Stochastic analysis of a two units’ complex repairable system with switch and human failure using copula approach

Abstract

This paper deals with the study of a complex system which consists of two subsystems in a series configuration (subsystem 1 and subsystem 2). The subsystem 2 is connected to subsystem 1 in a series configuration. The subsystem 1 has three identical units in parallel configuration and working under 2-out-of-3: G policy and its units are controlled by an instantaneous change over switch. Subsystem 2 has two identical units and uses 1-out-of-2: G scheme. A human operator operates the system, and human failure is considered to damage the entire system completely. All failure rates are assumed to follow exponential distribution and repairs follow two types of distribution (general distribution and Gumbel–Hougaard family copula) distribution. The system is analyzed using Supplementary variables technique, and the various measures of reliability have discussed. The computations for availability, reliability, MTTF, and profit benefit by operation of the system have done for different values of failure and repair rates. Graphs demonstrate results, and consequently, conclusions have done.