Advanced Censoring Schemes for Statistical Inference of Reliability in Engineering Contexts

Abstract

In practice, systems that are exposed to rigorous operational environments commonly malfunction. Researchers have yet to fully examine the crucial idea that system failure frequently occurs when these strict operating constraints are reached. This study covers this gap in an analysis of the multi-stress-strength model $\Upsilon=P(U<W<V)$, in which stresses ($U$  $\& V$) and strength ($W$) are defined using the exponentiated Weibull distribution. From an advanced censoring method called generalized progressive hybrid censoring, we obtain the point and interval estimators of $\Upsilon$. The maximum likelihood and Bayesian estimators of $\Upsilon$ under both the symmetric and asymmetric loss functions are obtained. We employ Markov chain Monte Carlo techniques due to the complexity of Bayesian estimators. We also provide Bayesian credible intervals, bootstrap-t intervals, and percentile bootstrap intervals. A simulation study is conducted to evaluate the efficacy of the proposed estimates. 
Numerical results lead us to the conclusion that the Bayesian estimates based on informative priors outperform classical estimates in terms of biases, mean squared error, and coverage probabilities. Real progressively censored engineering data application of real data is presented to demonstrate the efficacy of the proposed estimators.