6 - Losses from failures for repairable systems with components logically arranged in series

Abstract

The chapter examines the potential losses from failures for repairable systems whose component failures follow a homogeneous as well as non-homogeneous Poisson process. In the common case of a repairable system with the unknown components logically arranged in series operating during the finite time interval, if at least one of its components fails, and in this sense the system is equivalent to a component with unknown mutually exclusive failure modes. After each system failure, only the failed component is returned to as good as new condition by replacing it with an identical new component and the system is put back in operation. The downtimes after each system failure are neglected for the purposes of the presentation in this chapter. The chapter shows the Monte Carlo algorithm in pseudo-code, yielding the potential losses from a random number of failures in a specified time interval. The fact that a larger reliability of a repairable system does not necessarily mean lower expected losses from failures is demonstrated in the chapter on the simple system composed of a power block, control module and a mechanical device. Two systems of this type are compared, whose components' hazard rates and losses from failure are given in the chapter.