Reliability estimation stress–strength dependent model based on copula function using ranked set sampling

Abstract

In the stress-strength reliability analysis, it is usually assumed that both stress and strength are independent variables. In most cases, stress and strength depend on each other. In this paper, Clayton copula function is selected when stress and strength variables follow Kumaraswamy distribution and Weibull distribution respectively, and the maximum likelihood estimate and least squares estimate of unknown parameters of stress-strength dependent model are derived by two-step method under ranked set sample. At the same time, the approximate confidence intervals are constructed by using the asymptotic distribution of maximum likelihood and the parametric bootstrap percentile method. In addition, the simulation results of simple random sample and ranked set sample are compared by Monte Carlo simulation method. Finally, a real case is selected to illustrate the feasibility of the proposed model.