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題名 偏斜常態分配下損失管制圖之設計
Loss Control Charts Under Skew Normal Population作者 盧尚文 貢獻者 楊素芬
盧尚文關鍵詞 中位數損失函數
平均損失函數
偏斜常態分配
指數加權移動平均管制圖
調適性管制圖
管制圖日期 2013 上傳時間 21-七月-2014 15:37:16 (UTC+8) 摘要 本研究假設品質特性質服從偏斜常態分配下建立損失管制圖。當品質特性質的分配非對稱，本研究提出一中位數損失管制圖，可同時追蹤製程平均值與目標值之距離以及製程之變異。我們亦對此中位數損失管制圖之管制界線進行調整使其ARL1為unbiased。本研究亦在偏斜常態分配之假設下提出一平均損失管制圖，並與中位數損失管制圖比較其管制績效。為了提升管制圖之績效，本研究分別採用EWMA以及VSI之管制技術去提升中位數損失以及平均損失管制圖之績效。最後本研究提出之損失管制圖方法與已經存在之方法做比較，衡量當製程失控時之管制績效優劣。
In this study we construct loss-based control charts under skew-normal population. When the underlying distribution is skewed, we proposed a median loss control chart to simultaneously monitor the change of difference to process mean and target and the change of variance. An unbiased-ARL1 adjustment to the median loss chart is discussed. We also construct an average loss control chart under skew-normal population, and compare with the median loss control chart. Moreover, the EWMA or VSI charts are considered to improve the detection ability of the median loss or the average loss control charts. Out-of-control detection ability comparison among the median loss, average loss and some existed control charts for skewed population is discussed.參考文獻 A. Azzalini, A Class of Distributions which Includes the Normal Ones, Scandinavian journal of statistics 12 (1985) 171–178A. Azzalini, Further Results on a Class of Distributions which Includes the Normal Ones, Statistica 46 (1986) 199–208.A. F. B. Costa, Charts with Variable Sample Sizes and Sampling Intervals, CQPI Report N0. 133 (1995) 1–11.A. O` Hagan, T. Leonard, Bayes Estimation subject to Uncertainty About Parameter Constraints. Biometrika 63 (1976) 201–203.D. G. Jean, C. Subhabrata, Nonparametric Statistical Inference, 5th edition, Springer Berlin Heidelberg (2011).D. S. Bai, I. S. Choi, and R Control Charts for Skewed Populations, Journal of Quality Technology 27 (1995) 120–131.F. Pascual, Individual and Moving Ratio Charts for Weibull Processes, Stochastic Orders in Reliability and Risk, Springer New York (2013) 331–350.F.Y. Edgeworth, The law of error, Trans Camb Phil Soc 20 (1905) 113–141G. Taguchi, Introduction to Quality Engineering: Designing Quality into Products and Processes (1986).J. J. Pignatiello, C. A. Acosta-Mej´ıa, B.V. Rao, The Performance of Control Charts for Monitoring Process Dispersion. 4th Industrial Engineering Research Conference (1995) 320–328.J. Stewart, Multivariable Calculus: Concepts & Contexts, Brooks/Cole (2005).K. Gerald, Statistics for Management and Economics, 7th edition , Cengage Learning (2004)L. K. Chan, H. J. Cui, Skewness correction and R charts for skewed distributions, Naval Research Logistics 50 (2003) 555–573.L. Yang, S. Pai, Y. R. Wang, A Novel CUSUM Median Control Chart, Proceedings of International Multiconference of Engineers and Computer Scientists 3 (2010).M. A. Graham, S. W. Human, S. Chakraborti, A Phase I Nonparametric Shewhart-Type Control Chart based on the Median. Journal of Applied Statistics 37 (2010) 1795–1813.M. R. Reynolds, R. W. Amin, J. C. Arnold and J. A. Nachlas, Charts with Varia-ble Sampling Intervals, Technometrics 30 (1988) 181–192.M.R. Reynolds Jr, Z.G. Stoumbos, Monitoring the process mean and variance using individual observations and variable sampling intervals, Journal of Quality Technology 33 (2001) 181–205.P. Hall, The Bootstrap and Edgeworth Expansion, Springer (1992).S. F. Yang [b], Using a New VSI EWMA Average Loss Control Chart to Monitor Changes in the Difference between the Process Mean and Target and/or the Process Variability, Applied Mathematical Modelling 37 (2013) 7973–7982.S. F. Yang[a], Using a Single Average Loss Control Chart to Monitor Process Mean and Variability, Communications in Statistics-simulation and computation 42 (2013) 1549–1562.S. Knoth, M. C. Morais, On ARL-Unbiased Charts, XIth International Workshop on Intelligent Statistical Quality Control, Sydney, Australia (2013) 31–50. 描述 碩士
國立政治大學
統計研究所
101354018
102資料來源 http://thesis.lib.nccu.edu.tw/record/#G1013540182 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.author (作者) 盧尚文 zh_TW dc.creator (作者) 盧尚文 zh_TW dc.date (日期) 2013 en_US dc.date.accessioned 21-七月-2014 15:37:16 (UTC+8) - dc.date.available 21-七月-2014 15:37:16 (UTC+8) - dc.date.issued (上傳時間) 21-七月-2014 15:37:16 (UTC+8) - dc.identifier (其他 識別碼) G1013540182 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/67591 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 101354018 zh_TW dc.description (描述) 102 zh_TW dc.description.abstract (摘要) 本研究假設品質特性質服從偏斜常態分配下建立損失管制圖。當品質特性質的分配非對稱，本研究提出一中位數損失管制圖，可同時追蹤製程平均值與目標值之距離以及製程之變異。我們亦對此中位數損失管制圖之管制界線進行調整使其ARL1為unbiased。本研究亦在偏斜常態分配之假設下提出一平均損失管制圖，並與中位數損失管制圖比較其管制績效。為了提升管制圖之績效，本研究分別採用EWMA以及VSI之管制技術去提升中位數損失以及平均損失管制圖之績效。最後本研究提出之損失管制圖方法與已經存在之方法做比較，衡量當製程失控時之管制績效優劣。 zh_TW dc.description.abstract (摘要) In this study we construct loss-based control charts under skew-normal population. When the underlying distribution is skewed, we proposed a median loss control chart to simultaneously monitor the change of difference to process mean and target and the change of variance. An unbiased-ARL1 adjustment to the median loss chart is discussed. We also construct an average loss control chart under skew-normal population, and compare with the median loss control chart. Moreover, the EWMA or VSI charts are considered to improve the detection ability of the median loss or the average loss control charts. Out-of-control detection ability comparison among the median loss, average loss and some existed control charts for skewed population is discussed. en_US dc.description.tableofcontents Chapter 1. Introduction 21.1 Research Motivation 21.2 Literature Review 21.3 Research Method 5Chapter 2. The Sampling Distribution of the Median Loss for Skew Normal Population 62.1 Derivation the Distribution of the Sample Median Loss 62.1.1 The probability density and the distribution function of the skew-normal random variable 62.1.2 The pdf and cdf of Taguchi Loss 82.1.3 The pdf and cdf of the Median Loss 92.2 Cumulative Distribution Function derivation of the Sample Median Loss 10Chapter 3. Constructions of the Median Loss, EWMA and Optimal VSI Median Loss Control Charts 133.1 Construction of the Median Loss Control Chart 133.1.1 Control limits of the Median Loss chart 133.1.2 Performance Measurement of the Median Loss chart 163.2. An EWMA Median Loss Chart 443.2.1 Construction of the EWMA-ML Chart 443.2.2 The out-of-control detection Performance Measurement of the EWMA-ML Chart 473.2.3 The Out-of-Control Detection Performance Comparison between the Median Loss and the EWMA Median Loss Charts 493.3. An Optimal Variable Sampling Interval Median Loss Chart 513.3.1 Construction of the Optimal VSI Median Loss Chart 523.3.2 Performance Measurement of the VSI Median Loss Chart 533.3.3 ATS1s Comparison among the Median Loss Chart, specified VSI Median Loss Chart and the Optimal VSI Median Loss Chart 56Chapter 4. Constructions of the AL, EWMA-AL, Optimal VSI-AL Control Charts under Skew normal distribution 604.1 Construction of the Average Loss Chart 614.1.1 Approximate Distribution of Average Loss by Using Edgeworth Expansion Method 614.1.2 Control Limits of the Average Loss Chart 654.1.3 Out-of-Control Detection Performance Measurement of the AL Chart 684.2. An EWMA Average Loss Chart 734.2.1 Construction of the EWMA-AL Chart 734.2.2 Out-of-Control Detection Performance Measurement of the EWMA-AL Chart 744.2.3 Out-of-Control Detection Performance Comparison among the AL and the EWMA-AL Chart 754.3. An Optimal Variable Sampling Interval Average Loss Chart 774.3.1 Construction of the Optimal VSI Average Loss Chart 774.3.2 Out-of-control Detection Performance Measurement of the Optimal VSI Average Loss Chart 794.3.3 ATS1s Comparison among the AL Chart, specified VSI-AL Chart and the Optimal VSI-AL Chart 79Chapter 5. ATS1 Comparison among all Proposed Loss Control Charts and Other Existed Control Charts 845.1 Introduction of Some Existed Control Charts 845.2 ATS1 Comparison among all Proposed Loss Control Charts and Other Existed Control Charts 87Chapter 6. Conclusions and Future Study 98Reference 99 zh_TW dc.format.extent 2573502 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1013540182 en_US dc.subject (關鍵詞) 中位數損失函數 zh_TW dc.subject (關鍵詞) 平均損失函數 zh_TW dc.subject (關鍵詞) 偏斜常態分配 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) 調適性管制圖 zh_TW dc.subject (關鍵詞) 管制圖 zh_TW dc.title (題名) 偏斜常態分配下損失管制圖之設計 zh_TW dc.title (題名) Loss Control Charts Under Skew Normal Population en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) A. Azzalini, A Class of Distributions which Includes the Normal Ones, Scandinavian journal of statistics 12 (1985) 171–178A. Azzalini, Further Results on a Class of Distributions which Includes the Normal Ones, Statistica 46 (1986) 199–208.A. F. B. Costa, Charts with Variable Sample Sizes and Sampling Intervals, CQPI Report N0. 133 (1995) 1–11.A. O` Hagan, T. Leonard, Bayes Estimation subject to Uncertainty About Parameter Constraints. Biometrika 63 (1976) 201–203.D. G. Jean, C. Subhabrata, Nonparametric Statistical Inference, 5th edition, Springer Berlin Heidelberg (2011).D. S. Bai, I. S. Choi, and R Control Charts for Skewed Populations, Journal of Quality Technology 27 (1995) 120–131.F. Pascual, Individual and Moving Ratio Charts for Weibull Processes, Stochastic Orders in Reliability and Risk, Springer New York (2013) 331–350.F.Y. Edgeworth, The law of error, Trans Camb Phil Soc 20 (1905) 113–141G. Taguchi, Introduction to Quality Engineering: Designing Quality into Products and Processes (1986).J. J. Pignatiello, C. A. Acosta-Mej´ıa, B.V. Rao, The Performance of Control Charts for Monitoring Process Dispersion. 4th Industrial Engineering Research Conference (1995) 320–328.J. Stewart, Multivariable Calculus: Concepts & Contexts, Brooks/Cole (2005).K. Gerald, Statistics for Management and Economics, 7th edition , Cengage Learning (2004)L. K. Chan, H. J. Cui, Skewness correction and R charts for skewed distributions, Naval Research Logistics 50 (2003) 555–573.L. Yang, S. Pai, Y. R. Wang, A Novel CUSUM Median Control Chart, Proceedings of International Multiconference of Engineers and Computer Scientists 3 (2010).M. A. Graham, S. W. Human, S. Chakraborti, A Phase I Nonparametric Shewhart-Type Control Chart based on the Median. Journal of Applied Statistics 37 (2010) 1795–1813.M. R. Reynolds, R. W. Amin, J. C. Arnold and J. A. Nachlas, Charts with Varia-ble Sampling Intervals, Technometrics 30 (1988) 181–192.M.R. Reynolds Jr, Z.G. Stoumbos, Monitoring the process mean and variance using individual observations and variable sampling intervals, Journal of Quality Technology 33 (2001) 181–205.P. Hall, The Bootstrap and Edgeworth Expansion, Springer (1992).S. F. Yang [b], Using a New VSI EWMA Average Loss Control Chart to Monitor Changes in the Difference between the Process Mean and Target and/or the Process Variability, Applied Mathematical Modelling 37 (2013) 7973–7982.S. F. Yang[a], Using a Single Average Loss Control Chart to Monitor Process Mean and Variability, Communications in Statistics-simulation and computation 42 (2013) 1549–1562.S. Knoth, M. C. Morais, On ARL-Unbiased Charts, XIth International Workshop on Intelligent Statistical Quality Control, Sydney, Australia (2013) 31–50. zh_TW
