Performance comparison of the exact run-length distribution between the run sum X and EWMA X charts
The run sum (RS) X and exponentially weighted moving average (EWMA) X charts are very effective in detecting small and moderate process mean shifts. The design of the RS X and EWMA X charts based on the average run length (ARL) alone, can be misleading and confusing. This is due to the fact that...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia
2016
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| Online Access: | http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/1/jqma-12-1_2-paper2.pdf |
| Summary: | The run sum (RS) X and exponentially weighted moving average (EWMA) X charts are very
effective in detecting small and moderate process mean shifts. The design of the RS X and
EWMA X charts based on the average run length (ARL) alone, can be misleading and
confusing. This is due to the fact that the run-length distribution of a control chart is highly
right-skewed when the process is in-control or slightly out-of-control; while that for the out-ofcontrol
cases, the run-length distribution is almost symmetric. On the other hand, the percentiles
of the run-length distribution provide the probability of getting a signal by a certain number of
samples. This will benefit practitioners as the percentiles of the run-length distribution give
comprehensive information regarding the behaviour of a control chart. Accordingly, this paper
provides a thorough study of the run-length properties (ARL, standard deviation of the run
length and percentiles of the run-length distribution) for the RS X and EWMA X charts.
Comparative studies show that the EWMA X chart outperforms the RS X charts for detecting
small mean shifts when all the control charts are optimized with respect to a small shift size.
However, the RS X charts surpass the EWMA X chart for all sizes of mean shifts when all
the control charts are optimized with respect to a large shift size. |
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