Stress-strength reliability estimation for bivariate copula function with rayleigh marginals

In the classical stress-strength reliability model, the majority of the contributions focus on estimating system reliability with independent assumptions of stress and strength. In many real applications, such an assumption is violated because more or less dependence relations exist. Therefore, attempting dependent stress-strength reliability modelling is interesting. In this article, we assume stress and strength are linked by Fralie–Gumble–Morgenstern copula with Rayleigh marginals as the underlying distribution. The estimates of reliability and dependence parameters are obtained by using maximum likelihood estimation, inference function margin, and semi-parametric methods. In addition, the length of confidence interval and coverage probability of the dependence parameter are also reported. The performance of the proposed methods is shown by using Monte-Carlo simulation as well as three distinct real-life data sets.