Plumbing equipment failure rate reference book. See pages where the term failure rate is mentioned. High Availability Basics

When considering the laws of failure distribution, it was found that the failure rates of elements can be either constant or vary depending on the operating time. For long-term use systems, which include all transport systems, preventative maintenance is provided, which virtually eliminates the impact of wear-out failures, so only sudden failures occur.

This greatly simplifies reliability calculations. However, complex systems consist of many elements connected in different ways. When the system is in operation, some of its elements operate continuously, others only at certain periods of time, and others perform only short switching or connecting operations. Consequently, during a given period of time, only some elements have an operating time that coincides with the operating time of the system, while others operate for a shorter time.

In this case, to calculate the operating time of a given system, only the time during which the element is turned on is considered; This approach is possible if we assume that during periods when elements are not included in the system operation, their failure rate is zero.

From a reliability point of view, the most common scheme is serial connection elements. In this case, the calculation uses the rule of product of reliability:

Where R(ti)- reliability i-th element that is included on t i hours of the total system operating time t h.

For calculations, the so-called

employment rate equal to

i.e., the ratio of the operating time of the element to the operating time of the system. The practical meaning of this coefficient is that for an element with a known failure rate, the failure rate in the system, taking into account the operating time, will be equal to

The same approach can be used in relation to individual system nodes.

Another factor that should be considered when analyzing system reliability is the level of workload with which the elements operate in the system, as this largely determines the magnitude of the expected failure rate.

The failure rate of elements changes significantly even with small changes in the workload affecting them.

In this case, the main difficulty in the calculation is caused by the variety of factors that determine both the concept of element strength and the concept of load.

The strength of an element combines its resistance to mechanical loads, vibrations, pressure, acceleration, etc. The strength category also includes resistance to thermal loads, electrical strength, moisture resistance, corrosion resistance and a number of other properties. Therefore, strength cannot be expressed by some numerical value and there are no units of strength that take into account all these factors. The manifestations of load are also diverse. Therefore, to assess strength and load, statistical methods are used to determine the observed effect of failure of an element over time under the influence of a series of loads or under the influence of a predominant load.

Elements are designed so that they can withstand rated loads. When operating elements under rated load conditions, a certain pattern in the intensity of their sudden failures is observed. This rate is called the nominal sudden failure rate of the elements, and it is the reference value for determining the actual sudden failure rate of the real element (taking into account the operating time and workload).

For a real element or system, three main environmental influences are currently considered: mechanical, thermal and operating loads.

The influence of mechanical influences is taken into account by the coefficient, the value of which is determined by the installation location of the equipment, and can be taken equal to:

for laboratories and comfortable premises - 1

, stationary ground installations - 10

, railway rolling stock - 30.

Nominal sudden failure rate selected by

table 3, should be increased by times depending on the installation location of the device in operation.

Curves Fig. 7 illustrate the general nature of changes in the intensity of sudden failures of electrical and electronic elements depending on the heating temperature and the magnitude of the workload.

The intensity of sudden failures with increasing workload, as can be seen from the curves above, increases logarithmically. These curves also show how it is possible to reduce the rate of sudden failures of elements even to a value less than the nominal value. A significant reduction in the rate of sudden failures is achieved if the elements operate at loads below their rated values.

Rice. 16

Rice. 7 can be used when carrying out indicative (training) calculations of the reliability of any electrical and electronic elements. The nominal mode in this case corresponds to a temperature of 80°C and 100% of the working load.

If the calculated parameters of the element differ from the nominal values, then according to the curves in Fig. 7, the increase for the selected parameters can be determined and a ratio can be obtained by which the value of the failure rate of the element in question is multiplied.

High reliability can be built into the design of elements and systems. To do this, it is necessary to strive to reduce the temperature of the elements during operation and use elements with increased nominal parameters, which is equivalent to a reduction in workloads.

The increase in the cost of manufacturing the product in any case pays off by reducing operating costs.

Table value at rated voltage and temperature t i .

- failure rate at operating voltage U 2 and temperature t2.

It is assumed that the mechanical effects remain at the same level. Depending on the type and type of elements, the value P, varies from 4 to 10, and the value TO within 1.02 1.15.

When determining the actual failure rate of elements, it is necessary to have a good idea of ​​the expected load levels at which the elements will operate, and to calculate the values ​​of electrical and thermal parameters taking into account transient modes. Correct identification of loads acting on individual elements leads to a significant increase in the accuracy of reliability calculations.

When calculating reliability taking into account wear failures, it is also necessary to take into account the operating conditions. Durability values M, given in table. 3, as well as refer to the nominal load mode and laboratory conditions. All elements operating under other conditions have a durability that differs from the current one by an amount TO Magnitude TO can be taken equal to:

for the laboratory - 1.0

, ground installations - 0.3

, railway rolling stock - 0.17

Small fluctuations in the coefficient TO possible for equipment for various purposes.

To determine expected durability M it is necessary to multiply the average (nominal) durability determined from the table by a coefficient TO .

In the absence of materials necessary to determine failure rates depending on load levels, the coefficient method for calculating failure rates can be used.

The essence of the coefficient calculation method is that when calculating equipment reliability criteria, coefficients are used that relate the failure rate of elements various types with the failure rate of an element whose reliability characteristics are reliably known.

It is assumed that the exponential law of reliability is valid, and the failure rates of elements of all types vary depending on operating conditions to the same extent. The last assumption means that under different operating conditions the following relation is valid:

The failure rate of an element whose quantitative characteristics are known;

Reliability factor i-th element. An element with a failure rate ^ 0 is called the main element of the system calculation. When calculating the coefficients K i The wire-unregulated resistance is taken as the main element of the system calculation. In this case, to calculate the reliability of the system, it is not necessary to know the failure rate of elements of all types. It is enough to know only the reliability coefficients K i, the number of elements in the circuit and the failure rate of the main element of the calculation Since K i has a scatter of values, then the reliability is checked both for TO min , and for TO max. Values Ki, determined based on the analysis of data on failure rates, for equipment for various purposes are given in table. 5.

Table 5

The failure rate of the main element of the calculation (in this case, the resistance) should be determined as the weighted average value of the failure rates of the resistances used in the designed system, i.e.

AND N R- failure rate and number of resistances i-th type and rating;

T- number of types and ratings of resistances.

It is advisable to construct the resulting dependence of the system reliability on the operating time for both the values TO min , so for TO swing

Having information about the reliability of individual elements included in the system, we can give overall assessment system reliability and identify blocks and components that require further improvement. To do this, the system under study is divided into nodes according to constructive or semantic characteristics (compiled structural scheme). For each selected node, reliability is determined (nodes with less reliability require revision and improvement first).

When comparing the reliability of components, and even more so of different system options, it should be remembered that the absolute value of reliability does not reflect the behavior of the system in operation and its effectiveness. The same level of system reliability can be achieved in one case due to the main elements, the repair and replacement of which requires significant time and large material costs (for an electric locomotive, removal from train work); in another case, these are small elements, the replacement of which is carried out by the maintenance personnel without removing the machine from work. Therefore for comparative analysis of systems being designed, it is recommended to compare the reliability of elements that are similar in their significance and consequences arising from their failures.

When making approximate reliability calculations, you can use data from operating experience of similar systems. which to some extent takes into account operating conditions. In this case, the calculation can be carried out in two ways: by the average level of reliability of equipment of the same type or by a conversion factor to real operating conditions.

The calculation based on the average level of reliability is based on the assumption that the designed equipment and the operating sample are equal. This can be allowed with identical elements, similar systems and the same ratio of elements in the system.

The essence of the method is that

I is the number of elements and the mean time between failures of the sample equipment;

And - the same for the designed equipment. From this relationship it is easy to determine the mean time between failures for the designed hardware:

The advantage of the method is its simplicity. Disadvantages - the absence, as a rule, of a sample of operating equipment suitable for comparison with the designed device.

The basis of the calculation using the second method is the determination of the conversion factor, which takes into account the operating conditions of similar equipment. To determine it, a similar system operated in given conditions. Other requirements may not be met. For the selected operating system, reliability indicators are determined using the data in Table. 3, the same indicators are determined separately based on operational data.

The conversion factor is defined as the ratio

- mean time between failures according to operating data;

T oz- mean time between failures according to calculation.

For the designed equipment, reliability indicators are calculated using the same tabular data as for the operating system. Then the results obtained are multiplied by K e.

Coefficient K e takes into account real operating conditions - preventive repairs and their quality, replacement of parts between repairs, qualifications of maintenance personnel, condition of depot equipment, etc., which cannot be foreseen using other calculation methods. Values K e may be greater than one.

Any of the considered calculation methods can be carried out for a given reliability, i.e. by the method of the opposite - from the reliability of the system and mean time between failures to the choice of indicators of the constituent elements.

When considering reliability issues, it is often convenient to imagine the matter as if the element were subject to flow of failures with some intensity l(t); the element fails the moment the first event of this thread occurs.

The image of a “failure flow” takes on real meaning if the failed element is immediately replaced with a new one (restored). The sequence of random moments in time at which failures occur (Fig. 3.10) represents a certain flow of events, and the intervals between events are independent random variables distributed according to the corresponding distribution law.

The concept of “failure rate” can be introduced for any reliability law with density f(t); in the general case, the failure rate l will be a variable value.

Intensity(or otherwise “danger”) of failures is the ratio of the distribution density of the time of failure-free operation of an element to its reliability:

Let us explain the physical meaning of this characteristic. Let a large number N of homogeneous elements be tested simultaneously, each until it fails. Let us denote n(t) the number of elements that turned out to be serviceable at time t, and m(t, t+Dt), as before, the number of elements that failed in a short period of time (t, t+Dt). There will be an average number of failures per unit of time

Let us divide this value not by the total number of tested elements N, but by number of serviceable by time t elements n(t). It is easy to verify that for large N the ratio will be approximately equal to the failure rate l (t):

Indeed, for large N n(t)»Np(t)

But according to formula (3.4),

In reliability studies, approximate expression (3.8) is often considered as a determination of the failure rate, i.e. it is defined as average number of failures per unit of time per one working element.

The characteristic l(t) can be given one more interpretation: it is conditional probability density of element failure in this moment time t, provided that before time t it worked flawlessly. Indeed, consider the probability element l(t)dt - the probability that during time (t, t+dt) the element will move from the “working” state to the “not working” state, provided that it was working before moment t. In fact, the unconditional probability of failure of an element in the section (t, t+dt) is equal to f(t)dt. This is the probability of combining two events:

A - the element worked properly until moment t;

B - element failed at time interval (t, t+dt).

According to the rule of probability multiplication: f(t)dt = P(AB) = P(A) P(B/A).

Considering that P(A)=p(t), we get: ;

and the value l(t) is nothing more than the conditional probability density of the transition from the “working” state to the “failed” state for moment t.

If the failure rate l(t) is known, then the reliability p(t) can be expressed through it. Taking into account that f(t)=-p"(t), we write formula (3.7) in the form:

Integrating, we get: ,

Thus, reliability is expressed through the failure rate.

In the special case when l(t)=l=const, formula (3.9) gives:

p(t)=e - l t , (3.10)

those. the so-called exponential reliability law.

Using the image of a “failure flow”, one can interpret not only formula (3.10), but also a more general formula (3.9). Let us imagine (quite conventionally!) that an element with an arbitrary reliability law p(t) is subject to a flow of failures with a variable intensity l(t). Then formula (3.9) for p(t) expresses the probability that more than one failure will not appear in the time interval (0, t).

Thus, both with the exponential and with any other law of reliability, the operation of the element, starting from the moment of switching on t = 0, can be imagined in such a way that the Poisson failure law acts on the element; for an exponential reliability law, this flow will be with a constant intensity l, and for a non-exponential one, with a variable intensity l(t).

Note that this image is only suitable if the failed element not replaced with a new one. If, as we did before, we immediately replace the failed element with a new one, the failure flow will no longer be Poisson. Indeed, its intensity will depend not just on the time t that has passed since the beginning of the entire process, but also on the time t that has passed since random moment including precisely given element; This means that the flow of events has a consequence and is not Poisson.

If, throughout the entire process under study, this element is not replaced and can fail no more than once, then when describing a process that depends on its functioning, one can use the scheme of a Markov random process. but at a variable, and not at a constant, failure rate.

If the non-exponential reliability law differs relatively little from the exponential one, then, for the sake of simplification, it can be approximately replaced by an exponential one (Fig. 3.11).

The parameter l of this law is chosen so as to keep unchanged the mathematical expectation of the failure-free operation time, equal, as we know, to the area limited by the curve p(t) and the coordinate axes. To do this, you need to set the parameter l of the exponential law equal to

where is the area limited by the reliability curve p(t). Thus, if we want to characterize the reliability of an element by a certain average failure rate, we need to take as this intensity the value inverse to the average failure-free operation time of the element.

Above we defined the quantity as the area limited by the curve p(t). However, if you need to know only average uptime of an element, it is easier to find it directly from statistical material as average all observed values random variable T is the operating time of the element before its failure. This method can also be applied in the case where the number of experiments is small and does not allow one to construct the p(t) curve accurately enough.

Example 1. The reliability of the element p(t) decreases over time according to a linear law (Fig. 3.12). Find the failure rate l(t) and the average failure-free operation time of the element.

Solution. According to formula (3.7) in the section (0, t o) we have:

According to the given reliability law

(0

The second integral here is equal to .

As for the first, it is calculated approximately (numerically): ,

whence » 0.37+0.135=0.505.

Example 3. The distribution density of the element's failure-free operation time is constant in the section (t 0, t 1) and is equal to zero outside this section (Fig. 3.16). Find the failure rate l(t).

Solution. We have: , (t o

The failure rate graph is shown in Fig. 3.17; at t® t 1, l(t)® ¥ .

The average value of the operating time of products in a batch until the first failure is called the average time to the first failure. This term applies to both repairable and non-repairable products. For non-repairable products, instead of the above, the term mean time to failure can be used.

GOST 13377 - 67 for non-repairable products introduced another reliability indicator, called failure rate.

The failure rate is the probability that a non-repairable product, which worked without failure until moment t, will fail in the next unit of time, if this unit is small.

The failure rate of a product is a function of the time it takes to operate.

Assuming that the failure-free operation of a certain unit in the electronic control system of a vehicle is characterized by a failure rate numerically equal to the calculated one, and this intensity does not change throughout its entire service life, it is necessary to determine the time to failure TB of such a unit.

The control subsystem includes k series-connected electronic units (Fig. 2).

Fig.2 Control subsystem with sequentially connected blocks.

These blocks have the same failure rate, numerically equal to the calculated one. It is required to determine the failure rate of the subsystem λ P and its average time to failure, to plot the dependence of the probability of failure-free operation of one block RB (t) and the subsystem RP (t) on the operating time and to determine the probabilities of failure-free operation of the block RB (t) and the subsystem RP (t) to operating time t= T P.

The failure rate λ(t) is calculated using the formula:

, (5)

Where is the statistical probability of a device failure on an interval, or otherwise the statistical probability of a random variable T falling within a specified interval.

Р(t) – calculated in step 1 – probability of failure-free operation of the device.

Setpoint 10 3 h - 6.5

Interval =

λ(t) = 0.4 / 0.4*3*10 3 h = 0.00033

Let us assume that the failure rate does not change throughout the entire service life of the object, i.e. λ(t) = λ = const, then the time to failure is distributed according to an exponential (exponential) law.

In this case, the probability of failure-free operation of the unit is:

(6)

R B (t) = exp (-0.00033*6.5*10 3) = exp(-2.1666) = 0.1146

And the average operating time of a block to failure is found as:

1/0.00033 = 3030.30 hours.

When k blocks are connected in series, the failure rate of the subsystem they form is:

(8)

Since the failure rates of all blocks are the same, the failure rate of the subsystem is:

λ P = 4*0.00033 = 0.00132 hours,

and the probability of failure-free operation of the system:

(10)

R P (t) = exp (-0.00132*6.5*10 3) = exp (-8.58) = 0.000188

Taking into account (7) and (8), the average time to failure of the subsystem is found as:

(11)

1/0.00132 = 757.58 hours.

Conclusion: As we approach the limit state, the failure rate of objects increases.

Calculation of the probability of failure-free operation.

Exercise: For operating time t = it is necessary to calculate the probability of failure-free operation Рс() of the system (Fig. 3), consisting of two subsystems, one of which is a backup one.

Rice. 3 Scheme of a redundant system.

The calculation is carried out under the assumption that the failures of each of the two subsystems are independent.

The probabilities of failure-free operation of each system are the same and equal to R P (). Then the probability of failure of one subsystem is:

Q P () = 1 – 0.000188 = 0.99812

The probability of failure of the entire system is determined from the condition that both the first and second subsystems have failed, i.e.:

0,99812 2 = 0,99962

Hence the probability of failure-free operation of the system:

,

Р с () = 1 – 0.98 = 0.0037

Conclusion: In this task, the probability of failure-free operation of the system in the event of failure of the first and second subsystems was calculated. Compared to a sequential structure, the probability of failure-free operation of the system is less.

Annotation: Two types of means of maintaining high availability are considered: ensuring fault tolerance (neutralization of failures, survivability) and ensuring safe and fast recovery from failures (serviceability).

Availability

Basic Concepts

The information system provides its users with a certain set of services. They say that the required level of availability of these services is ensured if the following indicators are within specified limits:

• Service efficiency. The efficiency of the service is determined in terms of the maximum time to service a request, the number of supported users, etc. It is required that the efficiency does not fall below a predetermined threshold.
• Unavailability time. If the effectiveness of an information service does not satisfy the imposed restrictions, the service is considered unavailable. It is required that the maximum duration of the unavailability period and the total unavailability time for a certain period (month, year) did not exceed predetermined limits.

In essence, it is required that the information system operates with the desired efficiency almost always. For some critical systems (such as control systems) unavailability time should be zero, without any "almost". In this case, they talk about the probability of an unavailability situation occurring and require that this probability does not exceed a given value. To solve this problem, special fault-tolerant systems

, the cost of which is usually very high. unavailability time The vast majority of commercial systems are subject to less stringent requirements, but modern business life imposes quite severe restrictions here, when the number of users served can be measured in the thousands, response time should not exceed several seconds, and

– several hours a year. The task of ensuring high availability

must be solved for modern configurations built in client/server technology. This means that the entire chain needs protection - from users (possibly remote) to critical servers (including security servers).

The main threats to accessibility were discussed earlier. In accordance with GOST 27.002, under refusal

refers to an event that involves a malfunction of a product. In the context of this work, a product is an information system or its component. In the simplest case, we can assume that failures of any component of a composite product lead to an overall failure, and the distribution of failures over time is a simple Poisson flow of events. In this case, introduce the concept

failure rates

– and , which are related to each other by the relation,

– .

where is the component number, failure rate

Failure rates independent components add up: A

mean time between failures and , which are related to each other by the relation for a composite product is given by the relation independent components add up: Already these simple calculations show that if a component exists,

The Poisson model allows us to substantiate another very important point, namely that the empirical approach to building systems The task of ensuring cannot be implemented in an acceptable time. In a traditional software system testing/debugging cycle, optimistically, each bug fix results in an exponential decrease (by about half a decimal order) In the simplest case, we can assume that failures of any component of a composite product lead to an overall failure, and the distribution of failures over time is a simple Poisson flow of events.. It follows that in order to verify experimentally that the required level of availability has been achieved, regardless of the testing and debugging technology used, you will have to spend time almost equal to mean time between failures. For example, to achieve mean time between failures 10 5 hours will require more than 10 4.5 hours, which is more than three years. This means that other methods of building systems are needed The task of ensuring, methods whose effectiveness has been proven analytically or practically over more than fifty years of computing and programming development.

The Poisson model is applicable in cases where the information system contains single points of failure, that is, components whose failure leads to the failure of the entire system. A different formalism is used to study redundant systems.

In accordance with the statement of the problem, we will assume that there is a quantitative measure of the effectiveness of the information services provided by the product. In this case, the concepts are introduced performance indicators individual elements and the efficiency of functioning of the entire complex system.

As a measure of availability, we can take the probability of acceptability of the effectiveness of the services provided by the information system over the entire period of time under consideration. The greater the efficiency margin the system has, the higher its availability.

If there is redundancy in the system configuration, the probability that during the time period under consideration efficiency of information services will not fall below the permissible limit depends not only on the probability of component failure, but also on the time during which they remain inoperative, since in this case the overall efficiency decreases, and each subsequent failure can become fatal. To maximize system availability, it is necessary to minimize the downtime of each component. In addition, it should be taken into account that, generally speaking, repair work may require a reduction in efficiency or even temporary shutdown of functional components; this kind of influence also needs to be minimized.

A few terminological notes. Usually in the literature on reliability theory, instead of availability, they talk about readiness(including high availability). We preferred the term "availability" to emphasize that information service should not only be “ready” in itself, but accessible to its users in conditions where situations of unavailability may be caused by reasons that, at first glance, are not directly related to the service (for example, the lack of consulting services).

Next, instead of unavailability time usually talk about availability factor. We wanted to pay attention to two indicators - the duration of a single downtime and the total duration of downtime, so we preferred the term " unavailability time"as more capacious.

High Availability Basics

The basis for measures to improve accessibility is the use of a structured approach, embodied in an object-oriented methodology. Structuring is necessary in relation to all aspects and components of an information system - from architecture to administrative databases, at all stages of its life cycle - from initiation to decommissioning. Structuring, while important in itself, is also a necessary condition for the practical feasibility of other measures to improve accessibility. Only small systems can be built and operated as desired. Large systems have their own laws, which, as we have already pointed out, programmers first realized more than 30 years ago.

When developing security measures The task of ensuring

At the stage of approximate and approximate calculations of electrical devices, the main reliability indicators are calculated .

The main qualitative indicators of reliability are:

Failure Rate

Average time to failure.

Failure Rate l (t)- this is the number of those who refused n(t) elements of the device per unit of time, related to the average total number of elements N(t), operational at the moment of time Δ t[ 9]

l (t)=n(t)/(Nt*Δt) ,

Where Δt- a specified period of time.

For example: 1000 elements of the device worked for 500 hours. During this time, 2 elements failed. From here,

l (t)=n(t)/(Nt*Δt)=2/(1000*500)=4*10 -6 1/hour, that is, in 1 hour 4 elements out of a million can fail.

Failure rate indicators l (t) elements are reference data; Appendix D provides failure rates l (t) for elements often used in circuits.

An electrical device consists of a large number of component elements, therefore the operational failure rate l is determined (t) of the entire device as the sum of the failure rates of all elements, according to the formula [11]

where k is a correction factor that takes into account the relative change in the average failure rate of elements depending on the purpose of the device;

m – total number of groups of elements;

n i - the number of elements in the i-th group with the same failure rate l i (t).

Probability of failure-free operation P(t) represents the probability that within a specified period of time t, device failure will not occur. This indicator is determined by the ratio of the number of devices that have worked without failure up to the point in time t to the total number of devices operational at the initial moment.

For example, the probability of failure-free operation P(t)=0.9 represents the probability that within the specified time period t= 500 hours, a failure will occur in (10-9=1) one device out of ten, and out of 10 devices, 9 will operate without failure.

Probability of failure-free operation P(t)=0.8 represents the probability that within the specified time period t=1000 hours, failure will occur in two 2 devices out of a hundred, and out of 100 devices, 80 devices will operate without failure.

Probability of failure-free operation P(t)=0.975 represents the probability that within the specified time period t=2500 hours, failure will occur in 1000-975=25 devices out of a thousand, and 975 devices will operate without failure.

Quantitatively, the reliability of a device is assessed as the probability P(t) of the event that the device will perform its functions without failure during the time from 0 to t. The value P(t) of the probability of failure-free operation (the calculated value of P(t) should not be less than 0.85) is determined by the expression

where t is the operating time of the system, hours (t is selected from the range: 1000, 2000, 4000, 8000, 10000 hours);

λ – device failure rate, 1/h;

T 0 – time between failures, hours.

Reliability calculation consists of finding the total failure rate λ of the device and the time between failures:

The device failure recovery time includes the time to search for a faulty element, the time to replace or repair it, and the time to check the functionality of the device.

The average recovery time T in electrical devices can be selected from the range 1, 2, 4, 6, 8, 10, 12, 18, 24, 36, 48 hours. Smaller values ​​correspond to devices with high maintainability. The average recovery time T in can be reduced using built-in control or self-diagnosis, modular design of components, accessible installation.

The value of the availability factor is determined by the formula

where T 0 – time between failures, hours.

T in – average recovery time, hours.

The reliability of the elements largely depends on their electrical and temperature operating conditions. To increase reliability, elements must be used in light duty modes, determined by load factors.

Load factor – this is the ratio of the calculated parameter of an element in operating mode to its maximum permissible value. The load factors of different elements can vary greatly.

When calculating the reliability of a device, all system elements are divided into groups of elements of the same type and the same load factors Kn.

The failure rate of the i-th element is determined by the formula

(10.3)

where K n i is the load factor, calculated in operating mode maps, or set assuming that the element operates in normal modes, Appendix D provides the values ​​of the load coefficients of the elements;

λ 0і – the basic failure rate of the i -th element is given in Appendix D.

Often, to calculate reliability, failure rate data λ 0і of analogue elements are used.

Example of device reliability calculation consisting of a purchased imported BT-85W complex and a power source developed on an elemental basis for serial production.

The failure rate of imported products is determined as the reciprocal of the operating time (sometimes the warranty period for servicing the product is taken) based on the operation of a certain number of hours per day.

The guaranteed service life of a purchased imported product is 5 years, the product will work 14.24 hours a day:

T = 14.24 hours x 365 days x 5 years = 25981 hours – time between failures.

10 -6 1/hour - failure rate.

Calculations and initial data are performed on a computer using Excel programs and are presented in tables 10.1 and 10.2. An example of the calculation is given in Table 10.1.

Table 10.1 – Calculation of system reliability

Determine the overall failure rate of the device

Then the mean time between failures according to expression (10.2) and is accordingly equal to

To determine the probability of failure-free operation over a certain period of time, we will construct a dependence graph:

Table 10.2 - Calculation of the probability of failure-free operation

A graph of the probability of failure-free operation versus operating time is shown in Figure 10.1.

Figure 10.1 – Probability of failure-free operation versus operating time

For a device, the probability of failure-free operation is usually set from 0.82 to 0.95. According to the graph in Figure 10.1, we can determine for the developed device, with a given probability of failure-free operation P(t) = 0.82, the time between failures T o = 5000 hours.

The calculation was made for the case when the failure of any element leads to the failure of the entire system as a whole; such a connection of elements is called logically sequential or basic. Reliability can be increased by redundancy.

For example. Element technology ensures average failure rate of elementary parts l i =1*10 -5 1/h . When used in the device N=1*10 4 elementary parts total failure rate l o= N*li=10 -1 1/h . Then the average device uptime To=1/lo=10 h. If you make a device based on 4 identical devices connected in parallel, then the average non-failure time will increase by N/4=2500 times and will be 25,000 hours or 34 months or about 3 years.

Formulas make it possible to calculate the reliability of a device if the initial data are known - the composition of the device, the mode and conditions of its operation, and the failure rate of its elements.