A NOVEL THREE-STATE MODEL OF MARKOVIAN APPROACH TO RELIABILITY PREDICTION FOR PUBLIC TRANSIT TRAIN STSTEMS

Abstract

In this paper, a novel three–state reliability model of Markovian approach is introduced to calculate the MTBF (Mean Time Between Failure)/MTBSAF (Mean Time Between Service-Affecting Failures) for M-out-of-N redundant units consisting of three operational states: full operation state, functional operation state and failed state. In this three-state reliability model, a transition matrix is introduced to easily and correctly establish a set of state differentiating equations. Laplace transforms are also introduced to simplify the calculating process for the probability function. This model makes the Markovian analysis for three state operational systems become more simple, clear and robust. The concluded MTBF/MTBSAF formula is robust enough and can be used in all three-state models without performing another tedious calculation again. This model is illustrated by four different types of M-out-of-N Redundant units installed in the Public Transit Train: One of Two units, Two of Three voting units, Three of Four voting units and Two of Four voting units. The limitation and boundary of this method is also discussed and elaborated in this paper.