Optimality of Chain-based Threshold Policies for Machine Maintenance under Imperfect Predictions

70 Pages Posted: 20 Oct 2020

See all articles by Guanlian Xiao

Guanlian Xiao

University of Calgary - Haskayne School of Business

Alp Akçay

Eindhoven University of Technology (TUE) - Department of Industrial Engineering and Innovation Sciences

Lisa Maillart

University of Pittsburgh

Geert-Jan van Houtum

Eindhoven University of Technology (TUE)

Date Written: August 31, 2020

Abstract

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

Suggested Citation

Xiao, Guanlian and Akçay, Alp and Maillart, Lisa and van Houtum, Geert-Jan, Optimality of Chain-based Threshold Policies for Machine Maintenance under Imperfect Predictions (August 31, 2020). Available at SSRN: https://ssrn.com/abstract=3683983 or http://dx.doi.org/10.2139/ssrn.3683983

Guanlian Xiao (Contact Author)

University of Calgary - Haskayne School of Business ( email )

2500 University Drive, NW
Calgary, Alberta T2N 1N4
Canada

Alp Akçay

Eindhoven University of Technology (TUE) - Department of Industrial Engineering and Innovation Sciences ( email )

Den Dolech 2
Eindhoven
Netherlands

Lisa Maillart

University of Pittsburgh ( email )

135 N Bellefield Ave
Pittsburgh, PA 15260
United States

Geert-Jan Van Houtum

Eindhoven University of Technology (TUE) ( email )

PO Box 513
Eindhoven, 5600 MB
Netherlands

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