Distribution‐free precedence control charts with improved runs‐rules |
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| Authors: | J‐C Malela‐Majika S Chakraborti M A Graham |
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| Affiliation: | 1. Department of Statistics, University of Pretoria, Pretoria, South Africa;2. Department of Statistics, College of Science, Engineering and Technology, University of South Africa, Pretoria, South Africa;3. Department of Information Systems, Statistics and Management Science, University of Alabama, Tuscaloosa, AL, U.S.A. |
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| Abstract: | Distribution‐free (nonparametric) control charts are helpful in applications where we do not have enough information about the underlying distribution. The Shewhart precedence charts is a class of Phase I nonparametric charts for location. One of these charts, called the median precedence chart (Med chart hereafter), uses the median of the test sample as the charting statistic, whereas another chart, called the minimum precedence chart (Min chart hereafter), uses the minimum. In this paper, we first study the comparative performance of the Min and the Med charts, respectively, in terms of their in‐control and out‐of‐control run‐length properties in an extensive simulation study. It is seen that neither chart is best as each has its strength in certain situations. Next, we consider enhancing their performance by adding some supplementary runs‐rules. It is seen that the new charts present very attractive run‐length properties, that is, they outperform their competitors in many situations. A summary and some concluding remarks are given. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | improved modified runs‐rules improved runs‐rules nonparametric order statistics |
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