Abstract
In this paper, we consider the problem of estimating stress-strength reliability for inverse Weibull lifetime models having the same shape parameters but different scale parameters. We obtain the maximum likelihood estimator and its asymptotic distribution. Since the classical estimator doesn’t hold explicit forms, we propose an approximate maximum likelihood estimator. The asymptotic confidence interval and two bootstrap intervals are obtained. Using the Gibbs sampling technique, Bayesian estimator and the corresponding credible interval are obtained. The Metropolis-Hastings algorithm is used to generate random variates. Monte Carlo simulations are conducted to compare the proposed methods. Analysis of a real dataset is performed.
Highlights
The inference of stress-strength reliability in statistics is an important topic of interest
The first to the fifth row corresponds the results for maximum likelihood estimator (MLE), approximate maximum likelihood estimator (AMLE), bootstrap method (Boot-p) method, bootstrap-t method (Boot-t) method and Bayes estimates respectively
Based on Equations (14) and (29), we provide that the MLE and AMLE of R are 0.7576 and 0.7571
Summary
The inference of stress-strength reliability in statistics is an important topic of interest. In the stress-strength modeling, R = P(Y < X ) is a measure of component reliability. Classical and Bayesian estimation of reliability in a multicomponent stress-strength model under a general class of inverse exponentiated distributions was researched by Ref. [6] studied classical and Bayesian estimation of reliability in multicomponent stress-strength model under Weibull distribution. The inverse Weibull distribution has the ability to model failure rates, which is quite common in reliability and biological studies. We focus on the estimation of the stress-strength reliability R = P(Y < X ), where X and Y follow the inverse Weibull distribution. The layout of this paper is organized as follows: in Section 2, we introduce the distribution of the inverse Weibull.
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