Some results on successive failure times of a system with minimal instantaneous repairs
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TL;DR
This paper considers a system with minimal instantaneous repairs which is almost equivalent to a nonhomogeneous Poisson process (NHPP), and obtains IFR, DFR and log convex properties for the failure times of the system by using a method different from theirs.
Abstract
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 (Probab. Eng. Inform. Sci. 2 (1988) 475) have obtained IFR, IFRA and NBU properties for the occurrence time of NHPP. We further obtain IFR, DFR and log convex properties for the failure times of the system by using a method different from theirs. Our result for 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.