Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables |
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| Authors: | Kim Phuc Tran Sven Knoth |
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| Affiliation: | 1. Division of Data Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. Department of Economics and Social Sciences, Institute of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany |
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| 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. |
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| Keywords: | ARL‐unbiased Fredholm integral equation of the second kind Nyströ m method ratio distribution |
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