Reliability analysis of a cold standby repairable system with repairman extra work

Abstract

This paper deals with a cold standby repairable system with two identical units and one repairman who can do extra work in idle time. The authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.

Multi-objective optimization of job shops with automated guided vehicles: A non-dominated sorting cuckoo search algorithm

“…Note that upon failure of the primary system, this system is only stated. Zhang 31 described for a more extensive review of the studies on cold, hot, and warm standby problems.…”

Stochastic Analysis of a Computer System with Unit Wise Cold Standby Redundancy and Failure of Service Facility

“…Malik and Sureria (2012) have studied computer systems with these concepts that is, by taking redundancy of the entire computer system in cold standby. Manglik and Ram (2013), Ram et al (2013), Zhang (2015), Garg and Kadyan (2016) and Kumar and Goel (2016) discussed reliability models of cold standby systems with different repair strategies. However, these models have been analyzed under a common assumption that service facility remains busy in performing the assigned job continuously without any failure or difficulty.…”