Repairable Fault Tree Analysis Using Renewal Intensities

Abstract

Fault tree (FT) is one of powerful tools for reliability analysis. The conventional FT usually considers only failure occurrence as an input event. However, considering repair in FT improves the analysis capability of FT. This FT is referred to as a repairable FT (RFT). This paper deals with RFTs, including dynamic FTs. In RFTs, it is necessary to consider both the occurrence of a basic event and its disappearance. This means that the analysis of the RFT needs not only the information about whether basic/intermediate events occur, but also the one about in which states the event outputs are. This forces us into considering the state transition of a system with time domain. Markov analysis is usually adopted for the state transition analysis. The difficulty of this method is mainly due to the explosion of the number of states to be considered in the analysis. We try to handle the state transitions in the RFT analysis as equivalent event occurrences by using the concept of renewal process, and introduce a new approach to obtain the steady state top event probability. That is, the state transition of a gate output is regarded as an alternating renewal process. The renewal intensities of the process are derived applying the limit theorem of a renewal process with the up-time-ratio analysis, the mean up time and the down time analyses. Starting from the gate located at the bottom of an FT, the top event probability is calculated by a bottom up procedure.