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A New EWMA Chart Based on Weighted Loss Function for Monitoring the Process Mean and Variance
Author(s) -
Liang Wenjuan,
Pu Xiaolong,
Li Yan
Publication year - 2015
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.1647
Subject(s) - ewma chart , x bar chart , chart , cusum , control chart , statistics , standard deviation , statistic , mean shift , variance (accounting) , moving average , shewhart individuals control chart , growth chart , control limits , computer science , mathematics , process (computing) , artificial intelligence , pattern recognition (psychology) , accounting , business , operating system
With the weighted loss function, a new single Exponential Weighted Moving Average (EWMA) chart (WLE chart hereafter for short) is proposed to detect both mean and variance shifts simultaneously. It includes the EWMA control chart based on the semicircle statistic and weighted‐loss‐function control chart as special cases. Numerical studies show that the WLE chart is superior to the weighted‐loss‐function Cumulative Sum (CUSUM) chart when the mean and standard deviation shifts are both small, and offers at least comparable detection ability with the WLC chart in other cases. Compared with the Shiryaev–Roberts chart, the WLE chart has a better or comparable performance except for small and moderate mean shifts. Furthermore, an equivalent form of the WLE chart is developed to diagnose the source and direction of a process change. Copyright © 2014 John Wiley & Sons, Ltd.