Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality and Reliability Engineering International Wiley

Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0748-8017
eISSN
1099-1638
D.O.I.
10.1002/qre.2259
Publisher site
See Article on Publisher Site

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.

Journal

Quality and Reliability Engineering InternationalWiley

Published: Jan 1, 2018

Keywords: ; ; ;

References

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