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Open AccessArticle

Cumulative Sum Chart Modeled under the Presence of Outliers

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Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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Preparatory Year Mathematics Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 269; https://doi.org/10.3390/math8020269
Received: 26 December 2019 / Revised: 9 February 2020 / Accepted: 11 February 2020 / Published: 18 February 2020
(This article belongs to the Special Issue Statistics and Modeling in Reliability Engineering)
Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width of control limits resulting in a deprived performance of the control chart. In this study, we introduce a non-parametric Tukey’s outlier detection model in the design structure of a two-sided cumulative sum (CUSUM) chart with estimated parameters for process monitoring. Using Monte Carlo simulations, we studied the estimation effect on the performance of the CUSUM chart in terms of the average run length and the standard deviation of the run length. We found the new design structure is more stable in the presence of outliers and requires fewer amounts of Phase I observations to stabilize the run-length performance. Finally, a numerical example and practical application of the proposed scheme are demonstrated using a dataset from healthcare surveillance where received signal strength of individuals’ movement is the variable of interest. The implementation of classical CUSUM shows that a shift detection in Phase II that received signal strength data is indeed masked/delayed if there are outliers in Phase I data. On the contrary, the proposed chart omits the Phase I outliers and gives a timely signal in Phase II. View Full-Text
Keywords: average run length; control chart; cumulative sum; outlier; health care; statistical process control average run length; control chart; cumulative sum; outlier; health care; statistical process control
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Abbas, N.; Abujiya, M.R.; Riaz, M.; Mahmood, T. Cumulative Sum Chart Modeled under the Presence of Outliers. Mathematics 2020, 8, 269.

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