Some results on successive failure times of a system with minimal instantaneous repairs

This paper considers a system with minimal instantaneous repairs which is almost equivalent to a nonhomogeneous Poisson process (NHPP). We focus on aging and stochastic comparison properties of the failure times of the system (or the occurrence time of NHPP). Gupta and Kirmani have obtained Increasing Failure Rate (IFR), Increasing Failure Rate on Average and New Better than Used properties for the occurrence time of NHPP. We further obtain IFR, Decreasing Failure Rate and log convex properties for the failure times of the system by using a method different from theirs. Our result for the IFR case is more general than the corresponding result of Gupta and Kirmani. In addition, we obtain some stochastic comparison properties and inequalities concerning the expectation and the variance of the failure times.