HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.2, pp.587-605, 2022 (Journal Indexed in SCI)
A system of k components that functions as long as at least s components survive is termed as s-out-of-k:G system, where G refers to "good". In this study, we consider the s-outof-k:G system when X-1, X-2, ..., X-k are independent and identically distributed strength components and each component is exposed to common random stress Y when the underlying distributions all belong to the standard two-sided power distribution. The system is regarded as surviving only if at least s out of k (1 < s < k) strengths exceed the stress. The reliability of such a system is the surviving probability and is estimated by using the maximum likelihood and Bayesian approaches. Parametric and nonparametric boot-strap confidence intervals for the maximum likelihood estimates and the highest posterior density confidence intervals for Bayes estimates by using the Markov Chain Monte Carlo technique are obtained. A real data set is also analyzed to illustrate the performances of the estimators.