Reliability of degrading complex systems with two dependent components per element

The reliability of complex systems consisting of n independent elements each having two dependent components is investigated based on degradation data. A copula-based model is used to describe the dependence structure of the components. Considering gamma, Wiener and inverse Gaussian processes for degradation of each component, the reliability of a complex system is derived for some various copula functions. Also, reliability bounds are obtained by assuming that the components are positively associated for special cases of series and parallel systems. When the model parameters are unknown, a two-step method is proposed to derive the maximum likelihood estimators. A simulation study is conducted to evaluate the performance of the estimators. Also, the sensitivity of the system reliability is analyzed using simulation. Finally, the results of the paper are illustrated using two real examples.

Automated summary

The reliability of complex systems consisting of n independent elements, each with two dependent components, is investigated based on degradation data. A copula-based model is used to describe the dependence structure of the components. The reliability of a complex system is derived for different copula functions, considering gamma, Wiener, and inverse Gaussian processes for the degradation of each component. Reliability bounds are obtained by assuming positive association of components for special cases of series and parallel systems. A two-step method is proposed for estimating maximum likelihood estimators when model parameters are unknown. The performance of the estimators is evaluated through a simulation study, and the sensitivity of system reliability is analyzed using simulation. The results of the paper are illustrated using two real examples.