Copula-based Reliability Analysis for Multicomponent System Stress-Strength Model under Progressively Censoring

Abstract

In reliability analysis, the stress-strength model is of importance and interest issue. Usually, the stress variable and the strength variable are assumed to be independent. However, such an assumption may be unrealistic in some applications. In this paper, we consider the statistical analysis of multicomponent system stress-strength model when the stress and strength are dependent variables, and the dependency is modeled by two different copula functions. We obtain the maximum likelihood estimates of the model parameters and the expression for the probability R=P(Y<X). Confidence intervals are constructed based on the asymptotic normality of maximum likelihood estimate. In addition, to test the dependence between the stress and strength variables, we discuss the likelihood ratio tests for hypotheses of interest. Finally, simulation studies and one real data example are provided to support the proposed model and methods, and to examine the performance of estimators and testing.