Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation

Abstract

It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. The purpose of this article is to derive inference for multi reliability where stress-strength variables follow unit Kumaraswamy distributions based on the progressive first failure. Therefore, this article deals with the problem of estimating the stress-strength function, R when X,Y, and Z come from three independent Kumaraswamy distributions. The classical methods namely maximum likelihood for point estimation and asymptotic, boot-p and boot-t methods are also discussed for interval estimation and Bayes methods are proposed based on progressive first-failure censored data. Lindly’s approximation form and MCMC technique are used to compute the Bayes estimate of R under symmetric and asymmetric loss functions. We derive standard Bayes estimators of reliability for multi stress–strength Kumaraswamy distribution based on progressive first-failure censored samples by using balanced and unbalanced loss functions. Different confidence intervals are obtained. The performance of the different proposed estimators is evaluated and compared by Monte Carlo simulations and application examples of real data.

Keywords

• multi stress-strength
• progressive first failure censoring
• balanced loss functions
• Lindley’s approximation
• Markov Chain Monte Carlo
• symmetric and asymmetric loss functions