Reliability Testing for Small Sample Censored and Missing Data with Applications in Engineering
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In reliability engineering, the inference problem for complete samples and large data sets are commonly rare events. Typically, missing data are present and censoring has been applied. Moreover, samples are frequently small for many reasons (e.g. expensive observations or rare event structure or the failure process).
In this seminar we will discuss recent results on the exact likelihood ratio tests of scale and homogeneity hypotheses when samples are from exponential, Erlang, gamma, Weibull and generalized gamma distributions. Asymptotical tests are typically oversized and thus inappropriate for small samples. We will focus on the reliability prediction when some data is missing or is censored. The reliability prediction when some data is missing plays a major role in many reliability programs (e.g. for a variety of reasons over 90% of the data in the Reliability Analysis Center does not have the individual failure times recorded).
Inference for Type I and progressively Type II censored data from exponential distribution will be provided. The competing risk model, often modelled by the mixture, will be also mentioned and difference between the upper and lower contamination for the two component mixture alternative will be explained. The real data examples will illustrate the topics discussed.