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| 研究生： |
盧尚文 |
|---|---|
| 論文名稱： |
偏斜常態分配下損失管制圖之設計 Loss Control Charts Under Skew Normal Population |
| 指導教授： | 楊素芬 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2014 |
| 畢業學年度： | 102 |
| 語文別： | 英文 |
| 論文頁數： | 100 |
| 中文關鍵詞： | 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 |
| 相關次數： | 點閱：100 下載：11 |
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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.
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
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