Modelling condition monitoring intervals: A hybrid of simulation and analytical approaches

This paper reports on a study of modelling condition monitoring intervals. The model is formulated based upon two important concepts. One is the failure delay time concept, which is used to divide the failure process of the item into two periods, namely a normal working period followed by a failure delay time period from a defect being first identified to the actual failure. The other is the conditional residual time concept, which assumes that the residual time also depends on the history condition information obtained. Stochastic filtering theory is used to predict the residual time distribution given all monitored information obtained to date over the failure delay time period. The solution procedure is carried out in two stages. We first propose a static model that is used to determine a fixed condition monitoring interval over the item life. Once the monitored information indicates a possible abnormality of the item concerned, that is the start of the failure delay time, a dynamic approach is employed to determine the next monitoring time at the current monitoring point given that the item is not scheduled for a preventive replacement before that time. This implies that the dynamic model overrides the static model over the failure delay time since more frequent monitoring might be needed to keep the item in close attention before an appropriate replacement is made prior to failure. Two key problems are addressed in the paper. The first is which criterion function we should use in determining the monitoring check interval, and the second is the optimization process for both models, which can be solved neither analytically nor numerically since they depend on two unknown quantities, namely, the available condition information and a decision of the time to replace the item over the failure delay time. For the first problem, we propose five appealingly good criterion functions, and test them using simulations to see which one performs best. The second problem was solved using a hybrid of simulation and analytical solution procedures. We finally present a numerical example to demonstrate the modelling methodology.