on the importance of copula choice in the reliability evaluation of dependent stress-strength models

Reliability assessment, vital in high-stakes engineering, often employs the stress-strength model. however, traditional models frequently assume independence between stress and strength, an assumption that can lead to inaccurate reliability estimates when dependence exists due to real-world factors. to address this, the current study proposes a dependent stress-strength model using copula theory, which flexibly models dependence by separating marginal and joint distributions. four copula families—farlie-gumbel-morgenstern, ali-mikhail-haq, gumbel's bivariate exponential, and gumbel-hougaard—are investigated for their ability to capture diverse dependency patterns. the inverse lomax distribution is utilized for both stress and strength marginals due to its suitability for heavy-tailed reliability data. the copula dependence parameter θ is estimated via conditional likelihood and blomqvist's beta-based method of moments. the asymptotic distributions of these estimators are derived, and their performance is evaluated through extensive simulations. the research thoroughly examines how system reliability r changes with $theta$ across various model configurations. findings indicate that the gumbel-hougaard copula demonstrates the highest sensitivity of $r$ to θ, effectively capturing a wide range of dependency strengths. this paper highlights the critical need to incorporate dependence in stress-strength models and offers practical guidance for copula selection, thereby enhancing the accuracy and robustness of reliability predictions in complex engineering systems. a practical examination of a real dataset is conducted to demonstrate the concept.