Bayesian inference for dependent stress-strength reliability of series-parallel system based on copula

Area of Science:

• Reliability Engineering
• Statistical Modeling
• Dependence Analysis

Background:

• Assessing the reliability of complex systems is crucial.
• Understanding stress-strength relationships, especially when dependent, is challenging.
• Existing models may not fully capture intricate dependence structures.

Purpose of the Study:

• To develop inferential procedures for dependent stress-strength reliability in series-parallel systems.
• To model the dependence between stress and strength using the Clayton copula.
• To provide both frequentist and Bayesian estimations for system reliability.

Main Methods:

• Utilized the Clayton copula for dependence modeling.
• Established Maximum Likelihood Estimations (MLE) for parameters and reliability.
• Employed Bayesian inference with Gamma-Beta priors and Metropolis-Hastings algorithm.
• Conducted Monte Carlo simulations for performance assessment.

Main Results:

• Developed novel inferential procedures for dependent stress-strength reliability.
• Provided accurate estimations for system reliability using both MLE and Bayesian approaches.
• Demonstrated the effectiveness of the proposed methods through simulations.
• Analyzed a real-world dataset on Istanbul dam occupancy rates.

Conclusions:

• The proposed methods offer robust tools for analyzing dependent stress-strength reliability.
• The Clayton copula effectively models the dependence structure.
• The study provides valuable insights for complex system reliability assessment.