Number of failures

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. 

In test planning, the number to be placed on test n and the number of failures rmust be deterrnined. The operating characteristic curves in Reference 18 can be used to specify the test, and to control the errors. 

Metal loss from the internal surface of the types illustrated in Figs. 11.17 and 11.18 had affected approximately 45 tubes over the previous 4 months. It was noted that metal loss along the bottom half of the tubes was more severe. Significant numbers of failures of this type had not been experienced before, although it was known that entrainment of silt in the cooling water occurred seasonally. 

A value of Cp = 1.33 would indicate that the distribution of the product characteristics covers 75% of the tolerance. This would be sufficient to assume that the process is capable of producing an adequate proportion to specification. The numbers of failures falling out of specification for various values of Cp and Cp can be determined from Standard Normal Distribution (SND) theory (see an example later for how to determine the failure in parts-per-million or ppm). For example, at Cp = 1.33, the expected number of failures is 64 ppm in total. 

This says that the failure rate is less than or equal to the inverse cumulative chi-squared distribution with confidence a and degrees of freedom equal to twice the number of failures including pseudo- failures divided by twice the time including psuedo-time. 

A lrLL[uently encountered problem requires estimating a failure probability based on the number of failures, M, in N tests. These updates are assumed to be binomially distributed (equation 2.4-10) as p r N). Conjugate to the binomial distribution is the beta prior (equation 2.6-20), where / IS the probability of failure. 

AS r.dift lad iL v iifrtion or i iiiun.J c wk-di. failure and T., i. -did- riri d independent unavailability, d<)>.-cftid number of failures, and Cdi. dijcy of top event No Phased-mission analysis possible if fault tree is input, minini j1 cutsets will be calcuijidd rnc 7r/--r. Asail.iblc Ik -ii mvuuu-(. -nicT... 

Probability of failure on demand a) Number of failures Periodic icnI ffpint. . mainten-inco rcpi rt -.. 

Operating failure rate a) Number of failures Sec la above... 

Figure 4.3-1 shows the types of information flow for processing plant. In addition to counting the number of failures for each type of component, the number of components of each type in service at... 

Tanks made from fiberglass-reinforced plastic are being increasingly used, but a number of failures have occurred. In the United Kingdom 30 catastrophic failures are known to have occurred during the period 1973-1980, and a 1996 report shows that they seem to have been continuing at a similar rate [21J. The following typify the catastrophic failures that have occurred [11] ... 

Demand-related failure rates are presented as failures per 10 demands and are for equipment that is normally static but is called upon to operate at indeterminate intervals, for example, a switch or standby generator. In this case, data are gathered that can be converted to reflect the number of failures per demand on the equipment. 

There are a number of failure modes for the three failure severities and for active and passive equipment. Figures 2.1 and 2.2 illustrate these failure modes and severities by type of equipment. 

Failure rates are computed by dividing the total number of failures for the equipment population under study by the equipment s total exposure hours (for time-related rates) or by the total demands upon the equipment (for demand-related rates). In plant operations, there are a large number of unmeasured and varying influences on both numerator and denominator throughout the study period or during data processing. Accordingly, a statistical approach is necessary to develop failure rates that represent the true values. 

This article presents an overview of the causes and frequency of failures for submarine and cross-country pipelines handling oil and natural gas. It gives several tables and charts which include information on the type of pipeline, the cause of the failure, and the number of failures. Data from failures in the US and the North Sea are included. Failure rates based on the total length of piping are calculated. 

This data collection effort was concentrated on the following components because of their extensive populations and repair action documentation pumps, valves, electrical positioning devices, electric motors, and drives. For each component type, preface pages and data summary tables are provided. Separate data summary tables are provided for each component type and are structured in a format that allows for the inclusion of the number of pieces of operating equipment, the total number of operating hours, total number of failures, and hourly failure rates with upper and lower bounds. 

Number of demands Number of failures Value of Alfa ... 

Statistical Methods for Nonelectronic Reliability, Reliability Specifications, Special Application Methods for Reliability Prediction Part Failure Characteristics, and Reliability Demonstration Tests. Data is located in section 5.0 on Part Failure Characteristics. This section describes the results of the statistical analyses of failure data from more than 250 distinct nonelectronic parts collected from recent commercial and military projects. This data was collected in-house (from operations and maintenance reports) and from industry wide sources. Tables, alphabetized by part class/ part type, are presented for easy reference to part failure rates assuminng that the part lives are exponentially distributed (as in previous editions of this notebook, the majority of data available included total operating time, and total number of failures only). For parts for which the actual life times for each part under test were included in the database, further tables are presented which describe the results of testing the fit of the exponential and Weibull distributions. 

The Reliability of Emergency Diesel Gerterators at U.S. Nuclear Power Plants Nuclear Number of failures and demands lor 154 diesels Failure to start and failure to load and run data for Diesel Generators 106. 

NUMBER AND TYPE OF RECORDS Number of failures and demands for 154... 

Opening segments of the IP2 PRA data analysis section describe the definitions of terms and concepts employed, the assumptions made, and limitations recognized during the data base construction. A set of 39 plant-specific component failure mode summaries established the basis for component service hour determinations, the number of failures, and the test data source for each failure mode given for each component. Generic data from WASH-1400, IEEE Std 500, and the LER data summaries on valves, pumps, and diesels were combined with plant-specific failure data to produce "updated" failure information. All the IP2 specialized component hardware failure data, both generic and updated, are contained in Table 1.5.1-4 (IP3 1.6.1-4). This table contains (by system, component, and failure mode) plant-specific data on the number of failures and service hours or demands. For some components, it was determined that specifications of the system was warranted because of its impact on the data values. 

Rates of equipment failure are calculated by dividing the number of failures for an equipment population by its total exposure hours or total number of demands. The following key types of information, therefore, are needed to develop plant-specific failure rate data ... 

The records display a pattern of maintenance and repair that is rarely visible elsewhere and can show less severe equipment damage trends that can lead to total failure. As such, it is possible to determine the total number of failures and failure severity. 

Once it is determined that data exist, the next step is to begin the collection process. If sufficient thought and training is provided in the development and operation of the maintenance and operating reporting systems, much of the collection process can be automated. Automation assumes that a well-thought-out taxonomy is in place. If this is not the case, then an analyst must collect and review the records manually. In either case, the analyst must collect data from the plant sources previously discussed in order to determine the numerator (number of failures within a unique plant equipment population), and denominator (the operating time or number of demands for the equipment) of the equation to calculate failure rates. 

Various forms have been developed to collect plant data. Figures 6.1 and 6.2 are generic forms published in EuReDatA Project No. 3. The Specimen Inventory form, Figure 6.1, is designed to collect data needed to establish the equipment description and total equipment population. Many maintenance systems offer some of these data, but usually not in a useful format or to the extent desired. The Specimen Event or Failure Report form, Figure 6.2, is used to capture failure event data that, when summed, will allow determination of the failure rate numerator—the number of failures within a unique plant population. 

Due to such subtleties, the need to develop well-defined basic events, failure modes, and equipment boundaries prior to data encoding cannot be overemphasized. Familiarity with failure definitions and failure severities will be extremely helpful to the analyst. Figures 2.1 and 2.2, reprinted from IEEE Std. 500-19845, list a large number of failure modes by failure severity and may help encode failures. IPRDS also contains helpful information on failure encoding. Information on some equipment boundaries may be found in the Data Tables in Section 5.5. 

Figure 6.4 Example Failure Compilation Worksheet Note The format used to enter failure data is X[Y,Z], where X is the total number of failures, Y is the number of demand-related failures, and Z is the number of time-related failures. From Science Applications International Corporation.

The data presented in Figure 6.10 illustrate the need for complete information. As it stands, presented as failures per 10 hours, it is useless. These data are based on the total number of failures in 14.5 years of service for a system with an unknown number of pipe fittings. To give the data value, the number of fittings in the system must be known in order to derive usable failure rates per 10 hours per fitting. 

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