Journal of Quality Engineering and Management

The estimation of process standard deviation in statistical quality control: A review and comparison of methods

Document Type : Original Article

Authors

Mahdi Kalantari 1
Hormoz Rahmatan 2

1 Department of Statistics, Faculty of Science, Payame Noor University, Tehran, Iran.

2 Department of Mathematics, Faculty of Science, Payame Noor University, Tehran, Iran.

https://doi.org/10.48313/jqem.2025.553737.1580
Abstract
Purpose: This paper aims to compare and examine the statistical properties of four common estimators of process standard deviation for grouped data in statistical quality control.
Methodology: To achieve the research objectives, the bias and the Mean Squared Error (MSE) of the estimators will first be presented. Then, the estimators will be compared based on their MSEs.
Findings: It is shown that two estimators out of four estimators belong to two different classes of linear unbiased estimators with the minimum variance. Furthermore, numerical calculations show that the estimator based on the arithmetic mean of the group standard deviations is more efficient than the other estimators.
Originality/Value: Based on the results obtained in this study, it is suggested that for estimating the standard deviation of the process in grouped data, an estimator based on the arithmetic mean of the standard deviations of the groups should be used instead of estimators that are based on the arithmetic mean of the ranges of the groups.

Keywords

Statistical quality control
Process standard deviation
Estimator
Mean squared error
Relative efficiency
Subjects
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Journal of Quality Engineering and Management
Volume 15, Issue 4
Winter 2026
Pages 433-467

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