On the reliability characteristics of the standard two-sided power distribution

Abstract

In this study, the standard two-sided power (STSP) distribution is considered with regard to statistical reliability analysis in detail. For this purpose, along with the reliability and hazard functions of the distribution, particular reliability indices that are useful in maintenance and replacement policies are obtained and they are evaluated with their plots. The STSP distribution is classified based on aging according to various cases of its parameters. Then, we studied the classical and Bayesian estimations of the reliability and hazard functions. In Bayesian estimation, symmetric and different asymmetric loss functions are considered. For obtaining the Bayes estimates, Monte Carlo Markov Chain simulation using the Gibbs algorithm is performed. Various simulation schemes are performed for comparing the performances of the estimators. Further, the Bayesian predictions of the future observations based on the observed samples are obtained. A real data example is used to illustrate the theoretical outcomes.

Multicomponent stress-strength reliability estimation for the standard two-sided power distribution

“…The squared error loss function (SELF) is the most commonly used loss function because it is symmetrical and it provides equal distance to the losses through overestimation and underestimation. The performances of the Bayes estimations under the different loss functions are handled by [6] and it is observed that there are no significant differences between them. Therefore, we propose to use SELF as a symmetrical loss function.…”