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

TLDR

The study analyzes the reliability of a repairable system with multiple operating and warm standby units, including balking and reneging behaviors. The model assumes exponential failure and repair times, balking with constant probability (1‑b), reneging following an exponential distribution with rate r, and considers a K‑out‑of‑m+w system. The analysis derives system reliability and MTTF expressions and demonstrates, via graphical case studies, how parameters influence these metrics. © 2002 John Wiley & Sons, Ltd.

Abstract

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.