Modelling of a deteriorating system with repair satisfying general distribution

In this paper, we model a deteriorating system that cannot be repaired “as good as new” after failures, the model comes from [19, Applied Mathematics and Computation, 217(2011), 4980-4989]. Suppose that the system has one repairman who can have multiple vacations, and if the system fails when the repairman is on vacation, it will wait for repair until the repairman is available. Herein the repair time is taken into account and supposes that the repair satisfies the general distribution. Under these assumptions, by means of the geometric process and the supplementary variable techniques, we derive a complete model of the partial differential equations, which will correct an error of mathematical model in [19]. Moreover, we deduce some important reliability indices of the system such as the availability of system, the probability of the repairman working and the rate of occurrence of failures. In particular, we prove that the rate of occurrence of failures mf is not equal to zero.