Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables
Publication date
2018-01-15
Document type
Forschungsartikel
Author
Tran, Kim Phuc
Organisational unit
Scopus ID
Publisher
Wiley
Series or journal
Quality and Reliability Engineering International
ISSN
Periodical volume
34
Periodical issue
3
First page
377
Last page
390
Part of the university bibliography
✅
Language
English
Keyword
ARL-unbiased
Fredholm integral equation of the second kind
Nyström method
ratio distribution
Abstract
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 (ARL) biased, in the sense that some out‐of‐control ARL values are larger than the in‐control ARL. 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 ARL. 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 ARL. An example illustrates the use of this chart on a real quality control problem from the food industry.
Version
Published version
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