Research Article Open Access

A Simple Robust Control Chart Based on MAD

Moustafa Omar Ahmed Abu-Shawiesh1
  • 1 ,
Journal of Mathematics and Statistics
Volume 4 No. 2, 2008, 102-107

DOI: https://doi.org/10.3844/jmssp.2008.102.107

Submitted On: 4 August 2008 Published On: 30 June 2008

How to Cite: Abu-Shawiesh, M. O. A. (2008). A Simple Robust Control Chart Based on MAD. Journal of Mathematics and Statistics, 4(2), 102-107. https://doi.org/10.3844/jmssp.2008.102.107

Abstract

Control charts are one of the most powerful tools used to detect aberrant behavior in industrial processes. The Shewhart S-control chart is one of the most widely used statistical process control techniques developed to control the process variability based on the fundamental assumption that the underlying distribution of the quality characteristic is normal. When the underlying normality assumption is not met, the robust methods are one of the most commonly used statistical methods preferred in such situations. We presented a simple approach to robust estimation of the process standard deviation σ based on a very robust scale estimator, namely, the median absolute deviation from the sample median (MAD). The proposed method provides an alternative to the Shewhart S-control chart. A numerical example was given and a Mote Carlo simulation study was conducted to illustrate the performance of the proposed method and compare it with that of the Shewhart method. The proposed robust method was lead to a better performance than the Shewhart method and has good properties for the heavy tailed distributions and moderate sample sizes.

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Keywords

  • Average run length
  • breakdown point
  • influence function
  • median absolute deviation