ABSTRACT
The goal of this chapter is to provide an analytical framework for a warm standby 3-out-of-5: G system that considers a significant feature of priority and supporting units. The system under consideration has five parallel units which are divided into two groups, namely type-A and type-B. Three units in type-A categorized as priority units and two units in type-B as supporting units. Type-A units have higher performance than type-B units, and thus receive preference in both operation and maintenance. The failure rates of all the units are constant and are expected to be follow the exponential distribution. The two methods of repair, namely general repair and Goumbel–Hougaard copula repair, are used to restore the existing failed units of the system. Repairperson is full time available for the servicing of failed units in the facility. We also considered a catastrophic failure due to repeated changes in weather factors or man-made disturbances. We study the system with the help of supplementary variable technique, copula repair and Laplace transformation to derive differential equations and obtain important reliability physiognomies, namely the availability of the system, the reliability of the system, mean time to failure (MTTF) and expected profit analysis. Tables and figures demonstrate the computed results and accomplish that copula repair is better repair policy for increased efficiency of repairable systems. It offers engineers a different feature to understand multi-dimensional repair in the form of copula.
