Modelling the probability assessment of system state prognosis using available condition monitoring information

This paper reports on a model to assess the current and future states of a monitored system based on measured condition monitoring information to date. The true state of the system is unobservable, but is assumed to be related to the measured condition monitoring information in a stochastic way. We further assume that the transition of the system state follows a time-dependent Markov chain which has only three states, namely good, defective and failed. This assumption effectively defines a two-stage failure process which is widely used in delay time modelling of maintained systems. Three modelling techniques are used to establish the model. First, we use a hidden Markov model to describe the transitions between system states. Second, the transition matrix is established based on the well-known delay time concept. The last one is the use of the filtering technique to construct the relationship between measured condition information and the underlying true state of the system. We also discuss the procedure for model parameter estimation. A numerical example is presented to demonstrate the modelling ideas.