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Bayesian estimation of the parameters, reliability and hazard rate functions of mixtures under accelerated life tests. (English) Zbl 1101.62091

Summary: Suppose that the lifetimes of the first \(r_i\) items to fail in a random sample of size \(n_i\) (type-II censoring) at stress \(v_i\), are distributed according to a finite mixture model. The components of the model may represent different causes of failure and include, among others, the Weibull, compound Weibull, Pareto, power function, Gompertz and compound Gompertz distributions. In this paper, the Bayes estimates of the parameters, reliability and hazard rate functions are computed by using an approximate form due to L. Tierney and J. B. Kadane [Accurate approximations for posterior moments and marginal densities. J. Am. Stat. Assoc. 81, 82–86 (1986; Zbl 0587.62067)]. Special attention is paid to a mixture of two Weibull components where the mean squared errors of the Bayes estimators are compared with their maximum likelihood counterparts via a simulation study.

MSC:

62N05 Reliability and life testing
62F15 Bayesian inference
62N02 Estimation in survival analysis and censored data

Citations:

Zbl 0587.62067
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References:

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