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Run sum X ¯ control chart with estimated process parameters
Author(s) -
Saha Sajal,
Khoo Michael B. C.,
Teoh W. L.,
Lee Ming Ha
Publication year - 2017
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2153
Subject(s) - control chart , x bar chart , chart , statistics , standard deviation , ewma chart , mathematics , control limits , moving average , process (computing) , \bar x and r chart , statistical process control , computer science , operating system
The run sum X ¯ control chart is usually investigated under the assumption of known process parameters. In practice, process parameters are rarely known and they need to be estimated from an in‐control Phase I dataset. However, different practitioners use different numbers of Phase I samples to estimate the process parameters. As a result, the commonly used performance measure, ie, the average run length becomes a random variable. In this study, we present a run sum X ¯ control chart with estimated process parameters and use the standard deviation of the average run length to evaluate the average of the average run length performance of the run sum X ¯ chart when process parameters are estimated. Based on the standard deviation of the average run length criterion, the number of Phase I samples required by the estimated process parameter–based run sum X ¯ chart to have an average of the average run length performance close to that obtained under the assumption of known process parameters is recommended.