Failure rate

One of the fundamental steps in carrying out a probabilistic analysis is choosing the failure rates of components. In principle, specific plant figures should be used, that is obtained by the operating experience of the plant itself When this is not possible, data of similar plants should be used or, in the extreme case, generic applicable data. 

IAEA (1996) Procedures for conducting probabilistic safety assessments of nuclear power plants (Level 3) , Safety series 50-P-12. 

NUREG (1987) Reactor risk reference document , NUREG 1150. 

Petrangeli, G. and Zaffiro, C. (1985) Regulatory implications of source term studies , IAEA-SM-281/53. 

(1997) Reliability, Maintainability and Risk. Butterworth-Heinemann. 

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Early failures may occur almost immediately, and the failure rate is determined by manufacturing faults or poor repairs. Random failures are due to mechanical or human failure, while wear failure occurs mainly due to mechanical faults as the equipment becomes old. One of the techniques used by maintenance engineers is to record the mean time to failure (MTF) of equipment items to find out in which period a piece of equipment is likely to fail. This provides some of the information required to determine an appropriate maintenance strategy tor each equipment item. 

A considerable assumption in the exponential distribution is the assumption of a constant failure rate. Real devices demonstrate a failure rate curve more like that shown in Eigure 9. Eor a new device, the failure rate is initially high owing to manufacturing defects, material defects, etc. This period is called infant mortaUty. EoUowing this is a period of relatively constant failure rate. This is the period during which the exponential distribution is most apphcable. EinaHy, as the device ages, the failure rate eventually increases. 

Fig. 9. Failure rate curve for r eal components. A, infant mortality B, period of approximately constant p. and C, old age.

Table 3 lists typical failure rate data for a variety of types of process equipment. Large variations between these numbers and specific equipment can be expected. However, this table demonstrates a very fundamental principle the more compHcated the device, the higher the failure rate. Thus switches and thermocouples have low failure rates gas—Hquid chromatographs have high failure rates. 

Table 3. Failure Rate Data for Process Hardware ...

Fig. 10. Reliability and failure probability computations for components ia (a) series linkages where the failure of either component adds to the total system failure, and (b) parallel linkages where failure of the system requires the failure of both components. There is no convenient way to combine the failure rate...

The numbers computed usiag this approach are only as good as the failure rate data for the specific equipment. Frequendy, failure rate data are difficult to acquire. For this case, the numbers computed only have relative value, that is, they are useful for determining which configuration shows iacreased reUabiUty. 

Figure 11 shows a system for controlling the water dow to a chemical reactor. The dow is measured by a differential pressure (DP) device. The controller decides on an appropriate control strategy and the control valve manipulates the dow of coolant. The procedure to determine the overall failure rate, the failure probabiUty, and the reUabiUty of the system, assuming a one-year operating period, is outlined hereia. 

These process components are related in series, thus if any one of the components fails, the entire system fails. The failure rates for the various components are given in Table 3. The rehabiflty and failure probabiflty are computed for each individual component using equations 1 and 2 and assuming a one-year period of operation. The results are shown in Table 4. 

Component Failure rate, p.,faults/yr Rehabihty,- = e F ailureprob abiflty, P = - R... 

The overall failure rate is computed usiag the definition of the rehabiUty, equation 1. 

In usiag these failure rates an exponential distribution for time to failure was assumed. Such an assumption should be made with caution. Parallel Systems. A parallel (or redundant) system is not considered to be ia a failed state unless all subsystems have failed. The system rehabihty is calculated as... 

Failure Rate and Hazard Function. The failure rate is defined as the rate at which failures occur in a given time interval. Considering the time interval [/, the failure rate is given by... 

The ha2ard function is defined as the limit of the failure rate as the interval of time approaches 2ero. The resulting ha2ard function b(i) is defined by... 

The ha2ard function can be interpreted as the instantaneous failure rate. The quantity b(i)At for small A/ represents the probabiUty of failure in the interval At, given that the device was surviving at the beginning of the interval. 

The failure rate changes over the lifetime of a population of devices. An example of a failure-rate vs product-life curve is shown in Figure 9 where only three basic causes of failure are present. The quaUty-, stress-, and wearout-related failure rates sum to produce the overall failure rate over product life. The initial decreasing failure rate is termed infant mortaUty and is due to the early failure of substandard products. Latent material defects, poor assembly methods, and poor quaUty control can contribute to an initial high failure rate. A short period of in-plant product testing, termed bum-in, is used by manufacturers to eliminate these early failures from the consumer market. 

The ha2ard function is a constant which means that this model would be appHcable during the midlife of the product when the failure rate is relatively stable. It would not be appHcable during the wearout phase or during the infant mortaHty (early failure) period. 

Example 4. A particular microprocessor (MPU) is assigned for a fuel-injection system. The failure rate must be estimated, and 100 MPUs are tested. The test is terrninated when the fifth failure occurs. Failed items are not replaced. This type of testing, where n is the number placed on test and ris the number of failures specified, is termed a Type II censored life test. 

From equation 8 it was shown that the chance of surviving the mean life was 36.8% for the exponential distribution. However, this fact must be used with some degree of rationaHty in appHcations. For example, in the above situation the longest surviving MPU that was observed survived for 291.9 hours. The failure rate beyond this time is not known. What was observed was only a failure rate of A = 1.732 x lO " failures per hour over approximately 292 hours of operation. In order to make predictions beyond this time, it must be assumed that the failure rate does not increase because of wearout and... 

Low Flow Operation. The optimum operation of a pump is near the best efficiency point. Some manufacturers curves indicate the minimum allowable continuous stable flow (MCSF) limits for every pump (43). In the 1980s, the processing industry experienced a reduction in flow requirement as a result of business downturn and installation capacity downsizing. The pumping equipment, however, was generally not replaced by smaller pumps, but was forced to operate at reduced flow rates, often below allowable MCSF. This has resulted in increased failure rates and reduced pump component life. 

For many years the usual procedure in plant design was to identify the hazards, by one of the systematic techniques described later or by waiting until an accident occurred, and then add on protec tive equipment to control future accidents or protect people from their consequences. This protective equipment is often complex and expensive and requires regular testing and maintenance. It often interferes with the smooth operation of the plant and is sometimes bypassed. Gradually the industry came to resize that, whenever possible, one should design user-friendly plants which can withstand human error and equipment failure without serious effects on safety (and output and emciency). When we handle flammable, explosive, toxic, or corrosive materials we can tolerate only very low failure rates, of people and equipment—rates which it may be impossible or impracticable to achieve consistently for long periods of time. 

Once the fault tree is constructed, quantitative failure rate and probability data must be obtained for all basic causes. A number of equipment failure rate databases are available for general use. However, specific equipment failure rate data is generally lacking and. 

Human error probabilities can also be estimated using methodologies and techniques originally developed in the nuclear industry. A number of different models are available (Swain, Comparative Evaluation of Methods for Human Reliability Analysis, GRS Project RS 688, 1988). This estimation process should be done with great care, as many factors can affect the reliability of the estimates. Methodologies using expert opinion to obtain failure rate and probability estimates have also been used where there is sparse or inappropriate data. 

In some instances, plant-specific information relating to frequencies of subevents (e.g., a release from a relief device) can be compared against results derived from the quantitative fault tree analysis, starting with basic component failure rate data. 

The Failure rate and repair rate are consistent for each equipment item. 

Nonelectronic Parts Reliability Data I99P (NPRD-91) and Eailure Mode/Mechanism Distributions 1991 s (fMD-91) provide failure rate data for a wide variety of component (part) types, including mechanical, electromechanical, and discrete electronic parts and assemblies. They provide summary failure rates for numerous part categories by quality level and environment. 

If severity increases to, say, complete failure with probable severe injury and/or loss of life S = 9), the designer should reduce occurrence below the level afforded by two independent characteristics protecting against the fault. If each is designed to, then this implies a failure rate of ... 

Equation 4.34 represents probably one of the most important theories in reliability (Carter, 1986). The number of load applieations defines the useful life of the eompo-nent and is of appropriate eoneern to the designer (Bury, 1974). The number of times a load is applied has an effeet on the failure rate of the equipment due to the faet that the probability of experieneing higher loads from the distribution population has inereased. Eaeh load applieation in sequenee is independent and belongs to the same load distribution and it is assumed that the material suffers no strength... 

It is evident that an approximate — 1.5cr shift ean be determined from the data and so the Cpi value is more suitable as a model. Using the graph on Figure 6, whieh shows the relationship Cp, (at 1.5cr shift) and parts-per-million (ppm) failure at the nearest limit, the likely annual failure rate of the produet ean be ealeulated. The figure has been eonstrueted using the Standard Normal Distribution (SND) for various limits. The number of eomponents that would fall out of toleranee at the nearest limit, is potentially 30 000 ppm at = 0.62, that is, 750 eomponents of the 25 000 manufaetured per annum. Of eourse, aetion in the form of a proeess eap-ability study would prevent further out of toleranee eomponents from being produeed and avoid this failure rate in the future and a target Cp = 1.33 would be aimed for. 

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