Reliability measures of two dissimilar units parallel system using Gumbel-Hougaard family copula

Abstract

The goal of the present study is to investigate the availability and the reliability of the system, which has two dissimilar units in the parallel network under copula. Other key parameters, such as mean time to failure (MTTF) and expected profit are also evaluated. Simultaneous malfunctioning of units, common cause failure and human fault are the causes of system breakdown. The present mathematical model is examined under the assumption that each failure rate is constant and is exponentially distributed. The system undergoes repair in the completely failed state as well as in degraded state. In the case of complete failure, the system is repaired by two repair facilities and that are tackled by utilizing Gumbel-Hougaard family copula. The present system has been studied by applying the concepts of probability theory, supplementary variable technique and Laplace transformation.