Reliability analysis of a cold standby system attacked by shocks

This paper analyses the reliability of a two-component cold standby repairable system maintained by a repairman. The system can fail due to intrinsic or external factors such as shocks. The shocks arrive according to a Poisson process. Whenever the magnitude of a shock is larger than a pre-specified threshold of the working component, the working component fails. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, both the magnitude of the external shock and the threshold of the working component are non-negative random variables. This paper derives important reliability indices such as the rate of occurrence of the system failure and the mean time to the first failure of the system as well as a bivariate optimal replacement policy of the system. A case study and a numerical example are given to validate the derived indices.