Estimation of s -out-of- k stress–strength reliability under upper records: classical and Bayesian approaches

The present work elaborates on various methodologies for estimating multicomponent stress-strength reliability when the dataset is available in the form of upper records. The given model consists of k strengths, of which at least s strengths should exceed the common stress for the system to function, all adhering to a Lomax distribution. The distinct estimates are obtained under the classical and the Bayesian frameworks. Within the classical paradigm, the uniformly minimum variance unbiased estimate, the maximum likelihood estimate, and the asymptotic confidence interval are formulated. The Markov chain Monte Carlo technique and Tierney and Kadane's approximation technique under the Bayesian approach are utilized to determine point estimates, which are computed under three different loss functions: the squared error loss function, the linear exponential loss function, and the entropy loss function. For interval estimates, the highest posterior density credible interval, the Bayesian credible interval, and the credible interval using Laplace approximation are obtained. A simulation-based analysis is conducted to compare the performance of estimators based on the mean squared error, bias, interval length, and coverage probability. To assess the practical utility of the derived approach, a real-life dataset is also presented.