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Predictive ratio CUSUM (PRC): A Bayesian approach in online change point detection of short runs

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journal contribution
posted on 2023-01-27, 16:20 authored by Konstantinos Bourazas, Frederic Sobas, Panagiotis Tsiamyrtzis

The online quality monitoring of a process with low volume data is a very challenging task and the attention is most often placed in detecting when some of the underline (unknown) process parameter(s) experience a persistent shift. Self-starting methods, both in the frequentist and the Bayesian domain aim to offer a solution. Adopting the latter perspective, we propose a general closed-form Bayesian scheme, where the testing procedure is built on a memory-based control chart that relies on the cumulative ratios of sequentially updated predictive distributions. The theoretic framework can accommodate any likelihood from the regular exponential family and the use of conjugate analysis allows closed form modeling. Power priors will offer the axiomatic framework to incorporate into the model different sources of information, when available. A simulation study evaluates the performance against competitors and examines aspects of prior sensitivity. Technical details and algorithms are provided as supplementary material.

Funding

This work was supported by Research Center of the Athens University of Economics and Business (RC/AUEB) and Instrumentation Laboratory (IL), Bedford, Massachusetts, USA.

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