A GLR Control Chart for Monitoring the Process Variance

In this paper we derive control charts for the variance of a Gaussian process using the likelihood ratio approach, the generalized likelihood ratio approach, the sequential probability ratio method and a generalized sequential probability ratio procedure, the Shiryaev-Roberts procedure and a generalized Shiryaev-Roberts approach. Recursive presentations for the calculation of the control statistics are given for autoregressive processes of order 1. In an extensive simulation study these schemes are compared with existing control charts for the variance. In order to asses the performance of the schemes both the average run length and the average delay are used.

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“…Let {Y t } be a Gaussian process as assumed in Section 3.2. Following the SPRT approach sketched in Section 4 and using (19) we get sup…”

Section: A Variance Chart Based On the Generalized Sprtmentioning

confidence: 99%

On control charts for monitoring the variance of a time series

Lazariv

Schmid

Zabolotska

2013

Journal of Statistical Planning and Inference

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A Generalized Likelihood Ratio Control Chart for Monitoring the Process Mean Subject to Linear Drifts

Wang

Reynolds

2012

Quality & Reliability Eng

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This article considers the problem of monitoring a normally distributed process variable when a special cause may produce a time-varying linear drift in the mean. The design and application of a generalized likelihood ratio (GLR) control chart for drift detection are evaluated. The GLR drift chart does not require specification of any tuning parameters by the practitioner and has the advantage that, at the time of the signal, estimates of both the change point and the drift size are immediately available. An equation to accurately approximate the control limit is provided. The performance of the GLR drift chart is compared with that of other control charts such as a standard cumulative sum chart and a cumulative score chart designed for drift detection. We also compare the GLR chart designed for drift detection with the GLR chart designed for sustained shift detection because both of them require only a control limit to be specified. In terms of the expected time for detection and in terms of the bias and mean squared error of the change-point estimators, the GLR drift chart has better performance for a wide range of drift rates relative to the GLR shift chart when the out-of-control process is truly a linear drift.

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