Performance of Median Absolute Deviation and some Alternatives to Median Absolute Deviation Control Charts for Skewed and Heavily Tailed Process
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Date
2020
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Publisher
John Wiley & Sons, Ltd.
Abstract
In this paper, ̄X
charts based on robust scale estimators (known as 𝑆𝑛 and 𝑄𝑛 estimators)
are proposed, and the performance of control charts based on median
absolute deviation (MAD) is compared with those based on some alternatives to
MAD, which do not need any location estimate, for normal, skewed, and heavily
tailed distributions. MAD is often used as a substitute for standard deviation
in constructing control charts due to its robustness. Three alternatives to MAD
namely the Sn, Qn, and Downton (D) are considered in this paper as location-free
estimators. A simulation study was carried out to appraise the performance of
the control charts based on the MAD, 𝑆𝑛, 𝑄𝑛, and D estimators. The average run
length (ARL), median run length (MRL), standard deviation run length (SDRL),
and control limits interval (CLI) were used to assess the performance of the four
control charts. The results showed that MAD, 𝑆𝑛, and D are suitable estimators
for standard deviation for mean charts while 𝑆𝑛 and 𝑄𝑛 are suitable estimators
for standard deviation for dispersion charts for skewed and heavily tailed distributions.
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Keywords
alternative median absolute deviation, control charts, location-free estimators, median absolute deviation, skewed process data