Reliability and Sensitivity Analysis of the Controllable Repair System with Warm Standbys under the Recovery Threshold Policy

Abstract

Abstract This article performs reliability and sensitivity analyses of a controllable repair system with M operating units, S warm standby units, and an unreliable repair server under the recovery threshold policy. Failure times and service times of an operating unit or a standby unit are assumed to follow exponential distributions. When the repair server normally operates, it is subject to breakdowns; while a breakdown occurs, the repair server requires repair at another repair facility, and the repair of the breakdown server cannot be initiated until there are more than or equal to q failed units. The times to breakdown and repair times of the server are also assumed to be exponentially distributed. A server during a breakdown period can provide partial service with lower service rates. This article derives expressions for system reliability as well as the mean time to failure. The sensitivity analyses of both system performance measures are performed. Finally, some numerical experiments are designed and performed to demonstrate how the system performance measures are affected by the change of each system parameter.