Abstract
ABSTRACTWe develop a partially observable Markov decision process model to incorporate population heterogeneity when scheduling replacements for a deteriorating system. The single-component system deteriorates over a finite set of condition states according to a Markov chain. The population of spare components that is available for replacements is composed of multiple component types that cannot be distinguished by their exterior appearance but deteriorate according to different transition probability matrices. This situation may arise, for example, because of variations in the production process of components. We provide a set of conditions for which we characterize the structure of the optimal policy that minimizes the total expected discounted operating and replacement cost over an infinite horizon. In a numerical experiment, we benchmark the optimal policy against a heuristic policy that neglects population heterogeneity.
Highlights
Capital goods, such as lithography machines in semiconductor fabrication plants, baggage handling systems at airports, and medical equipment in hospitals, are essential for the primary processes of their users
Population heterogeneity is increasingly taken into account. This is done by including random parameters in the degradation model that differ over the components in a population; e.g., random drift and diffusion parameters in a Brownian motion (Peng and Tseng, 2009; Wang, 2010; Bian and Gebraeel, 2012) or random scale parameters in a gamma process (Lawless and Crowder, 2004; Tsai et al, 2012)
The key difference between the Condition-Based Maintenance (CBM) model we present here and the aforementioned models is that we consider population heterogeneity by assuming that the population of spare components consists of multiple component types that cannot be distinguished by their exterior appearance but deteriorate according to different transition probability matrices
Summary
Capital goods, such as lithography machines in semiconductor fabrication plants, baggage handling systems at airports, and medical equipment in hospitals, are essential for the primary processes of their users. Crowder and Lawless (2007) and Zhang et al (2014) study a fairly simple maintenance scheme to cope with population heterogeneity, in which only one inspection can be performed to observe a component’s deterioration level before scheduling a preventive replacement They apply their proposed policy to gamma process and Brownian motion degradation models with random parameters. We complement the analytical results by conducting a numerical experiment to identify factors that make it especially important to account for population heterogeneity in replacement decisions To perform this experiment, we adapt Hansen’s policy iteration algorithm (Hansen, 1998) such that it can be used as a solution technique for our POMDP model, in which one state variable is completely observable.
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