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CCC‐ r charts' performance with estimated parameter for high‐quality process
Author(s) -
Zhang Min,
Hou Xuejun,
Chen Hui,
He Shuguang
Publication year - 2019
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.2438
Subject(s) - cusum , control chart , chart , x bar chart , statistics , statistical process control , ewma chart , control limits , standard deviation , process (computing) , mathematics , computer science , \bar x and r chart , operating system
Abstract CCC‐ r charts are effective in detecting process shifts in the nonconforming rate especially for a high‐quality process. The implementation of the CCC‐ r charts is usually under the assumption that the in‐control nonconforming rate is known. However, the nonconforming rate is never known, and accurate estimation is difficult. We investigate the effect of estimation error on the CCC‐ r charts' performances through the expected value of the average number of observations to signal (EANOS) as well as the standard deviation of the average number of observations to signal (SDANOS). By comparing the in‐control performance of the CCC‐ r charts, the CCC‐ r chart with a larger value of r is more susceptible to the effects of parameter estimation. Meanwhile, the performance of the CCC‐ r charts can converge when detecting upward shifts in p of out‐of‐control processes. We recommend the use of the CCC‐4 chart when considering its effectiveness in detecting shifts as well as its easier construction in practice. Furthermore, it is investigated that the CCC‐4 chart is less sensitive to parameter estimation while being more effective in detecting different process shifts when compared with Geometric CUSUM chart and synthetic chart.