Reliability estimation in dependent stress-strength model with Clayton copula and modified Weibull margins

TL;DR

This paper develops a flexible dependent stress-strength reliability model using Clayton copula and modified Weibull margins, with various estimation methods and real data application.

Contribution

It introduces a novel seven-parameter dependent model for stress-strength reliability with multiple estimation procedures and demonstrates its practical use with dam occupancy data.

Findings

The model effectively captures dependence between stress and strength variables.

Simulation results show the estimators perform well across different scenarios.

Application to dam data illustrates the model's practical utility in water management.

Abstract

Stress-strength models are widely used to assess the reliability of systems under uncertain conditions. While most studies assume independence between stress and strength variables, such an assumption may be unrealistic in many practical situations where these components are inherently dependent. In this study, we investigate stress-strength reliability under a dependent framework, where both stress and strength variables follow modified Weibull distributions and their dependence is modeled via a Clayton copula. The proposed model allows distinct parameter sets, resulting in a flexible seven-parameter structure that extends Weibull-based models. We consider several estimation procedures for the model parameters and reliability, including two-step maximum likelihood, least squares, weighted least squares, and maximum product of spacings, with interval estimation obtained via asymptotic and bootstrap confidence intervals. The performance of the proposed estimators is evaluated through an extensive Monte Carlo simulation study under various parameter configurations and sample sizes. Finally, the applicability of the proposed model is illustrated using monthly occupancy data from Istanbul's two largest dams, with the Clayton copula capturing their dependence structure. This application demonstrates how stress-strength reliability can inform water management decisions and mitigate inter-regional operational risks.