Inference for Coherent Systems with Weibull Components Under a Simple Step-Stress Model

Coherent systems are widely studied in reliability experiments. Under the assumption that the components of a coherent system follow a two-parameter Weibull distribution, maximum likelihood inference for n-component coherent systems with known signatures under a simple step-stress model is discussed in this paper. The detailed steps of the stochastic expectation maximization algorithm under this setup are also developed to obtain estimates of the model parameters. Asymptotic confidence intervals for the model parameters are constructed using the observed Fisher information matrix and missing information principle. Parametric bootstrap approach is used also to construct confidence intervals for the parameters. A method based on best linear unbiased estimators is developed to provide initial values that are needed for numerical computation of maximum likelihood estimates. The performance of the methods developed is assessed through an extensive Monte Carlo simulation study. Finally, two numerical examples are presented for illustrative purpose.