Reliability Estimation in a Multicomponent Stress-Strength Model Based on Inverse Weibull Distribution

Reliability inference in a multicomponent stress-strength (MSS) model is studied when components are exposed to a specific random stress. Stress and strength variables are assumed to follow inverse Weibull distributions with different scale and same shape parameter. A s-out-of-k:G system fails if s or more components simultaneously become inoperative. Different estimates of MSS reliability are obtained from frequentist and Bayesian viewpoint. In particular Bayes estimates are evaluated from Lindley method and Metropolis-Hastings algorithm. Unbiased estimation is also considered when shape parameter is known. We construct asymptotic intervals and obtain corresponding coverage probabilities using observed information matrix. In sequel credible intervals are also obtained. A simulation study is performed to examine the estimated risks of proposed estimation methods and analyze two numerical examples from application viewpoint. Finally, optimal plans are discussed for the multicomponent system.