Should Observations Be Grouped for Effective Process Monitoring?

Marion R. Reynolds · Zachary G. Stoumbos

162 citations0/0 files storedJournal of Quality Technology

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

When control charts are used to monitor processes to detect special causes, it is usually assumed that a special cause will produce a sustained shift in a process parameter that lasts until the shift is detected and the cause is removed. However, some special causes may produce a transient shift in a process parameter that lasts only for a short period of time. Control charts are usually based on samples of n ≥ 1 observations using a sampling interval of fixed length, say d. When n > 1, the usual practice, based on the so-called rational subgroups concept, is to take a concentrated sample at one time point at the end of the sampling interval d, but another option is to disperse the sample over the interval d. In this paper, we investigate the question of whether it is better to use n = 1, or to use n > 1 and either concentrated or dispersed samples. The objective of monitoring is assumed to be the detection of special causes that may produce either a sustained or transient shift in the process mean %mU and/or process standard deviation σ. It is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so that the ratio n/d is fixed. The best sampling strategy depends on the type of control chart being used, so Shewhart and cumulative sum (CUSUM) charts are considered. For both types of control charts, a combination of two charts is investigated; one chart is designed to monitor μ, and the other is designed to monitor σ. The overall conclusion is that it is best to take samples of n = 1 and use a CUSUM chart combination. The Shewhart chart combination with the best overall performance is based on n > 1, but this combination has inferior statistical performance compared with the CUSUM chart combination.

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References

1954CONTINUOUS INSPECTION SCHEMES 1971Procedures for Reacting to a Change in Distribution 1986Optimal Stopping Times for Detecting Changes in Distributions 1998Cumulative Sum Charts and Charting for Quality Improvement 2001Monitoring the Process Mean and Variance Using Individual Observations and Variable Sampling Intervals 2004Control Charts and the Efficient Allocation of Sampling Resources

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2004Control Charts and the Efficient Allocation of Sampling Resources 2005A Change-Point Model for a Shift in Variance 2011A synthetic control chart for the coefficient of variation 2010An Evaluation of a GLR Control Chart for Monitoring the Process Mean 2011A comparison study of effectiveness and robustness of control charts for monitoring process mean 2006Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix 2008Optimization designs of the combined Shewhart-CUSUM control charts 2006

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