Cost analysis of a three-state repairable redundant complex system under various modes of failures

Abstract

In this paper, a mathematical model for the evaluation of expected profit during the time interval (0, t] and availability at an instant t under human failure has been set up. The model consists of two subsystems arranged in parallel having three states for operation. The first subsystem consists of two identical units in series whereas the second subsystem has only one unit. Failure and repair times for the system follow exponential and general distributions respectively. Repair is undertaken only when the system is in a reduced efficiency state. Using supplementary variable and Laplace transforms techniques, time dependent probabilities of the complex system being in various states have been computed along with the steady state behaviour of the system. A particular case has also been discussed to highlight the important results.