Optimal design of the adaptive EWMA chart for the mean based on median run length and expected median run length. Issue 4 (4th July 2019)

• Record Type: Journal Article
• Authors: Tang, Anan; Castagliola, Philippe; Sun, Jinsheng; Hu, Xuelong
• Is Part Of: Quality technology & quantitative management. Volume 16:Issue 4(2019)
• Page Start: 439
• Page End: 458
• Publication Date: 2019-07-04
• Subjects: Adaptive EWMA chart -- median run length -- average run length; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2018.1460908
• Languages: English
• ISSNs: 1684-3703

Abstract

Abstract: The Adaptive Exponentially Weighted Moving Average (AEWMA) chart, which combines the Shewhart and classical EWMA schemes, is usually designed using the Average Run Length ( A R L ) as the criterion to be optimized. The shape of the run length distribution is known to change according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control or nearly to approximately symmetric when the shift is large. Therefore, the Median Run Length ( M R L ) provides a more meaningful interpretation than the A R L . In this paper, the M R L is used as an alternative performance criterion, and the AEWMA X ¯ chart is optimized for a wide range of mean shifts using zero and steady state modes. Comparative results show that the suggested AEWMA X ¯ chart offers a more balanced protection for detecting both small and large shifts in the process mean than the classical EWMA X ¯ chart, in terms of the M R L performance. The construction of the M R L -based AEWMA X ¯ chart is also illustrated using an example, and it is compared with competing charts.