Classical, Bayesian, and generalized inferences of the reliability of a multicomponent system with censored data

In this study, we discuss the classical, Bayesian, and generalized inference of the reliability parameter Rs,k=Pr(At least <i>s</i> of the (X1,X2,…,Xk) exceed Y)= Pr(Xk−s+1:k&gt;Y) of an <i>s</i>-out-of-<i>k</i>:<i>G</i> system with strength components X1,X2,…,Xk subjected to a common stress <i>Y</i> whose probability densities are independent two-parameter <i>general class of exponentiated inverted exponential distributions</i>. These statistical analyses are carried out based on the progressively type-II right censored data with uniformly random removals. Under squared error and LINEX loss functions, Bayes estimates are developed by using Lindley's approximation and the Markov Chain Monte Carlo method due to the lack of closed forms of the posterior distributions. Generalized inferences are performed based on the generalized variable method. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed. Comparison and contrast among the classical, Bayesian, and generalized inferences of the reliability parameter in the multicomponent stress-strength model are performed.