Bayesian and classical inference of reliability in multicomponent stress-strength under the generalized logistic model

In this paper, a multicomponent system which has k independent and identical strength components X1,X2,…,Xk is considered. Each component is exposed to a common random stress Y when distributions are generalized logistic. This system is operating or failing only if at least s out of k (1≤s≤k) strength variables exceeds the random stress. The Bayesian and classical inferences of multicomponent stress-strength reliability under the generalized logistic distribution are studied. The small sample comparison of the reliability estimates is made through Monte Carlo simulation and asymptotic confidence interval is obtained based on maximum likelihood estimation. Also the highest posterior density credible interval is calculated based on Bayesian estimation with Gibbs and Metropolis Hastings algorithms. Finally analysis of a real data set has been presented for illustrative purposes too.