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SXC control chart

SXC control chart. 指導教授：童超塵 作者： Zhang Wu, Ming Xie, Qingchuan Lin and Yu Zhang 主講人：廖莉芳. The International Journal of Advanced Manufacturing Technology Volume 30, Numbers 5-6 / September, 2006. Outline. Introduction Design of the SXC chart

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SXC control chart

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  1. SXC control chart 指導教授：童超塵 作者：Zhang Wu, Ming Xie, Qingchuan Lin and Yu Zhang 主講人：廖莉芳 The International Journal of Advanced Manufacturing Technology Volume 30, Numbers 5-6 / September, 2006

  2. Outline • Introduction • Design of the SXC chart • Comparative studies • Conclusions and discussions

  3. Introduction • SXC (sum of xs with curtailment) control chart. • as simple as the X-bar chart ; as effective as the CUSUM chart

  4. Design of the SXC chart • Some parameters need to be specified: • Calculation of ATS • Two key samples： • Shifting sample – mean shift takes place • Signalling sample – mean shift is detected

  5. Design of the SXC chart • The steps for calculating ATS are outlined below. (1) Calculate p(m) • p(m) is the probability that the mean shift is detected after inspecting the mth unit in the signalling sample (2) Calculate Q • Q is the probability that the out-of-control condition is detected in a single sample. (3) Calculate q • q is the average number of units inspected in the signalling sample. (4) Finally,compute ATS

  6. Design of the SXC chart

  7. Design of the SXC chart • The optimization design of the SXC chart • How to choose n? • The sample size n will be increased from Nmin in step of one until ATS can not be further reduced. • The steps are outlined below:

  8. Design of the SXC chart

  9. Comparative studies • Compares the performance of three control, X-bar chart、CUSUM chart and the SXC chart. • The sample size and control limits of all the charts are determined by the same optimization model. • Nmin =4 • Study one • τ=1850 (ARL0=370 and n=5) • 0.0≦δ ≦3.4

  10. Comparative studies • There are several interesting findings： • ATS0 that are very close toτ (=1850) • very similar false alarm rates • When the mean shift becomes large, the curtailment mechanism enables the SXC chart to signal the out-of-control condition before all of the n units in a sample are inspected. • The ATS values of the two charts do not differ significantly for any given mean shift value.

  11. average ratio

  12. Study two

  13. Conclusions and discussions • SXC 管制圖比X-bar管制圖好，平均可縮短74％的ATS。 • 雖然SXC跟CUSUM管制圖效率差不多，但是SXC管制圖比較簡單。 • 即使換成random inspection或uniform inspection 結果也差不多。 • 也許可以將相同的手法用在R或其他管制圖上

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