Safety constraints applied to an adaptive Bayesian condition-based maintenance optimization model

A model is described that determines an optimal inspection and maintenance scheme for a deteriorating unit with a stochastic degradation process with independent and stationary increments and for which the parameters are uncertain. This model and resulting maintenance plans offers some distinct benefits compared to prior research because the uncertainty of the degradation process is accommodated by a Bayesian approach and two new safety constraints have been applied to the problem: (1) with a given subjective probability (degree of belief), the limiting relative frequency of one or more failures during a fixed time interval is bounded; or (2) the subjective probability of one or more failures during a fixed time interval is bounded. In the model, the parameter(s) of a condition-based inspection scheduling function and a preventive replacement threshold are jointly optimized upon each replacement and inspection such as to minimize the expected long run cost per unit of time, but also considering one of the specified safety constraints. A numerical example is included to illustrate the effect of imposing each of the two different safety constraints.