Condition-based maintenance using the inverse Gaussian degradation model

•This paper studied the joint optimal replacement policy and optimal inspection interval when the unit degrades over time.•Unit heterogeneity is considered, which leads to a monotone control limits policy.•The sensitivity to different cost parameters and model parameters is studied.

Condition-based maintenance has been proven effective in reducing unexpected failures with minimum operational costs. This study considers an optimal condition-based replacement policy with optimal inspection interval when the degradation conforms to an inverse Gaussian process with random effects. The random effects parameter is used to account for heterogeneities commonly observed among a product population. Its distribution is updated when more degradation observations are available. The observed degradation level together with the unit’s age are used for the replacement decision. The structure of the optimal replacement policy is investigated in depth. We prove that the monotone control limit policy is optimal. We also provide numerical studies to validate our results and conduct sensitivity analysis of the model parameters on the optimal policy.