Nonparametric Moving Average Control Charts Using Sign and Signed-Rank Statistics

Vilas Yashwant Pawar¹ , Digambar Tukaram Shirke² , Shashikant Kuber Khilare³

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.4 , pp.171-178, Aug-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.171178

Online published on Aug 31, 2018

Copyright © Vilas Yashwant Pawar, Digambar Tukaram Shirke , Shashikant Kuber Khilare . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we provide two nonparametric moving average control charts based on well-known nonparametric statistics namely sign and signed-rank statistic. These control charts are useful in detecting shifts in the median of the symmetric process distributions. Average run length of these control charts has been studied for various symmetric process distributions. These include the normal, double exponential and Cauchy distributions. Performance of the proposed nonparametric moving average control chart based on the sign statistic is compared with the nonparametric sign chart and the Shewhart X-bar chart. Also, the performance of the proposed nonparametric control chart based on signed-rank statistic is compared with the Shewhart X-bar chart and the 2-of-2 control chart based on the signed-rank statistic. The study reveals that the proposed nonparametric moving average control chart based on sign statistic perform significantly better than the nonparametric sign chart and Shewhart X-bar chart. Also, the performance of the proposed nonparametric moving average control chart based on the signed-rank statistic perform significantly better than the Shewhart X-bar chart and the 2-of-2 chart based on the signed-rank statistics. The gain in the performance is substantial for heavy-tail distributions as compared to light-tail distribution. Robustness study against contamination by outliers for both the proposed charts show satisfactory performance. These chars can be used in practice, since they are simple to use and do not need any distributional assumptions, except symmetry.

Key-Words / Index Term :
Nonparametric, Sign Statistic, Sign-Rank Statistic, Average Run Length.

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