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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-Jul-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) 171–178
A. 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) 113–141
G. 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 (Authors) 盧尚文zh_TW
dc.creator (作者) 盧尚文zh_TW
dc.date (日期) 2013en_US
dc.date.accessioned 21-Jul-2014 15:37:16 (UTC+8)-
dc.date.available 21-Jul-2014 15:37:16 (UTC+8)-
dc.date.issued (上傳時間) 21-Jul-2014 15:37:16 (UTC+8)-
dc.identifier (Other Identifiers) G1013540182en_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) 101354018zh_TW
dc.description (描述) 102zh_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 2
1.1 Research Motivation 2
1.2 Literature Review 2
1.3 Research Method 5
Chapter 2. The Sampling Distribution of the Median Loss for Skew Normal Population 6
2.1 Derivation the Distribution of the Sample Median Loss 6
2.1.1 The probability density and the distribution function of the skew-normal random variable 6
2.1.2 The pdf and cdf of Taguchi Loss 8
2.1.3 The pdf and cdf of the Median Loss 9
2.2 Cumulative Distribution Function derivation of the Sample Median Loss 10
Chapter 3. Constructions of the Median Loss, EWMA and Optimal VSI Median Loss Control Charts 13
3.1 Construction of the Median Loss Control Chart 13
3.1.1 Control limits of the Median Loss chart 13
3.1.2 Performance Measurement of the Median Loss chart 16
3.2. An EWMA Median Loss Chart 44
3.2.1 Construction of the EWMA-ML Chart 44
3.2.2 The out-of-control detection Performance Measurement of the EWMA-ML Chart 47
3.2.3 The Out-of-Control Detection Performance Comparison between the Median Loss and the EWMA Median Loss Charts 49
3.3. An Optimal Variable Sampling Interval Median Loss Chart 51
3.3.1 Construction of the Optimal VSI Median Loss Chart 52
3.3.2 Performance Measurement of the VSI Median Loss Chart 53
3.3.3 ATS1s Comparison among the Median Loss Chart, specified VSI Median Loss Chart and the Optimal VSI Median Loss Chart 56
Chapter 4. Constructions of the AL, EWMA-AL, Optimal VSI-AL Control Charts under Skew normal distribution 60
4.1 Construction of the Average Loss Chart 61
4.1.1 Approximate Distribution of Average Loss by Using Edgeworth Expansion Method 61
4.1.2 Control Limits of the Average Loss Chart 65
4.1.3 Out-of-Control Detection Performance Measurement of the AL Chart 68
4.2. An EWMA Average Loss Chart 73
4.2.1 Construction of the EWMA-AL Chart 73
4.2.2 Out-of-Control Detection Performance Measurement of the EWMA-AL Chart 74
4.2.3 Out-of-Control Detection Performance Comparison among the AL and the EWMA-AL Chart 75
4.3. An Optimal Variable Sampling Interval Average Loss Chart 77
4.3.1 Construction of the Optimal VSI Average Loss Chart 77
4.3.2 Out-of-control Detection Performance Measurement of the Optimal VSI Average Loss Chart 79
4.3.3 ATS1s Comparison among the AL Chart, specified VSI-AL Chart and the Optimal VSI-AL Chart 79
Chapter 5. ATS1 Comparison among all Proposed Loss Control Charts and Other Existed Control Charts 84
5.1 Introduction of Some Existed Control Charts 84
5.2 ATS1 Comparison among all Proposed Loss Control Charts and Other Existed Control Charts 87
Chapter 6. Conclusions and Future Study 98
Reference 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/#G1013540182en_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 Populationen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) A. Azzalini, A Class of Distributions which Includes the Normal Ones, Scandinavian journal of statistics 12 (1985) 171–178
A. 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) 113–141
G. 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