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Data collection and empirical reliability models Data Collection and Empirical Reliability Models The primary problem addressed in this section is the selection and specification of the most appropriate reliability and maintainability models. This requires the collection and analysis of failure and repair data in order to empirically fit the model to the observed failure or repair process. Obviously, the collection and analysis of failure or repair data requires the use of inferential statistics. There are two approaches to fit reliability distribution to the failure or repair data. They are discussed below: 1. To fit a theoretical distribution, such as exponential, Weibull, normal, lognormal etc. This is the most preferred approach. 2. To derive, directly from the data, an empirical reliability function or hazard rate function. This approach is discussed below. Failure or Repair Data Collection Prior to fitting any reliability model, it is important to record or collect failure data. The generation or observation of failure (or repair) times can be represented by n , t , , t t 2 1 , where, i t represents the time of failure of the th i unit (or in the case of repair data, the th i observed repair time). It is assumed that each failure represents an independent sample from the same population. The population is the distribution of all possible failure times and may be represented by ) ( t f , ) ( t R , ) ( t F or ) ( t . The problem is to determine the best failure distribution implied by the n failure times comprised in the sample. In all cases, the sample is assumed to be a simple random sample. Failure data may be classified in several ways as given below: Operational versus test-generated failures Grouped versus ungrouped data Large samples versus small samples Complete versus censored data Sources of failure times are either field data reflecting the normal use of the component, or failures observed from some reliability testing. For large sample sizes, grouping data into intervals may be preferred. 1
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Data collection and empirical reliability models Testing may result in small sample sizes because of time and resource limitations, but they are likely to be more precise and timely than field data. Field data, on the other hand, will provide large samples, and it will reflect the actual operating environment. A common problem in generating reliability data is censoring. Censoring occurs when the data are incomplete because, units are removed from consideration prior to their failure or because the test is completed prior to all units failing. Units may be removed, when they fail because of other failure modes than the one being measured. Censoring may be further categorized as follows: Censored Data I. Singly censored data : All units have the same test time, and test is concluded before all units failed.
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