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Recent research in cumulative damage models for strengths of systems has yielded various statistical distributions that incorporate a system size variable and follow a generalized Birnbaum-Saunders form. These models can be unified as a three-parameter Birnbaum-Saunders-type family of distributions, where the third parameter arises from the size variable(More)
—The 2-parameter family of probability distributions introduced by Birnbaum & Saunders characterizes the fatigue failure of materials subjected to cyclic stresses and strains. It is shown that the methods of accelerated life testing are applicable to the Birnbaum–Saunders distribution for analyzing accelerated lifetime data, and the (inverse) power law(More)
Based on a generalized cumulative damage approach with a stochastic process describing degradation, new accelerated life test models are presented in which both observed failures and degradation measures can be considered for parametric inference of system lifetime. Incorporating an accelerated test variable, we provide several new accelerated degradation(More)
An important problem in reliability and survival analysis is that of modeling degradation together with any observed failures in a life test. Here, based on a continuous cumulative damage approach with a Gaussian process describing degradation, a general accelerated test model is presented in which failure times and degradation measures can be combined for(More)
Inference for R = P(Y < X) is considered when X and Y are independently distributed as scaled Burr type X random variables. Under this model, exact inference procedures for R cannot be found. Hence, based on the expected Fisher information matrix which is derived here, asymptotic inference procedures for R and other general functions of the parameters are(More)
Randomly right censored data often arise in industrial life testing and clinical trials. Several authors have proposed asymptotic confidence bands for the survival function when data are randomly censored on the right. All of these bands are based on the empirical estimator of the survival function. In this paper, families of asymptotic (1-alpha) 100% level(More)
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