Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

This paper considers the reliability analysis of a two-component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensityλ>0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.

Sir Harry Raymond Pitt. 3 June 1914 — 8 October 2005

Sir Harry Pitt worked (as H. R. Pitt) with Norbert Wiener in 1938 on Wiener's general Tauberian theory. Mathematically, he is best known for Pitt's form of Wiener's Tauberian theorem, and as the author of the first (1958) monograph on Tauberian theory. He is otherwise best known for having been Vice–Chancellor of Reading University from 1964 to 1978.