Optimal Inspection Policy under Imperfect Predictions: Structural Analysis and Insights

52 Pages Posted: 20 Oct 2020 Last revised: 20 Nov 2024

See all articles by Guanlian Xiao

Guanlian Xiao

VU Amsterdam

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 with a deterioration process, modeled as a three-state discrete-time Markov chain with a self-announcing failed state and two unobservable operational states: good and defective. Periodic monitoring by a defect-prediction model generates imperfect binary signals. To optimize the inspection decision and minimize the expected total discounted cost, we develop an infinite-horizon partially observable Markov decision process (POMDP). Our analysis demonstrates that the optimal policy exhibits a threshold structure. By introducing the novel concept of a chain-based threshold policy, we classify threshold policies into chain-based and non-chain-based categories. We provide sufficient conditions for a threshold policy to be chain-based and derive a set of equations to compute its value function exactly. For non-chain-based threshold policies, we present an easy-to-implement algorithm to identify the most impactful discontinuous beliefs and construct a modified policy accordingly. Implementing the modified policy allows us to approximate the value function and establish an error bound on the gap between the approximated and exact value functions. Furthermore, we establish criteria for determining the optimality of a threshold policy and propose methods for improving suboptimal policies.

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,
Optimal Inspection Policy under Imperfect Predictions: Structural Analysis and Insights
(August 31, 2020). Available at SSRN: https://ssrn.com/abstract=3683983 or http://dx.doi.org/10.2139/ssrn.3683983

Guanlian Xiao (Contact Author)

VU Amsterdam ( email )

Netherlands

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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