Abstract:

A unit repairable system, with the working time follows phasetype distribution, and with the repair time is exponentially distributed, was considered. The original Markov repairable system model was modeled. Based on the model, if the system repair time is less than given nonnegative constant τ, then the repair time can be omitted, we think that the system is also working during the repair time. Otherwise, if the system repair time is greater than given nonnegative constant τ, then the repair time cannot be omitted, the system is thought of as failure during the repair time. Based on these assumptions, the new system model with repair time omission was modeled. Some reliability indexes of the original model and the new model were respectively derived by using aggregated stochastic process theory. Finally, a numerical example was given to illustrate these results obtained.

Key words: Markov repairable system; PH distribution; reliability; repair time omission