The reliability analysis of balking and reneging in a repairable system with warm standbys

Abstract We study the reliability analysis of a repairable system with $m$ operating units, $w$ warm standby units and $R$ repairmen in which the balking and reneging of units are considered. It is assumed that failed units balk (refuse to join) with a constant probability ( $1-b$ ) and renege (leave the queue after joining) according to a negative exponential distribution with parameter $r$ . The failure times of the operating unit and of a standby unit are assumed to be exponentially distributed with parameters λ and α, respectively. The repair time distribution is also exponential. The repairable system is $K$ out of $m+w$ , in which $K=1,2,\dots,m$ . The reliability characteristics, such as the system reliability and the mean time to system failure ( MTTF ), in a repairable system are derived. Several cases are analysed graphically to study the effect of various parameters on the reliability and MTTF of the system. Copyright © 2002 John Wiley & Sons, Ltd.