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題名 具量測誤差校正的變異數管制圖
Adjustment of Measurement Error Effects on the Distribution-free Dispersion Control Chart
作者 林政寬
Lin, Cheng-Kuan
貢獻者 楊素芬<br>陳立榜
Yang, Su-Fen<br>Chen, Li-Pang
林政寬
Lin, Cheng-Kuan
關鍵詞 量測誤差校正
指數加權移動平均管制圖
變異數管制圖
Measurement error elimination
Exponentially weighted moving average control chart
Dispersion control chart
日期 2022
上傳時間 8-Feb-2023 15:42:32 (UTC+8)
摘要 在工業製程中，管制圖是監測產品品質和檢測製成是否失控的有效工具。雖然有許多類型的管制圖可供數據分析者使用，但使用這些管制圖的前提是在變量被精確測量的情況下。然而，在實際應用中，當資料被調查者錯誤得記錄或被未經調整的機器不精確得收集時，量測誤差是無可避免的。儘管量測誤差對不同類型的管制圖的影響已經被探討過，但誤差修正的管制圖仍然很少被討論。因此在此研究中，我們提出了一種新的帶有誤差修正的變異數管制圖來填補這一研究空白。我們的主要想法是將觀察到的製程變量轉換為符號統計量，然後以一個函數來調整符號統計量，以校正量測誤差的影響。最後，我們根據修正後的符號統計量提出帶有量測誤差修正的指數加權移動平均數變異數管制圖。我們所開發的誤差修正的變異數管制圖不僅消除了量測誤差的影響，而且為監測製程變異數提供了更可靠的管制界線。透過數值分析，我們發現所提出的誤差修正變異數管制圖能夠有效處理中等和較大程度的量測誤差，並對監測製程是否失控有著良好的表現。最後，我們使用半導體資料來驗證所提出的誤差修正變異數管制圖之應用。
In industrial processes, control charts are useful tools to monitor the quality of products and detect possibly out-of-control processes. While many types of control charts have been available for data analysts, they were developed by assuming that the variables are precisely measured. In applications, however, measurement error is ubiquitous when data are falsely recorded by investigator or imprecisely collected by unadjusted machines. Even though the impacts of measurement error for different types of control charts have been explored, error-corrected control charts are still unavailable. In this study, we propose a new dispersion control chart with error correction to fill out this research gap. Our key idea is to convert the observed process variables into a flexible sign statistic, and then adopt a function to adjust the measurement error effects on the sign statistic. Finally, we develop the exponentially weight moving average dispersion control chart with measurement error correction based on the corrected sign statistic. The proposed error-corrected dispersion control chart not only eliminates measurement error effects, but also provides more reliable control limits for monitoring process dispersion. Throughout numerical examination, we find that the proposed error-corrected dispersion control chart is effective in handling the moderate and large levels of measurement error and shows well out-of-control detection performance. Finally, the proposed error-corrected dispersion control chart is implemented to the semiconductor data.
參考文獻 Abbas, N., Riaz, M., & Does, R. J. (2014). An EWMA-type control chart for monitoring the process mean using auxiliary information. Communications in Statistics-Theory and Methods, 43(16), 3485-3498.
Amin, R. W., Reynolds Jr, M. R., & Saad, B. (1995). Nonparametric quality control charts based on the sign statistic. Communications in Statistics-Theory and Methods, 24(6), 1597-1623.
Asif, F., Khan, S., & Noor-ul-Amin, M. (2020). Hybrid exponentially weighted moving average control chart with measurement error. Iranian Journal of Science and Technology, Transactions A: Science, 44(3), 801-811.
Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), 613-623.
Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757.
Case, K. E. (1980). The p control chart under inspection error. Journal of Quality Technology, 12(1), 1-9.
27. Chen, L.-P. and Yang, S.-F. A new p-control chart with measurement error correction. Quality and Reliability Engineering In-ternational 2022, 1-18. DOI: 10.1002/qre.3219
Chowdhury, S., Mukherjee, A., & Chakraborti, S. (2014). A new distribution‐free control chart for joint monitoring of unknown location and scale parameters of continuous distributions. Quality and Reliability Engineering International, 30(2), 191-204.
Daryabari, S. A., Malmir, B., & Amiri, A. (2019). Monitoring Bernoulli processes considering measurement errors and learning effect. Quality and Reliability Engineering International, 35(4), 1129-1143.
Daryabari, S. A., Hashemian, S. M., Keyvandarian, A., & Maryam, S. A. (2017). The effects of measurement error on the MAX EWMAMS control chart. Communications in Statistics-Theory and Methods, 46(12), 5766-5778.
McCann, M. and Johnston, A. UCI Machine Learning Repository. Available online: https://archive.ics.uci.edu/ml/datasets/SECOM (accessed on 1 December 2021)
Huwang, L., & Hung, Y. (2007). Effect of measurement error on monitoring multivariate process variability. Statistica Sinica, 749-760.
Linna, K. W., & Woodall, W. H. (2001). Effect of measurement error on Shewhart control charts. Journal of Quality technology, 33(2), pp. 213-222.
Linna, K. W., Woodall, W. H. & Busby, K. L. (2001). The performance of multivariate control charts in the presence of measurement error, Journal of Quality Technology, 33, pp. 349–355.
Lu, X. S., Xie, M., & Goh, T. N. (2000). An investigation of the effects of inspection errors on the run-length control charts. Communications in Statistics-simulation and Computation, 29(1), 315-335.
Maravelakis, P., Panaretos, J., & Psarakis, S. (2004). EWMA chart and measurement error. Journal of Applied Statistics, 31(4), pp. 445-455.
Mittag H-J, & Stemann D. (1998). Gauge imprecision effect on the performance of the \\overline{X}-S control chart. Journal of Applied Statistics, 25, pp. 307–317.
McFadden, D. (1984). Econometric analysis of qualitative response models. In: Griliches, Z., Intriligator, M.D. (Eds.), Handbook of Econometrics, vol. 2. North–Holland, Amsterdam.
Noor-ul-Amin, M., Riaz, A., & Safeer, A. (2019). Exponentially weighted moving average control chart using auxiliary variable with measurement error. Communications in Statistics-Simulation and Computation, pp. 1-13.
Nojavan, M., Alishahi, M., Rezaee, M., & Rahaee, M. A. (2021). The effect of measurement error on the performance of Mann‐Whitney and Signed‐Rank nonparametric control charts. Quality and Reliability Engineering International, 37(6), 2365-2383.
Riaz, M., Abid, M., Shabbir, A., Nazir, H. Z., Abbas, Z., & Abbasi, S. A. (2021). A non‐parametric double homogeneously weighted moving average control chart under sign statistic. Quality and Reliability Engineering International, 37(4), 1544-1560.
Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(1), pp. 239-250.
Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), pp. 43-87.
Shu, M.-H. and Wu, H. C. (2010). Monitoring imprecise fraction of conforming items using p control charts. Journal of Applied Statistics, 37, 1283-1297.
Stemann, D., & Weihs, C. (2001). The EWMA-XS-control chart and its performance in the case of precise and imprecise data. Statistical Papers, 42(2), pp. 207.
Tang, A., Castagliola, P., Hu, X., & Sun, J. (2019). The adaptive EWMA median chart for known and estimated parameters. Journal of Statistical Computation and Simulation, 89(5), 844-863.
Yang, S. F., Lin, J. S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert Systems with Applications, 38(5), 6239-6243.
Yang, S. F., Cheng, T. C., Hung, Y. C., & W. Cheng, S. (2012). A new chart for monitoring service process mean. Quality and Reliability Engineering International, 28(4), 377-386.
Yang, S. F., & Arnold, B. C. (2014). A simple approach for monitoring business service time variation. The Scientific World Journal, 2014.
Yang, S. F., & Arnold, B. C. (2016). A new approach for monitoring process variance. Journal of Statistical Computation and Simulation, 86(14), 2749-2765.
描述 碩士
國立政治大學
統計學系
110354004
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110354004
資料類型 thesis
dc.contributor.advisor 楊素芬<br>陳立榜zh_TW
dc.contributor.advisor Yang, Su-Fen<br>Chen, Li-Pangen_US
dc.contributor.author (Authors) 林政寬zh_TW
dc.contributor.author (Authors) Lin, Cheng-Kuanen_US
dc.creator (作者) 林政寬zh_TW
dc.creator (作者) Lin, Cheng-Kuanen_US
dc.date (日期) 2022en_US
dc.date.accessioned 8-Feb-2023 15:42:32 (UTC+8)-
dc.date.available 8-Feb-2023 15:42:32 (UTC+8)-
dc.date.issued (上傳時間) 8-Feb-2023 15:42:32 (UTC+8)-
dc.identifier (Other Identifiers) G0110354004en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/143341-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 110354004zh_TW
dc.description.abstract (摘要) 在工業製程中，管制圖是監測產品品質和檢測製成是否失控的有效工具。雖然有許多類型的管制圖可供數據分析者使用，但使用這些管制圖的前提是在變量被精確測量的情況下。然而，在實際應用中，當資料被調查者錯誤得記錄或被未經調整的機器不精確得收集時，量測誤差是無可避免的。儘管量測誤差對不同類型的管制圖的影響已經被探討過，但誤差修正的管制圖仍然很少被討論。因此在此研究中，我們提出了一種新的帶有誤差修正的變異數管制圖來填補這一研究空白。我們的主要想法是將觀察到的製程變量轉換為符號統計量，然後以一個函數來調整符號統計量，以校正量測誤差的影響。最後，我們根據修正後的符號統計量提出帶有量測誤差修正的指數加權移動平均數變異數管制圖。我們所開發的誤差修正的變異數管制圖不僅消除了量測誤差的影響，而且為監測製程變異數提供了更可靠的管制界線。透過數值分析，我們發現所提出的誤差修正變異數管制圖能夠有效處理中等和較大程度的量測誤差，並對監測製程是否失控有著良好的表現。最後，我們使用半導體資料來驗證所提出的誤差修正變異數管制圖之應用。zh_TW
dc.description.abstract (摘要) In industrial processes, control charts are useful tools to monitor the quality of products and detect possibly out-of-control processes. While many types of control charts have been available for data analysts, they were developed by assuming that the variables are precisely measured. In applications, however, measurement error is ubiquitous when data are falsely recorded by investigator or imprecisely collected by unadjusted machines. Even though the impacts of measurement error for different types of control charts have been explored, error-corrected control charts are still unavailable. In this study, we propose a new dispersion control chart with error correction to fill out this research gap. Our key idea is to convert the observed process variables into a flexible sign statistic, and then adopt a function to adjust the measurement error effects on the sign statistic. Finally, we develop the exponentially weight moving average dispersion control chart with measurement error correction based on the corrected sign statistic. The proposed error-corrected dispersion control chart not only eliminates measurement error effects, but also provides more reliable control limits for monitoring process dispersion. Throughout numerical examination, we find that the proposed error-corrected dispersion control chart is effective in handling the moderate and large levels of measurement error and shows well out-of-control detection performance. Finally, the proposed error-corrected dispersion control chart is implemented to the semiconductor data.en_US
dc.description.tableofcontents 1. Introduction 1
2. Using the Error-corrected EWMA Variance Chart to Monitor Process Dispersion 3
2.1. Design of the EWMA Variance Chart 3
2.2. The EWMA Variance Chart with Measurement Error 7
2.3. Design of the Error-corrected EWMA Variance Chart 11
3. Performance of the Error-corrected EWMA Variance Chart 14
4. The Effect of Measurement Error for EWMA Variance Chart under Different Distribution 18
5. Example 29
6. Conclusions 31
Reference 32
Appendix 35		zh_TW
dc.format.extent 6814962 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110354004en_US
dc.subject (關鍵詞) 量測誤差校正zh_TW
dc.subject (關鍵詞) 指數加權移動平均管制圖zh_TW
dc.subject (關鍵詞) 變異數管制圖zh_TW
dc.subject (關鍵詞) Measurement error eliminationen_US
dc.subject (關鍵詞) Exponentially weighted moving average control charten_US
dc.subject (關鍵詞) Dispersion control charten_US
dc.title (題名) 具量測誤差校正的變異數管制圖zh_TW
dc.title (題名) Adjustment of Measurement Error Effects on the Distribution-free Dispersion Control Charten_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Abbas, N., Riaz, M., & Does, R. J. (2014). An EWMA-type control chart for monitoring the process mean using auxiliary information. Communications in Statistics-Theory and Methods, 43(16), 3485-3498.
Amin, R. W., Reynolds Jr, M. R., & Saad, B. (1995). Nonparametric quality control charts based on the sign statistic. Communications in Statistics-Theory and Methods, 24(6), 1597-1623.
Asif, F., Khan, S., & Noor-ul-Amin, M. (2020). Hybrid exponentially weighted moving average control chart with measurement error. Iranian Journal of Science and Technology, Transactions A: Science, 44(3), 801-811.
Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), 613-623.
Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757.
Case, K. E. (1980). The p control chart under inspection error. Journal of Quality Technology, 12(1), 1-9.
27. Chen, L.-P. and Yang, S.-F. A new p-control chart with measurement error correction. Quality and Reliability Engineering In-ternational 2022, 1-18. DOI: 10.1002/qre.3219
Chowdhury, S., Mukherjee, A., & Chakraborti, S. (2014). A new distribution‐free control chart for joint monitoring of unknown location and scale parameters of continuous distributions. Quality and Reliability Engineering International, 30(2), 191-204.
Daryabari, S. A., Malmir, B., & Amiri, A. (2019). Monitoring Bernoulli processes considering measurement errors and learning effect. Quality and Reliability Engineering International, 35(4), 1129-1143.
Daryabari, S. A., Hashemian, S. M., Keyvandarian, A., & Maryam, S. A. (2017). The effects of measurement error on the MAX EWMAMS control chart. Communications in Statistics-Theory and Methods, 46(12), 5766-5778.
McCann, M. and Johnston, A. UCI Machine Learning Repository. Available online: https://archive.ics.uci.edu/ml/datasets/SECOM (accessed on 1 December 2021)
Huwang, L., & Hung, Y. (2007). Effect of measurement error on monitoring multivariate process variability. Statistica Sinica, 749-760.
Linna, K. W., & Woodall, W. H. (2001). Effect of measurement error on Shewhart control charts. Journal of Quality technology, 33(2), pp. 213-222.
Linna, K. W., Woodall, W. H. & Busby, K. L. (2001). The performance of multivariate control charts in the presence of measurement error, Journal of Quality Technology, 33, pp. 349–355.
Lu, X. S., Xie, M., & Goh, T. N. (2000). An investigation of the effects of inspection errors on the run-length control charts. Communications in Statistics-simulation and Computation, 29(1), 315-335.
Maravelakis, P., Panaretos, J., & Psarakis, S. (2004). EWMA chart and measurement error. Journal of Applied Statistics, 31(4), pp. 445-455.
Mittag H-J, & Stemann D. (1998). Gauge imprecision effect on the performance of the \\overline{X}-S control chart. Journal of Applied Statistics, 25, pp. 307–317.
McFadden, D. (1984). Econometric analysis of qualitative response models. In: Griliches, Z., Intriligator, M.D. (Eds.), Handbook of Econometrics, vol. 2. North–Holland, Amsterdam.
Noor-ul-Amin, M., Riaz, A., & Safeer, A. (2019). Exponentially weighted moving average control chart using auxiliary variable with measurement error. Communications in Statistics-Simulation and Computation, pp. 1-13.
Nojavan, M., Alishahi, M., Rezaee, M., & Rahaee, M. A. (2021). The effect of measurement error on the performance of Mann‐Whitney and Signed‐Rank nonparametric control charts. Quality and Reliability Engineering International, 37(6), 2365-2383.
Riaz, M., Abid, M., Shabbir, A., Nazir, H. Z., Abbas, Z., & Abbasi, S. A. (2021). A non‐parametric double homogeneously weighted moving average control chart under sign statistic. Quality and Reliability Engineering International, 37(4), 1544-1560.
Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(1), pp. 239-250.
Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), pp. 43-87.
Shu, M.-H. and Wu, H. C. (2010). Monitoring imprecise fraction of conforming items using p control charts. Journal of Applied Statistics, 37, 1283-1297.
Stemann, D., & Weihs, C. (2001). The EWMA-XS-control chart and its performance in the case of precise and imprecise data. Statistical Papers, 42(2), pp. 207.
Tang, A., Castagliola, P., Hu, X., & Sun, J. (2019). The adaptive EWMA median chart for known and estimated parameters. Journal of Statistical Computation and Simulation, 89(5), 844-863.
Yang, S. F., Lin, J. S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert Systems with Applications, 38(5), 6239-6243.
Yang, S. F., Cheng, T. C., Hung, Y. C., & W. Cheng, S. (2012). A new chart for monitoring service process mean. Quality and Reliability Engineering International, 28(4), 377-386.
Yang, S. F., & Arnold, B. C. (2014). A simple approach for monitoring business service time variation. The Scientific World Journal, 2014.
Yang, S. F., & Arnold, B. C. (2016). A new approach for monitoring process variance. Journal of Statistical Computation and Simulation, 86(14), 2749-2765.		zh_TW