A phase II run sum chart for monitoring process mean and variability

This article proposes a run sum Max chart for monitoring a process and detecting changes in mean and variability simultaneously. A Markov chain method is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteri...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2023-09, Vol.93 (13), p.2276-2296
Main Authors: Antzoulakos, D. L., Fountoukidis, K. G., Rakitzis, A. C.
Format: Article
Language:English
Subjects:
Average run length
Control charts
expected average run length
Markov chain
Markov chains
Max chart
Mean
Monitoring
Numerical analysis
Performance evaluation
Process parameters
statistical process control
Sums
Variability
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Summary:This article proposes a run sum Max chart for monitoring a process and detecting changes in mean and variability simultaneously. A Markov chain method is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteria. The numerical analysis demonstrates an improved performance of the run sum Max control chart over the usual Max chart. In addition, a numerical comparison with the Max-EWMA control chart as well as with the Max chart supplemented with runs rules, reveals that the run sum Max chart outperforms these charts in the detection of moderate to large shifts in both process parameters. Furthermore, we provide practical guidance for the selection of the appropriate charting procedure, while the use of the proposed run sum Max chart in practice is illustrated via a numerical example.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2023.2178652