Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively Type-I hybrid censored Weibull life data

In this paper, we discuss the maximum likelihood and Bayesian estimation under the progressively Type‐I hybrid censored Weibull life data. The Weibull unknown parameters and acceleration factor in the step‐stress partially accelerated life tests with competing risks are estimated based on the tampered failure rate model. The asymptotic confidence intervals and highest posterior density credible intervals are given by using the asymptotic normality theory and Gibbs sampling method. In particular, the acceptance–rejection algorithm is used to sample from the truncated density function, and the adaptive rejection algorithm is employed to sample from the log‐concave density family. Finally, a simulation study is carried out to present simulated results and compare maximum likelihood estimates with Bayesian estimates. It is concluded that Bayesian estimation performs better.