d2* in Estimating Variability in a Normal Universe (original) (raw)

Quality Engineering, 1996

Abstract

ABSTRACT In an ordinary X and R control chart, the process standard deviation may be estimated using the average range divided by the constant d2. This statistic is typically used when the process is in a state of statistical control, follows the normal distribution, and there are 20 or more subgroups. In some applications involving control charts there are only a small number of subgroups available for estimating the standard deviation: In these cases, a modified version of d2 known as d*2 is in use. In this article, the estimator based on d*2 is shown to be superior in certain applications because it has a smaller mean square error, particularly for a small number of subgroups. A relationship between d2 and d*2 is presented and several of the elementary statistical properties are contrasted between the estimators R̄/d2 and R̄/d*2. In conclusion, some guidelines for use are suggested.

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