Estimating the Standard Deviation in Quality-Control Applications

By Mahmoud A. Mahmoud, Robin Henderson, Eugenio K. Epprecht, William H. Woodall. 2010

100 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/35ea2af260c52cf097863c0fbe9e438bedb66ef7

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

The Difficulty in Designing Shewhart X̄ and X Control Charts with Estimated Parameters (2015, methodology): “In terms of relative e ciency, Mahmoud et al. (2010) strongly recommended against the use of the range-based estimator (̂1) because of its low e ciency compared with the other four estimators.”
Effect of the Amount of Phase I Data on the Phase II Performance of S2 and S Control Charts (2015, background): “Maravelakis et al. (2002) stated that at least m = 200 subgroups are needed with sample sizes of up to 20 units and recommended therefore using larger sample sizes (n > 20) and taking 100 samples in phase I.”
Two perspectives for designing a phase II control chart with estimated parameters: The case of the Shewhart Chart (2020, methodology): “The unbiased pooled estimator we use here has been highly recommended in the recent literature (see Mahmoud et al. 2010 and Saleh et al. 2015a, b).”
Design and Analysis of Control Charts for Standard Deviation with Estimated Parameters (2011, unknown): “Mahmoud et al. (2010) studied the relative e ciencies of these estimators for di↵erent sample sizes n and number of samples k.”
Another Look at the EWMA Control Chart with Estimated Parameters (2015, methodology): “Among the di↵erent forms of the pooled estimator, Derman and Ross (1995) recommended the use of ̂5, while Vardeman (1999) and Mahmoud et al. (2010) showed that ̂4 has the lowest MSE.”
Shewhart control charts for dispersion adjusted for parameter estimation (2017, methodology): “For example, a commonly used estimator of σ0 in the Phase I control limit is the square root of pooled variances (also recommended by Mahmoud et al. (2010)), defined as Sp = √ S2p = √∑m i=1 (n − 1)S2i m(n − 1) = √∑m i=1 S2i m .”