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# A Comparison of Performances of Three Types of Control Charts for Skewed Distributions

Khoo, Michael B.C., and Mazidah Kassim, (2008) A Comparison of Performances of Three Types of Control Charts for Skewed Distributions. Matematika, 24 (2). pp. 169-185. ISSN 01278274

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## Affiliations

Universiti Sains Malaysia, School of Mathematical Studies
Universiti Sains Malaysia, School of Mathematical Studies

## Abstract

This paper compares three different types of control charting methods used in the monitoring of a process mean from a skewed distribution. The skewed distributions considered are the Weibull, lognormal and gamma distributions while the control charts for skewed distributions studied are the weighted variance ¯X chart `WV − ¯X chart´ , weighted standard deviation ¯X chart `WSD − ¯X chart´ and skewness correction ¯X chart (SC − ¯X chart). These charts will be evaluated based on their in-control average run length (ARL0) performances. ARL is defined as the average number of sample points that must be plotted on a control chart before the first point plots beyond the control limits. Since these charts are designed based on the three standard deviation width, ARL0 _ 370 is considered when the underlying distribution of a process is normal. A good chart has a large ARL0 value when the process follows a skewed distribution. A performance comparison based on a simulation study using the Statistical Analysis System (SAS) version 9 program shows that the SC − ¯X and WSD − ¯X charts have better ARL0 performances than the WV − ¯X chart. The SC − ¯X and WSD − ¯X charts have about the same ARL0 performances.

Item Type: Journal Control chart; skewed distribution; weighted variance (WV); weighted; standard deviation (WSD); skewness correction (SC); average run length (ARL); process mean. Q Science, Computer ScienceL Education 5394

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