Reliability analysis for multi-level stress testing with Weibull regression model under the general progressively Type-II censored data

In this article, we discuss the problem of point and interval estimates of the Weibull(Extreme value) regression model in a multi-level stress test under the general progressive Type-II censoring. The maximum likelihood and Bayes methods are used for estimating the unknown parameters as well as some lifetime parameters (reliability, hazard rate function and the mean time to failure (MTTF)) at four fixed stress levels. We derive the maximum-likelihood estimates (MLEs) of regression parameters through the Conjugate Gradient (CG) method and their asymptotic variance-covariance matrix. Furthermore, we also obtain the MLEs' changing tendency of the lifetime parameters along with logarithmic stress level. We propose to apply the Metropolis-Hasting (MH) algorithm to carry out a Bayesian estimation procedure. The Bayesian estimates are obtained under squared error loss (SEL) function, which can be easily extended to other loss function situations. Meanwhile, we obtain the Bayes estimates' changing tendency of the lifetime parameters along with logarithmic stress level. Finally, one real data set has been analyzed for illustrative purposes.