Estimation of reliability of multicomponent stress-strength inverted exponentiated Rayleigh model

Abstract

In this paper, we consider the estimation of the multicomponent reliability by assuming the inverted exponentiated Rayleigh distribution. Both stress and strength are assumed to have an inverted exponentiated Rayleigh distribution with common scale parameter. The random variable Y representing the stress experienced by the system and X representing the strength of system available to overcome the stress. The system works flawlessly only if at least s out of k (1≤s≤k) strength variables exceed the random stress. The multicomponent reliability of the system is given by Rs,k=P(atleastsof(X1,X2,…,Xk)exceedY). We estimate Rs,k by using frequentist and Bayesian approaches. Bayes estimates of Rs,k have been obtained by using Markov Chain Monte Carlo methods since joint posteriors of the parameters does not have the explicit forms. We also construct asymptotic and highest probability density credible intervals for Rs,k. The behavior of the proposed estimators is studied on the basis of estimated risks through Monte Carlo simulations. Finally, a data set is analyzed for illustrative purposes.Abbreviations: PDF: Probability Density Function; CDF: Cumulative Density Function; IER: Inverted Exponentiated Rayleigh; MLE: Maximum likelihood estimators; HPD: Highest Posterior Density; UBT: Upside down Bathtub; HNC: Head and Neck Cancer data; MCMC: Monte-Carlo Markov Chains; CP: Coverage Probability; KS: Kolmogorov - Smirnov.