Event-Triggered Bayesian Control Chart

This paper develops the Bayesian analogue to the Shewhart type control chart previously developed for systems monitored by online sensors. Unlike previous work, we allow production sampling to be part of the decision process, so that a decision to take a sample is first made when a sensor generates a warning signal, followed immediately by another decision to interrupt operation. We apply optimal stopping theory along with dynamic programming analysis to prove the average cost optimality of a novel Bayesian control chart. A computational procedure for obtaining the optimal control limits and the minimal average cost is subsequently proposed. Through an empirical study, adapted from the literature, we illustrate the ease of implementation and the economic advantage of our control chart. This paper is particularly relevant within the context of wireless sensor networks, wherein power-aware communication of sensor measurements is crucial. Interestingly, the adopted signaling mechanism achieves such power-awareness, without too much compromise on the sensors' monitoring capability. More generally, our paper is relevant to any fault detection problem involving an unobservable change in the rate of a Poisson process, for example, condition-based maintenance of systems subject to a failure rate increase.

Funding: This work was supported by Mitacs Accelerate [Grant IT11444] and the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN 121384-11].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://orcid.org/10.1287/opre.2021.0427.