The Design of the S2 Control Charts Based on Conditional Performance via Exact Methods

In this paper, we consider the conditional performance of the equal‐tailed and average run lengths (ARL)‐unbiased two‐sided S2 charts when the in‐control variance of a normal process is estimated. We derive the exact probability distributions of the conditional ARL for the two S2 charts. Then we eva...

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Bibliographic Details
Published inQuality and reliability engineering international Vol. 33; no. 7; pp. 1567 - 1575
Main Authors Guo, Baocai, Wang, Bing Xing
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 01.11.2017
Wiley Subscription Services, Inc
Subjects
Control charts
estimation effect
Parameter estimation
Performance evaluation
Standard deviation
standard deviation of average run length
statistical process control
unbiased control chart
variance monitoring
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Summary:In this paper, we consider the conditional performance of the equal‐tailed and average run lengths (ARL)‐unbiased two‐sided S2 charts when the in‐control variance of a normal process is estimated. We derive the exact probability distributions of the conditional ARL for the two S2 charts. Then we evaluate the performance of each S2 chart in terms of the percentiles, mean and standard deviation of the conditional in‐control ARL distribution. Because the parameter estimation seriously affects the conditional performance of these S2 charts, we propose an exact method to design the equal‐tailed and ARL‐unbiased S2 charts with desired conditional in‐control performance. The results indicate that the new ARL‐unbiased S2 chart has far smaller standard deviation ARL values and the unconditional ARL values are more close to the desired value than the corresponding new equal‐tailed S2 chart. Copyright © 2017 John Wiley & Sons, Ltd.
ISSN:0748-8017
1099-1638
DOI:10.1002/qre.2125