The Design of the S2 Control Charts Based on Conditional Performance via Exact Methods |
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| Authors: | Baocai Guo Bing Xing Wang |
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| Affiliation: | School of Statistics, Zhejiang Gongshang University, Hangzhou, China |
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| Abstract: | 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. |
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| Keywords: | estimation effect variance monitoring unbiased control chart standard deviation of average run length statistical process control |
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