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Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables
Author(s) -
Tran Kim Phuc,
Knoth Sven
Publication year - 2018
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.2259
Subject(s) - ewma chart , control chart , statistics , x bar chart , statistical process control , control limits , chart , mathematics , shewhart individuals control chart , computer science , process (computing) , operating system
Very recently, control charts for monitoring the ratio of 2 normal variables have been investigated in statistical process control. In the two‐sided case, however, these control charts tend to be average run length ( A R L ) biased, in the sense that some out‐of‐control A R L values are larger than the in‐control A R L . This paper proposes an ARL‐unbiased EWMA control chart for monitoring of this kind of ratio with each subgroup consisting of n ⩾1 sample units. Also, to study the long‐term properties of ARL‐unbiased EWMA‐RZ control chart, we investigate the steady‐state A R L . Several tables and figures are given to show the statistical properties of the proposed control charts. The comparison results show that the proposed ARL‐unbiased chart outperforms other two‐sided control charts in terms of the zero‐state and steady‐state A R L . An example illustrates the use of this chart on a real quality control problem from the food industry.