Nonparametric Bayesian reliability analysis of masked data with dependent competing risks.

The characteristic of dependence widely exists among different failure modes of systems, which brings extra difficulty for the reliability analysis. In this paper, a nonparametric Bayesian analysis method is proposed for dependent masked data under accelerated lifetime test with censoring. Using the copula function, the dependence structure is constructed among the competing failure modes which can be viewed as the components in a series system. By establishing the transformational relationship between the subsurvival functions and the survival functions, the estimators of components’ reliability can be derived from the nonparametric Bayesian estimators of the subsurvival functions when a Dirichlet multivariate process prior is considered. A simulation study is given to illustrate the effectiveness of the proposed methods and the influence of the degree of dependence on the performance of the estimation procedure. It is shown that the dependence between failure modes should not be ignored because ignoring the dependence may lead to serious errors. A numerical example based on a life test of rolling ball bearings is presented as an application of the proposed methodology.