Controlling the exponentially weighted moving average šĀ² control chart false alarm behavior when the inācontrol variance level must be estimated
Publication date
2021-03-23
Document type
Forschungsartikel
Author
Organisational unit
Scopus ID
Publisher
Wiley
Series or journal
Applied Stochastic Models in Business and Industry
ISSN
Periodical volume
37
Periodical issue
4
First page
725
Last page
743
Part of the university bibliography
ā
Language
English
Keyword
Control charting
False alarm probability
Phase I/II
S2 EWMA
Abstract
Investigating the problem of setting control limits for an exponentially weighted moving average (EWMA) chart in the case of parameter uncertainty is more accessible when monitoring the variance because only one parameter has to be estimated. Simply ignoring the induced uncertainty frequently leads to control charts with poor false alarm performances. Adjusting the unconditional inācontrol (IC) average run length (ARL) makes the situation even worse. Guaranteeing a minimum conditional IC ARL with some given probability is another very popular approach to solving these difficulties. However, it is very conservative as well as more complex and more difficult to communicate. We utilize the probability of a false alarm within the planned number of points to be plotted on the control chart. It turns out that adjusting this probability produces notably different limit adjustments compared to controlling the unconditional IC ARL. We then develop numerical algorithms to determine the respective modifications of the upper and twoāsided EWMA charts based on the sample variance for normally distributed data. These algorithms are made available within an
R
package. Finally, the impacts of the EWMA smoothing constant and the size of the preliminary sample on the control chart design and its performance are studied.
R
package. Finally, the impacts of the EWMA smoothing constant and the size of the preliminary sample on the control chart design and its performance are studied.
Description
This is an open access article under the terms of the Creative Commons Attribution License CC BY 4.0 ( https://creativecommons.org/licenses/by/4.0/).
Version
Published version
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Metadata only access