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系統識別號 U0026-1507202013585700
論文名稱(中文) 偏斜常態分佈下線性輪廓監控之適應性管制圖設計
論文名稱(英文) Design of Adaptive Control Charts for Linear Profile Monitoring under Skew Normal Distribution
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 108
學期 2
出版年 109
研究生(中文) 蘇毓雯
研究生(英文) Yu-Wen Su
學號 R26071058
學位類別 碩士
語文別 中文
論文頁數 49頁
口試委員 指導教授-李俊毅
口試委員-潘浙楠
口試委員-鄭春生
中文關鍵字 偏斜常態分配  適應性管制圖  輪廓監控 
英文關鍵字 skew normal distribution  adaptive control chart  profile monitoring 
學科別分類
中文摘要 傳統的統計品質管制當中,係針對單一或數個品質特性進行監控。然而,某些產品或製程的品質特性可藉由線性迴歸中反應變數與解釋變數的函數關係來描述,此種函數關係我們稱為輪廓(profile),至於輪廓監控(profile monitoring)則是針對輪廓資料的函數關係建立管制圖,並監控此輪廓是否隨著時間改變而發生變化。一般而言,傳統管制圖的判定是在固定樣本數與抽樣間隔情況下所進行,而適應性管制圖(adaptive control chart)由於可以變動樣本數與抽樣間隔,故在製程發生小偏移(small shift)時有較好的偵測效果。本研究係藉由簡單線性迴歸模型來描述輪廓資料,並假設線性輪廓資料的誤差項彼此相互獨立並服從偏斜常態分配(skew normal distribution),在考慮第Ⅱ階段的製程監控情況下,我們運用殘差管制圖的概念建立線性輪廓資料的適應性管制圖。最後,本研究考慮在不同偏斜程度及製程偏移量的情況下,利用統計模擬及數值實例分析的方式進行管制圖的表現以及偵測製程偏移能力的評估,結果發現適應性管制圖的偵測能力比傳統管制圖更有效率。另外,在敏感度分析中可得知大樣本 n_2及短間隔 h_2對於製程敏感度大,其設定值的改變會明顯影響評估指標AATS,因此,在參數設定上需要更加注意。
英文摘要 In statistical process control (SPC) applications, the quality of products cannot be represented by a single or several quality characteristics. However, the quality characteristic is represented by a functional relationship between a response variable and explanatory variables, that is, the quality is expressed by profile. Linear profile monitoring is used to verify stability of this functional relationship over time. The standard Shewhart (SS) X ̅ chart is developed with fixed sample size and sampling interval to monitor the process mean. SS-X ̅ chart is effective to detect large shifts in process mean. To improve the ability of the SS-X ̅ chart on detecting small shifts in process mean, an adaptive control chart is proposed. An adaptive control chart scheme has variable sample size or sampling interval. In this study, we consider that the error terms in a linear profiles model are independent and identically skew normal distributed random variables. An adaptive control chart is constructed based on the residuals to monitor the linear profile in phase II. Under different skewness and shifts in the process, SN VSSI-e ̅ chart is established through using Markov chain approach. The simulation results show that the SN VSSI-e ̅ chart has good ability to detect small shifts in process. Moreover, a sensitivity analysis is conducted to study the robustness of the proposed methods According to the results of the sensitivity analysis, we find that the most important parameters are n_2 and h_2.
論文目次 第一章 緒論 1
1.1 前言 1
1.2 研究背景與動機 2
1.3 研究目的 2
1.4 研究架構 3
第二章 文獻探討 4
2.1適應性管制圖 4
2.2 輪廓監控 8
第三章 研究方法 9
3.1 簡單線性輪廓模型 9
3.2 模型殘差之分配 9
3.3 適應性管制圖之設計 11
3.4 評估指標 13
第四章 統計模擬與實例分析 15
4.1評估指標之真實值與模擬值 16
4.2 統計模擬之比較分析 18
4.3 SN SS管制圖與SN VSSI管制圖比較 21
4.4 敏感度分析 25
4.5 數值實例分析 28
第五章 結論與未來研究 31
參考文獻 32
附錄1 33
附錄2 36
附錄3 38
附錄4 39
附錄5 48
參考文獻 1.Abdella, G. M., Yang, K., & Alaeddini, A. (2014). Multivariate adaptive approach for monitoring simple linear profiles. International Journal of Data Analysis Techniques and Strategies, 6(1), 2-14.
2.Amiri, A., Zand, A., & Soudbakhsh, D. (2011). Monitoring simple linear profiles in the leather industry (a case study). Paper presented at the Proceedings of the 2011 International Conference on Industrial Engineering and Operations Management.
3.Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian journal of statistics, 171-178.
4.Chiang, J. Y., Tsai, T. R., & Su, N. C. (2018). Adaptive control charts for skew‐normal distribution. Quality and Reliability Engineering International, 34(4), 589-608.
5.Costa, A. F. (1997). X chart with variable sample size and sampling intervals. Journal of Quality Technology, 29(2), 197-204.
6.De Magalhães, M. S., & Von Doellinger, R. O. S. (2016). Monitoring linear profiles using an adaptive control chart. The International Journal of Advanced Manufacturing Technology, 82(5-8), 1433-1445.
7.Kazemzadeh, R. B., Amiri, A., & Kouhestani, B. (2016). Monitoring simple linear profiles using variable sample size schemes. Journal of Statistical Computation and Simulation, 86(15), 2923-2945.
8.Li, C. I., Su, N. C., Su, P. F., & Shyr, Y. (2014a). The design of and R control charts for skew normal distributed data. Communications in Statistics-Theory and Methods, 43(23), 4908-4924.
9.Li, C. I., & Tsai, T. R. (2019). Linear profiles monitoring in the presence of nonnormal random errors. Quality and Reliability Engineering International, 35(8), 2579-2592.
10.Li, Z., Zou, C., Gong, Z., & Wang, Z. (2014b). The computation of average run length and average time to signal: an overview. Journal of Statistical Computation and Simulation, 84(8), 1779-1802.
11.Lin, T. I., Lee, J. C., & Yen, S. Y. (2007). Finite mixture modelling using the skew normal distribution. Statistica Sinica, 909-927.
12.Reynolds, M. R., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). Charts with variable sampling intervals. Technometrics, 30(2), 181-192.
13.Su, N. C., & Gupta, A. K. (2015). On some sampling distributions for skew-normal population. Journal of Statistical Computation and Simulation, 85(17), 3549-3559.
14.林裕章, & 周昭宇. (2004). 適應性 (平均值) X 管制圖變動管制參數之評估. 管理學報, 21(3), 375-389.
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