Stochastic analysis of a two‐unit cold standby system with maximum repair time and correlated failures and repairs

Abstract

Investigates a stochastic model of a two identical unit cold standby system. Assumes that, if repair of the failed unit is not completed within a specified time, then an order is placed to replace the failed unit by the new one. The specified time is also known as the maximum repair time limit which may change from user to user of the system, so that it is assumed as a random variable. Joint distribution of failure and repair times is bivariate exponential whereas the distributions of lead time (difference between order and delivery time for a new unit) and replacement time of the new unit are negative exponential. Obtains various reliability characteristics of the system under study by using regenerative point technique. Also studied characteristics through graphs.