Analysis Simple Step Stress Model under Competing Extension Weibull Failure Distribution Based on Progressive Type-II Censoring

Abstract

Accelerated life testing (ALT), a procedure utilized in reliability analysis, allows testing units to be subject to increasingly elevated grades of stress during an experiment.Stepstress tests are a subclass of accelerated tests in which the stress levels rise consecutively at prearranged cycles, consequently, the researcher might find out results more swiftly than in ordinary working settings about the parameter of the lifetime distribution. Moreover, there are frequently multiple fatal causes for a test element's failure, for instance, technical or electric. These causes are recognized as "competing risks". The purpose of the analysis is to assess simple step stress accelerated life testing (SS-ALT) with competing Risks originating from the extension of Weibull distribution by applying a progressive Type-II censoring scheme. In this case, under the assumption of a cumulative exposure model, the authors successfully obtained the Bayes estimates (BEs) and maximum likelihood estimators (MLEs) of the undetermined average parameters of the various causes. For Bayesian computations, the squared error loss functions are considered. Additionally, the estimators' asymptotic variance-covariance matrix was created. Additionally, credible intervals and asymptotic confidence intervals (CIs) are provided. For a large sample size, the CIs of the unidentified parameters are developed. A numerical study is also involved to exhibit the accuracy and variability of various estimators for several sample sizes. An example is being used to exemplify the inference method that's also considered here. This study concludes that the mean lengths of credible intervals and asymptotic confidence intervals get shorter as the number of failures rises. The credible interval technique is suggested, nevertheless.