Inference and physics applications of the logistic-exponential parameters using adaptive progressively hybrid censoring

Abstract

To save test time and costs and to improve the efficiency of the experiments, an adaptive Type-II progressively hybrid censored technique has been developed. Besides two standard methods of parameter inference, namely, likelihood and product of spacing approaches, the Bayesian method is further used in this study to explore the issue of estimating model parameters, reliability, and hazard rate functions of the logistic-exponential distribution via the adaptive Type-II progressively hybrid censored mechanism. The relevant approximate confidence intervals for unknown parameters of life are also acquired using the normal approximations of the frequentist estimators. Under the squared error loss function, Bayesian estimators are obtained using independent gamma priors. Because of the complicated form of the posterior distributions, the Bayes estimators and associated credible intervals cannot be computed analytically, but they can be examined by employing Monte Carlo Markov Chain methodologies. The actual performance of the offered estimation procedures is examined using Monte Carlo simulations. Four optimality criteria are also utilized to select the optimum censoring scheme. Two physical applications are considered to show the operability and applicability of the various methods. The numerical findings show that our proposed methodologies perform well and demonstrate that the offered estimates are satisfactory in practice.