance, electrical erosion of contacts, etc.

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

Failures with combined patterns of occurrence are typical for situations when several causal schemes are active at the same time. An example of this scheme could be a motor failure due to a short circuit due to reasons for reducing the insulation resistance of the windings and overheating.
When analyzing reliability, it is necessary to identify the prevailing causes of failures and only then, if necessary, take into account the influence of other causes.

According to the time aspect and the degree of predictability, failures are divided into sudden and gradual.
By the nature of elimination over time, there are stable (final) and self-eliminating (short-term) failures. Short-term failure is called a failure. A characteristic sign of failure is that the restoration of working capacity after its occurrence does not require the repair of equipment. An example would be a short-term interference in receiving a signal, program defects, etc.
For the purposes of analyzing and investigating reliability, causal failure patterns can be represented as statistical models that, due to the probability of occurrence of damage, are described by probability laws.

Types of failures and causal relationships The

failures of system elements are the main subjects of research in the analysis of 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 of all these categories may have different reasons given in the outer ring. When the exact type of failures is determined and the data on them is received, and the final event is critical, they are considered as initial failures.

The primary failure of an element is defined as the inoperative state of this element, the cause of which is itself, and repair work is necessary to return the element to a working state. Primary failures occur at input effects, the value of which is within the limits of the calculated range, and failures are explained by the natural aging of the elements. A reservoir rupture due to aging (fatigue) of a material is an example of a primary failure.
Secondary failure is the same as primary, except that the element itself is not the cause of failure. Secondary failures are due to the effect of previous or current excess voltages on the elements. Amplitude, frequency, duration of action of these voltages can go beyond the tolerances or have reverse polarity and are caused by various sources of energy: 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, subsidence), as well as exposure to other technical systems.


Fig. 4.1.2. Characteristics of element failures.

An example of secondary failures is the "operation of a fuse from increased electrical current", "damage to storage tanks in case of an earthquake." It should be noted that the elimination of sources of high voltages does not guarantee the return of the element to its working condition, since the previous overload could cause irreversible damage to the element, which then requires repair.
Initiated failures (erroneous commands). People, for example, operators and service technicians, are also possible sources of secondary failures, if their actions lead to the failure of elements. Erroneous commands are represented as an element that is inoperative due to an incorrect control signal or interference (it only sometimes requires repair to return this element to a working state). Spontaneous control signals or interference often do not leave consequences (damage), and in normal subsequent modes the elements operate in accordance with the specified requirements. Typical examples of erroneous commands are: "voltage is applied spontaneously to the relay winding", "the switch accidentally did not open due to interference", "interference at the control system input to the security system caused a false signal to stop, "the operator did not press the emergency button" (erroneous *** but from the emergency button).

Multiple failure (general failures) is an event in which several elements fail for the same reason. The following can be attributed to such reasons:
- design defects of equipment (defects not identified at the design stage and leading to failures due to the interdependence between electrical and mechanical subsystems or elements of the redundant system);
- operating and maintenance errors (incorrect adjustment or calibration, operator negligence, improper handling, etc.);
- environmental exposure (moisture, dust, dirt, temperature, vibration, as well as extreme modes of normal operation);
- external catastrophic effects (natural external phenomena, such as flood, earthquake, fire, hurricane);
- a common manufacturer (redundant equipment or its components supplied by the same manufacturer may have common structural or manufacturing defects. For example, manufacturing defects may be caused by the wrong choice of material, errors in installation systems, poor soldering, etc.);
- common external power supply (common power supply for main and backup equipment, redundant subsystems and components);
- malfunctioning (incorrectly selected set of measuring instruments or unsatisfactorily planned protection measures).

There are a number of examples of multiple failures: for example, some parallel-connected spring relays failed at the same time and their failures were caused by a common cause; due to improper clutch disengagement during maintenance, the two valves were installed in the wrong position; due to the destruction of the steam line, several failures of the switching board took place at once. In some cases, the common cause causes not a complete failure of the redundant system (simultaneous failure of several nodes, i.e., a limiting case), but a less serious general decrease in reliability, which leads to an increase in the probability of joint failure of the system nodes. Such a phenomenon is observed in the case of exceptionally unfavorable environmental conditions, when degradation of characteristics leads to the failure of the reserve site.The presence of common, unfavorable external conditions leads to the fact that the failure of the second node depends on the failure of the first node and is paired with it.

For each common cause, it is necessary to determine all the source events it triggers. At the same time determine the scope of each common cause, as well as the location of the elements and the time of the incident. Some common reasons have only a limited scope. For example, leakage of fluid can be limited to one room, and electrical installations, their elements in other rooms will not be damaged due to leaks, unless these rooms communicate with each other.

Failure is considered in comparison with another more critical, if it is preferable to consider it first of all when developing issues of reliability and safety. When comparing 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 interrelated. So, with unsatisfactory reliability of an object, one should 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, 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.

1. Надежность: основные понятия и определения 2. Показатели надежности 2.1. Основные показатели безотказности объектов 2.1.1. Вероятность безотказной работы 2.1.2. Средняя наработка до отказа 2.1.3. Интенсивность отказов 2.1.4. Средняя наработка на отказ 2.1.5. Параметр потока отказов