THE CUSUM MEDIAN CHART FOR KNOWN AND ESTIMATED PARAMETERS

* The usual CUSUM chart for the mean (CUSUM-[bar.X]) is a chart used to quickly detect small to moderate shifts in a process. In presence of outliers, this chart is known to be more robust than other mean-based alternatives like the Shewhart mean chart but it is nevertheless affected by these unusua...

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Bibliographic Details
Published inRevstat Vol. 17; no. 3; pp. 345 - 370
Main Authors Castagliola, Philippe, Figueiredo, Fernanda Otilia, Maravelakis, Petros E
Format Journal Article
LanguageEnglish
Published Instituto Nacional de Estatistica 01.07.2019
Instituto Nacional de Estatística | Statistics Portugal
Subjects
average run length
CUSUM chart
estimated parameters
Markov processes
median
order statistics
Other Statistics
Statistics
CUSUM chart
estimated parameters
order statistics
average run length
median
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Summary:* The usual CUSUM chart for the mean (CUSUM-[bar.X]) is a chart used to quickly detect small to moderate shifts in a process. In presence of outliers, this chart is known to be more robust than other mean-based alternatives like the Shewhart mean chart but it is nevertheless affected by these unusual observations because the mean ([bar.X]) itself is affected by the outliers. An outliers robust alternative to the CUSUM-[bar.X] chart is the CUSUM median (CUSUM-[??]) chart, because it takes advantage of the robust properties of the sample median. This chart has already been proposed by other researchers and compared with other alternative charts in terms of robustness, but its performance has only been investigated through simulations. Therefore, the goal of this paper is not to carry out a robustness analysis but to study the effect of parameter estimation in the performance of the chart. We study the performance of the CUSUM-[??] chart using a Markov chain method for the computation of the distribution and the moments of the run length. Additionally, we examine the case of estimated parameters and we study the performance of the CUSUM-[??] chart in this case. The run length performance of the CUSUM-[??] chart with estimated parameters is also studied using a proper Markov chain technique. Conclusions and recommendations are also given. Key-Words: * average run length; CUSUM chart; estimated parameters; median; order statistics. AMS Subject Classification: * 62G30, 62P30.
ISSN:1645-6726
2183-0371
DOI:10.57805/revstat.v17i3.271