A multivariate CBM model with a random and time-dependent failure threshold

In a condition-based maintenance setting, the degradation of an item is usually represented by several condition variables, and they can be combined into a composite condition variable. In this case, the functional failure threshold associated with the composite condition variable is usually not a fixed and known constant. It is an open issue to model the failure threshold and accordingly determine a threshold of preventive maintenance (PM). This paper addresses this issue. The condition variables are combined using a weighted power model, the failure threshold is represented by the Gaussian process model, and the PM threshold is determined by two approaches. Based on the gamma process and stress–strength interference models, the distributions of time to failure and to the PM threshold are derived, respectively. The appropriateness of the approach is illustrated by a real-world example.