The Estimation of Sigma for an X Chart: or S/c₄?

Abstract

The standard approach to estimating sigma for an individual observations control chart is to use moving ranges. We show that, for independent, normally distributed observations, this approach is very inefficient compared to using the sample standard deviation. Thus, for future process monitoring the estimation of sigma should be based on the sample standard deviation. It is also shown that the moving range approach can provide especially poor results when the observations are correlated over time. This is demonstrated with some real chemical data and it is shown how certain processes that are in control can produce correlated data. Some recommendations are given concerning the estimation of sigma for individual observations control charts.

• Control Charts
• Correlated Data
• Moving Range
• Sample Standard Deviation

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Additional information

Notes on contributors

Jonathan D. Cryer

Dr. Cryer is an Associate Professor in the Department of Statistics and Actuarial Science.

Thomas P. Ryan

Dr. Ryan is a visiting Associate Professor in the Department of Statistics. He is a Member of ASQC.