Probabilistic analysis of a two-unit standby redundant system with repair efficiency and imperfect switch-over

Abstract

A two-unit warm standby redundant system with exponential failure and general repair-time distributions is considered. There is a switch used to switch the standby unit to operate as and when operative unit fails. The probability that the switch operates successfully at the time of need is fixed. After each repair, a unit is examined to see if it meets repair specification. A unit meets specifications only on a fixed proportion of time. If a unit does not meet specification, it is sent to ‘ post-repair ’. The system has been analysed by studying the underlying semi-Markov chain and mean-time-to-system-failure (MTSF), expected number of visits to a state, steady-state availability, first two moments of time in transient states and time to absorption, absorption probabilities are obtained. In the sequence Howard's reward structure has been superimposed on the semi-Markov process to obtain expected profit of the system. Several earlier models are included as special cases.