ImprovedRandscontrol charts for monitoring the process variance

Guoyi Zhang

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

Abstract

The Shewhart R control chart and s control chart are widely used to monitor shifts in the process spread. One fact is that the distributions of the range and sample standard deviation are highly skewed. Therefore, the R chart and s chart neither provide an in-control average run length (ARL) of approximately 370 nor guarantee the desired type I error of 0.0027. Another disadvantage of these two charts is their failure in detecting an improvement in the process variability. In order to overcome these shortcomings, we propose the improved R chart (IRC) and s chart (ISC) with accurate approximation of the control limits by using cumulative distribution functions of the sample range and standard deviation. Simulation studies show that the IRC and ISC perform very well. We also compare the type II error risks and ARLs of the IRC and ISC and found that the s chart is generally more efficient than the R chart. Examples are given to illustrate the use of the developed charts.

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References

1992Introduction to Statistical Quality Control 2007Introduction to Statistical Quality Control 2003Skewness correction X and R charts for skewed distributions 1999Statistical Quality Assurance Methods for Engineers 2010New EWMA Charts for Monitoring Process Dispersion 2011Design and Analysis of Control Charts for Standard Deviation with Estimated Parameters 2012On monitoring process variability under double sampling scheme 2012CS‐EWMA Chart for Monitoring Process Dispersion

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2020A new S2‐TEWMA control chart for monitoring process dispersion 2015A new approach for monitoring process variance 2015On process monitoring using location control charts under different loss functions 2019On Designing a New Bayesian Dispersion Chart for Process Monitoring 2016Synthetic double samplingschart 2023Monitoring simple linear profiles in the presence of within‐ and between‐profile autocorrelation

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