Analysis for Xgamma Parameters of Life under Type-II Adaptive Progressively Hybrid Censoring with Applications in Engineering and Chemistry

Abstract

Censoring mechanisms are widely used in various life tests, such as medicine, engineering, biology, etc., as they save (overall) test time and cost. In this context, we consider the problem of estimating the unknown xgamma parameter and some survival characteristics, such as reliability and failure rate functions in the presence of adaptive type-II progressive hybrid censored data. For this purpose, the maximum likelihood and Bayesian inferential approaches are used. Using the observed Fisher information under s-normal approximation, different asymptotic confidence intervals for any function of the unknown parameter were constructed. Using the gamma flexible prior, Bayes estimators against the squared-error loss were developed. Two procedures of Bayesian approximations—Lindley’s approximation and Metropolis–Hastings algorithm—were used to carry out the Bayes estimates and to construct the associated credible intervals. An extensive simulation study was implemented to compare the performance of the different methods. To validate the proposed methodologies of inference—two practical studies using datasets that form engineering and chemical fields are discussed.

Keywords

• adaptive progressively hybrid censoring
• Bayes estimator
• maximum likelihood estimator
• Metropolis–Hasting algorithm
• reliability characteristics
• xgamma distribution