Copula based Measures of Repairable Parallel System with Fault Coverage

The main objective of this study is to analyse the reliability behaviour of parallel systems with three types of failure, namely unit failure, human failure and major failure. For this purpose, we apply three different statistical techniques, namely copula, coverage and copula-coverage. More precisely, this study presents a stochastic model for analysing the behaviour of a multi-state system consisting of two non-identical units by incorporating the concept of coverage factor and two types of repair facilities between failed state to a normal state. The system could be characterized as being in a failed state due to unit failures, human failure and major failures, such as catastrophic and environmental failure. All failure rates are constant and it is assumed that these are exponentially distributed whereas, repair rates follow the Gumbel-Hougaard copula distribution. The entire system is modelled as a finite-state Markov process. Time-dependent reliability measures like availability, reliability and mean time to failure (MTTF) are obtained by supplementary variable techniques and Laplace transformations. The present study provides a comparative analysis for reliability measures among the aforementioned techniques, while a discussion referring to which technique makes the system more reliable is also developed. Furthermore, numerical simulations are presented to validate the analytical results. KeywordsPerfect coverage, Gumbel-Hougaard copula, Parallel system, Human failure, MTTF, Markov process.