Statistical Analysis of Inverse Weibull based on Step-Stress Partially Accelerated Life Tests with Unified Hybrid Censoring Data

Hassan, Amal Soliman; Hagag, Abd ELwahab; Metwally, Nader; Sery, Omar Hussein

doi:10.21608/cjmss.2024.319502.1072

Statistical Analysis of Inverse Weibull based on Step-Stress Partially Accelerated Life Tests with Unified Hybrid Censoring Data

Document Type : Original Article

Authors

¹ Department of Mathematical Statistics Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt

² Department of Mathematical Statistics, Faculty of Commerce, AL-AZHAR University, Cairo, Egypt

10.21608/cjmss.2024.319502.1072

Abstract

Accelerated life testing (ALT) is a primary method for rapidly evaluating product reliability. This paper focuses on statistical inference for the invertedWeibull distribution under a step-stress partially ALT (SSPALT) model with a unified hybrid censoring scheme. This censoring scheme enhances the efficiency of statistical analysis and reduces overall test time. The inverted Weibull distribution is widely used in reliability engineering to model various failure mechanisms, including infant mortality, wear-out periods, and general life testing scenarios. For the purpose of estimating the model parameters and acceleration factor, the maximum likelihood approach is applied along with the maximum product of the spacing procedure to generate point and interval estimates. The squared error loss function is used to calculate the Bayes point estimates based on the assumption of independent gamma priors. Since Bayesian estimators cannot be derived analytically, we employ the Markov chain Monte Carlo technique. This method allows us to construct credible intervals for the involved parameters of interest and the Bayesian estimates themselves. Asymptotic confidence intervals and confidence intervals using bootstrap-p and bootstrap-t methods are constructed. Moreover the performances of the various estimators of the SSPALT are compared through the simulation study. Based on the numerical results, the Bayes estimates are better than the corresponding other estimates with respect to smallest precision measures. The lengths of creditable interval for Bayesian estimates less than the approximate and Bootstrap confidence intervals for different sample sizes, observed failures, and censoring schemes, in most cases. Additionally, given different sample sizes, reported failures, and censoring techniques, the percentile Bootstrap confidence intervals give more accurate outcomes than Bootstrap-t in most cases. A real data set is used to illustrate the results derived.

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