A parallel redundant complex system with two types of failure under preemptive-repeat repair discipline

Abstract

This paper presents the availability analysis of a complex system, which consists of two s-independent repairable subsystems A and B in series (1-out-of-2: F). Subsystem A has two identical units arranged in parallel redundancy (1-out-of-2: G), sub-system B is a single unit with two types of failure, viz., partial and catastrophic. There is only one repair facility, which is always available. The failure and repair times for both subsystems follow exponential and general distributions respectively. The model so developed is analysed under “preemptive-repeat repair discipline”. By employing supplementary variable technique Laplace transforms of various probability states are obtained along with steady-state behaviour of the system. Inversions have also been carried out so as to obtain time dependent probabilities, which determine availability of the system at any time.