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Economic Analysis for Detection of Out-of-Control of Process Using 2 of 2 Runs Rules  

Kim, Young Bok (Department of Industrial Engineering, Seoul National University)
Hong, Jung Sik (Department of Industrial and Information Systems Engineering, Seoul National University of Technology)
Lie, Chang Hoon (Department of Industrial Engineering, Seoul National University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.34, no.3, 2008 , pp. 308-317 More about this Journal
Abstract
This research investigates economic characteristics of 2 of 2 runs rules under the Shewhart $\bar{X}$ control chart scheme. A Markov chain approach is employed in order to calculate the in-control average run length (ARL) and the average length of analysis cycle. States of the process are defined according to the process conditions at sampling time and transition probabilities are derived from the state definitions. A steady state cost function is constructed based on the Lorezen and Vance(1986) model. Numerical examples show that 2 of 2 runs rules are economically superior to the Shewhart $\bar{X}$ chart in many cases.
Keywords
Shewhart Control Chart; 2 of 2 Runs Rule; ARL; Economic Analysis;
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Times Cited By KSCI : 2  (Citation Analysis)
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