A Bayesian Scheme to Detect Changes in the Mean of a Short-Run Process

Panagiotis Tsiamyrtzis

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Bayesian Methods and Mixture Models

Abstract

In this article we propose a model suitable for statistical process control in short production runs. We wish to detect on-line whether the mean of the process has exceeded a prespecified upper threshold value. The theoretical basis of the model is a Bayesian formulation, leading to a mixture of normal distributions. Issues of decisions about whether the process is within specification and forecasting are addressed. The Kalman filter model is shown to be related to a special case of our model. The calculations are illustrated with a clinical chemistry example. The tool wear problem is another potential candidate for our approach.

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References

1992Introduction to Statistical Quality Control 2000Control Chart Tests Based on Geometric Moving Averages 1998Bayesian Forecasting and Dynamic Models (2nd edn)1991Some Statistical Process Control Methods for Autocorrelated Data 1964Estimating the Current Mean of a Normal Distribution which is Subjected to Changes in Time 1959Control Chart Tests Based on Geometric Moving Averages 1991SPCQCharts for Start-Up Processes and Short or Long Runs 1987Self-Starting Cusum Charts for Location and Scale

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