Cost analysis of a three-unit standby system subject to random shocks and linearly increasing failure rates

Abstract This paper deals with the cost analysis of a single-server three identical unit cold standby system. The operating unit is subject to random shocks occurring from time to time. Due to each shock it may happen with a fixed known probability that (i) the operating unit is not at all affected, (ii) the failure rate of the unit increases and the unit is said to work in quasi-normal mode, and (iii) the operating unit fails totally. Failure time distributions of the operative unit are taken to be Rayleigh with different parameters while the repair and shock time distributions are negative exponentials. The system is observed at suitable regenerative epochs in order to obtain various interesting measures of system effectiveness.