Applications of Reliability Analyses of Standby

SOME APPLICATIONS OF RELIABILITY ANALYSES OF STANDBY REDUNDANT SYSTEMS WITH REPAIR Michikazu Kumagai , Toshiba Research & DeveZopment Center 169 Some applications are discussed concerning reliability analyses of a standby redundant system with repair. The system consists of a series subsystem composed of N identical units and n spares. Failed units are assumed to be repaired by r repair facilities and rep,ired units join the spares. For this system, two cases which can be ana1yzed by means of the semi-Markov process method are considered. The first case is the system with N = 1 in which the failure time distribution of a unit is general and the repair time distribution is exponential. The second one is the case with r = 1 where a unit has an ex-· ponentia1 failure time and a general repair time distribution. An application of the first model to an ion source system for a particle accelerator is investigated. The second model is applied to a centrifuge uranium enrichment plant, error correcting terminals for an automatic newspaper editing system, and an autobus system. The general distribution is assumed to be a gamma distribution in the applications. For a proton synchrotron, a proposal to use a redundant ion source system in a design study reported in 1965, when the life time of a duop1asmatron ion source was not long enough, is investigated. Concerning a cascade system of uranium enrichment centrifuges, a production plant composed of 100,000 centrifuges is proposed to be divided into 20 groups, each of which consists of 5,000 centrifuges, and to have n spare groups. An example of a bus company office possessing N + n + 2 (= 61) buses is discussed, where N, nand 2 of them are in operation, spares, and in regular maintenance, respectively. A failed bus which is substituted by a spare one is repaired in temporary maintenance. The number of spares needed to attain to a target value of the mean time to system failure (MTSF) is obtained for a given repair capacity. ~%JiI~Jlc:*ztl€.'i5-liIf~i'Ji "i" 2 1 0 Jllibiljm$[8jJ\iilJ*zt'JJ 1 © 1978 The Operations Research Society of Japan