Reliability and sensitivity analysis of the controllable repair system with warm standbys and working breakdown

• We investigate the reliability and sensitivity analysis of a controllable repairable system.
• Warm standbys and working breakdown condition are considered.
• The explicit expressions for reliability function RY(t)RY(t) and MTTF are derived.
• Perform sensitive analysis and relative sensitivity analysis on the system reliability and the mean time to system failure.
• Discuss the order of magnitude of the sensitivity to RY(t)RY(t) and MTTF.

This paper deals with the reliability and sensitivity analysis of a controllable repair system with M operating units, S   warm standby units, and an unreliable service station. Failure times and service times of operating units or standby units are assumed to follow exponential distributions. When the service station normally operates, it is subject to breakdowns; while a breakdown occurs, the service station requires repair at the repair facility. The times to breakdown and repair times of the service station are also assumed to be exponentially distributed. During a breakdown period of the service station, the service station is allowed to provide partial service with lower service rate. A practical justification of the system is also provided. This paper develops the expressions for system reliability, RY(t)RY(t), as well as the mean time to first failure, MTTFF  . The sensitivity and relative sensitivity analyses of RY(t)RY(t) and MTTFF are performed. Finally, some numerical experiments are designed and performed to demonstrate the effects of system performance measures are affected by the change of each system parameter.