Optimality of Chain-based Threshold Policies for Machine Maintenance under Imperfect Predictions
70 Pages Posted: 20 Oct 2020
Date Written: August 31, 2020
We consider a critical component that deteriorates according to a three-state discrete time Markov chain with a self-announcing failed state and two un-observable operational states: good and defective. The componentis periodically monitored by an imperfect defect-prediction model to make immediate recommendations to inspect the component or do nothing. The defect-prediction model is imperfect in the sense that a no-alert-signal can be generated for a defective component, while an alert signal can be generated for a component in the good state. We build a partially observable Markov decision process model that updates the belief of being in the good state by using the binary signals from the defect-prediction model and minimizes the expected discounted total cost by optimizing the inspection decisions. We characterize the optimal policy as a threshold type and provide a necessary and sufficient condition to ensure a unique non-zero critical threshold on the belief variable. By introducing a new concept referred to as a chain-based threshold policy,we formalize specific properties of the belief space to explicitly link the optimal maintenance action to a specific number of signals from the prediction model. We characterize when a threshold-type policy is a chain-based threshold policy and then analytically derive the critical threshold.
Keywords: Maintenance Optimization, POMDP, Imperfect Signals
JEL Classification: C18, C61, O14
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