System Reliability and Component Importance Under Dependence: A Copula Approach

ABSTRACT

System reliability and component importance are of great interest in reliability modeling, especially when the components within the system are dependent. We characterize the influence of dependence structures on system reliability and component importance in coherent systems with discrete marginal distributions. The effects of dependence are captured through copula theory. We extend our framework to coherent multi-state system. Applications of the derived results are demonstrated using a Gaussian copula, which yields simple interpretations. Simulations and two examples are presented to demonstrate the importance of modeling dependence when estimating system reliability and ranking of component importance. Proofs, algorithms, code, and data are provided in supplementary materials available online.

KEYWORDS:

• Dependent coherent system
• Discrete marginal
• Gaussian copula
• Multi-state system

Supplementary Materials

Proofs, Algorithms, and Additional Numerical Examples: Proofs of the theorems and propositions in the article, details of the MCMC algorithm, numerical examples based on simulated data, and additional results from real data examples. (PDF file)

Code: R and C$++$ code used in the numerical examples. (Zip file)

Data: Real data used in the numerical examples. (Zip file)

Acknowledgments

We thank Dr. Christine Anderson-Cook from the Statistical Sciences Group at Los Alamos National Laboratory for providing data for the examples and for valuable feedback on the article.