On multicomponent stress-strength reliability under competing risk

An s-out-of-k type of multi-component system is handled in the case of strength components exposed to common random stress. In this reliability scheme, random stress has been considered in the competing risk setup. Each stress and strength component is assumed to follow the general scale family of distributions. Classical inferences are obtained using the maximum likelihood method with the corresponding approximate confidence intervals. Bootstrap confidence intervals are also provided using the logit transformation method as an alternative to the asymptotic confidence intervals. Further, Bayesian inferences and their corresponding highest posterior density credible intervals with the conjugate priors are obtained using Lindley's approximation method and Monte Carlo Markov chains. In Bayesian process, different loss functions are considered as symmetric and asymmetric. The theoretical outcomes' performance is evaluated with simulated data sets and real-data examples.