Reliability nonparametric Bayesian estimation for the masked data of parallel systems in step-stress accelerated life tests

The accelerated life tests with two groups of step-stress levels are considered for the parallel systems, in which the masked data are observed. We assume the power function as accelerated function for the life transformation between different stress levels, which covers the shortage of linear accelerated function. Then the estimators of coefficient vectors in accelerated function are obtained. The relationship among survival and subsurvival functions of components is discussed under a regular condition. It does not require that the discontinuity points of survival functions have to be disjointed. With the help of that transformational relationship, nonparametric Bayesian estimators of reliability functions corresponding to any components’ set are derived. Due to the complexity of masked data, a group of computational algorithms are developed to obtain the estimates. Finally, a simulated example is presented to illustrate the proposed nonparametric Bayesian method.