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Optimal design of one‐sided exponential cumulative sum charts with known and estimated parameters based on the median run length
Author(s) -
Qiao YuLong,
Hu XueLong,
Sun JinSheng,
Xu Qin
Publication year - 2021
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.2725
Subject(s) - cusum , control chart , x bar chart , chart , statistics , exponential function , ewma chart , mathematics , markov chain , shewhart individuals control chart , statistical process control , exponential distribution , computer science , process (computing) , mathematical analysis , operating system
As a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high‐quality processes. Considering both known and estimated parameter cases, the one‐sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run length ( R L ) distribution of the one‐sided exponential CUSUM charts is skewed and it also changes with the mean shift size and the number of Phase I samples used to estimate the process parameter, the median run length ( M R L ) is employed as a good alternative performance measure for the charts. The optimal design procedures based on M R L of the one‐sided exponential CUSUM charts with known and estimated parameters are discussed. By comparing the M R L performance of the chart with known parameters with the one of the chart with estimated parameters, we investigate the effect of estimated process parameters on the properties of the chart. Finally, an application is illustrated to show the implementation of the chart.