Reliability estimation of [formula omitted]-out-of-[formula omitted] system in a multicomponent stress–strength dependent model based on copula function

Abstract

In reliability analysis of the traditional stress–strength models, the stress and strength are often assumed to be independent variables. However the case where this two variables are dependent is more realistic in engineering. To evaluate multicomponent system reliability in such case, the stress and strength are assumed to have dependent Kumaraswamy variable and unit Gompertz variable based on Clayton copula. Then the maximum likelihood (ML), least squares (LS), maximum product of spacings (MPS), Cramér–von-Mises and LS (CL) hybrid estimates of the unknown parameters and system reliability are derived using two-step estimation procedure under order sample. Also the asymptotic distribution of the ML estimation and the parametric bootstrap percentile method are used to construct approximate confidence intervals (CI). Moreover, Monte Carlo simulations are implemented to compare the performance of the proposed methods. Finally, one real data set is analyzed for illustrative purposes.