New results for two-sided CUSUM-Shewhart control charts
Publication date
2018-06-16
Document type
Konferenzbeitrag
Author
Organisational unit
Conference
12th International Workshop on Intelligent Statistical Quality Control ; Hamburg, Germany ; August 16-19, 2016
Publisher
Springer
Series or journal
Periodical volume
12
Book title
Frontiers in Statistical Quality Control 12
Part of the university bibliography
✅
Language
English
Abstract
Already Yashchin (IBM J Res Dev 29(4):377–391, 1985), and of course Lucas (J Qual Technol 14(2):51–59, 1982) 3 years earlier, studied CUSUM chart supplemented by Shewhart limits. Interestingly, Yashchin proposed to calibrate the detecting scheme via P ∞ (RL > K) ≥ 1 − α for the run length (stopping time) RL in the in-control case. Calculating the RL distribution or related quantities such as the ARL (Average Run Length) are slightly complicated numerical tasks. Similarly to Capizzi and Masarotto (Stat Comput 20(1):23–33, 2010) who utilized Clenshaw-Curtis quadrature to tackle the ARL integral equation, we deploy less common numerical techniques such as collocation to determine the ARL. Note that the two-sided CUSUM chart consisting of two one-sided charts leads to a more demanding numerical problem than the single two-sided EWMA chart.
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Published version
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