Availability Analysis of an Unreliable Single Unit System Operating in a Doubly Stochastic Shock Environment

This paper considers an unreliable system together with a repairman operating in a doubly stochastic environment. The system operates in a stochastic environment which alternates between two levels, namely less load and heavy load. The intrinsic life-time of the system is exponentially distributed with varying means depending on whether the system is working in less load period or heavy load period. Environment dependent shocks arrive to the system according to a Poisson process with different rates depending on whether the environment is in less load or in heavy load period. At the occurrence of a shock, the operating system fails and it is immediately taken to the repair facility and the repair commences instantaneously. The repair time is exponentially distributed whose mean is dependent on the type of failure and the level of the environment. After each repair, the system begins to function in heavy load environment or less load environment according to the level of the environment at the time of completion of the repair. The repair facility is unaffected by shocks. Kolmogorov equations governing the behaviour of the system are derived and the probability distribution of the states is obtained. The availability function is also obtained and the model is highlighted with a numerical illustration.