Time-Dependent Failure Rates

It is frequently impossible to determine time dependence because of inadequate data and limited available observation periods. In (he case of some components, e.g., electronic parts, failure rate time dependence does not exist for practical purposes. Hierefore, in such cases, constant failure rates A(t) = A = const are often used. 

The Poisson distribution for observing M events in time r is given by equation 2.5-1, where / is the failure rate estimated as M/i. This model may be used if the failure rate is time dependent rather than demand... 

This FMEA/FMECA shows failure rates that are both demand and time dependent. Adding the demand failure rates gives a train failure rate of 5. 1 E-3/demand. The sum of the time dependent failure rates is 3Ei-10/hr. A standby system such as this, does not exhibit its operability until it is actuated for which the probability is needed that the train has failed since the last use Val " are considered to be part o ng envelope and... 

Fleming et al. (1985) define this as similar to the model of Marshall and Olkin (1967) except that BPM is only for time-dependent failure rates. Equations 3.5.8-la-d are for four parameters, but the method may be generalized to n components. These parameters may be related to the MGL parameters as shown in equations 3.5.8-2a-d. 

A type of time dependence that is available in most codes evaluates the exponential distribution at specified times. This is the constant failure rate - constant repair rate approximation ( Section 2.5.2). This may not be realistic as indicated by Figure 2.5-2 in which the failure rate is not constant. Furthermore, Lapides (1976) shows that repair rates are not constant but in many casc. appear to be lognormally distributed. 

There are two reliability modeling codes used for Tech. Spec, modification to address time-dependent failure rate and repair FRANTIC developed by BNL/NRC and SOCRATES developed by BCl,/EPRI. 

Soufc. No. of failures No. of demands or service time Test interval No. of maintenances No. of dependent failures Failure rate Failures/ demand Repair lime... 

Notice that one event has units of per-demand and the others have a per-unit-time dimension. From elementary considerations, the top event can only have dimensions of per-demand (pure probability) or per-unit-time dimensions. Which dimensions they have depends on the application. If the fault tree provides a nodal probability in an event tree, it must have per-demand dimensions, if the fault tree stands alone, to give a system reliability, it must have per-unit-time dimensions. Per-unit-time dimensions can be converted to probability using the exponential model (Section 2.5.2.6). This is done by multiplying the failure rate and the "mission time" to give the argument of the exponential which if small may be... 

Since dependency analysis is not needed, we can go on to the BUILD program. Go to FTAPSUIT and select 5 "Run Build." It asks you for the input file name including extender. Type "pv.pch," It asks you for name and extender of the input file for IMPORTANCE. Type, for examle, "pv.ii . It next asks for the input option. Type "5" for ba.sic event failure probabilities. This means that any failure rates must be multiplied by their mission times as shown in Table 7.4-1. (FTAPlus was written only for option 5 which uses probabilities and error factors. Other options will require hand editing of the pvn.ii file. The switch 1 is for failure rate and repair time, switch 2 is failure rate, 0 repair time, switch 3 is proportional hazard rate and 0 repair time, and switch 4 is mean time to failure and repair time.)... 

For catastrophic demand-related pump failures, the variability is explained by the following factors listed in their order of importance system application, pump driver, operating mode, reactor type, pump type, and unidentified plant-specific influences. Quantitative failure rate adjustments are provided for the effects of these factors. In the case of catastrophic time-dependent pump failures, the failure rate variability is explained by three factors reactor type, pump driver, and unidentified plant-specific Influences. Point and confidence interval failure rate estimates are provided for each selected pump by considering the influential factors. Both types of estimates represent an improvement over the estimates computed exclusively from the data on each pump. The coded IPRDS data used in the analysis is provided in an appendix. A similar treatment applies to the valve data. 

The Landau-Zener expression is calculated in a time-dependent semiclassical manner from the diabatic surfaces (those depicted in Fig. 1) exactly because these surfaces, which describe the failure to react, are the appropriate zeroth order description for the long-range electron transfer case. As can be seen, in the very weak coupling limit (small A) the k l factor and hence the electron transfer rate constant become proportional to the absolute square of A ... 

The robustness of an assay becomes critical when evaluating its performance in a QC environment for the release of therapeutic proteins and antibodies. Over the past 5 — 10 years of product release experience in the biotech industry, assay failure rate is in the range of 5—30% depending on the method type and system suitability criteria. The types of assay failure are mainly as follows technical error (including analyst error), equipment error, and system suitability/assay acceptance errors. A periodic review of an assay s performance in the QC labs and timely feedback to the development labs are crucial to minimize the assay failure rate. A concerted effort in working with vendor is also helpful to ensure that instruments are in good condition to minimize the assay failure rate. 

Based upon results obtained from monotonic tensile experiments conducted with 0° SCS-6 SiCf/HPSN, 0790° Q/SiC, and 0° Nicalon SiCf/CAS-II composites, Shuler and Holmes38 have recommended a loading rate of 20-100 MPa/s to minimize time-dependent deformation during room temperature and elevated temperature monotonic tensile or flexural testing. Equivalent times-to-failure should be used in displacement controlled tests. 

The toughness of PMMA is observed to increase slightly with increasing loading rate. For this material, only crazing takes place so that the variation of the toughness with the loading rate reflects the influence of the time dependent craze mechanism in the failure process. 

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