On the Reliability of Standby Redundant Systems with Repair

The reliability of repairable stand by systems is investigated using semi-Markov processes. The systems are composed of n units having general failure time distribution with mean 1/). and of r repair facilities having exponential repair time distribution with mean l/p. For these systems, the Laplace-Stieltjes transform (LST) of the system failure time distribution is derived in the form of a generating function. For indefinitely large n, asymptotic values of the mean time to system failure (MTSF) and limiting distributions of system failure time are given. It is shown that under certain conditions, the system failure time distribution tends to an exponential distribution as n increases indefinitely. The results can be applied to the first passage time problem of the maximal queue size of the queuing system G/MJr1). Some numerical examples of the MTSF and stationary availability are shown in figures for gamma failure time distributions of units. 1) Kendall's notation AIBls means that A and B stand for distributions of the time to unit failure and repair, respectively, and s denotes the number of repair facilities. 226 © 1973 The Operations Research Society of Japan On the Reliability of' Standby Redundant Systems with Repair 227