臺灣博碩士論文加值系統

產品生產的過程中，如何提升製程的穩定與產品的品質是非常重要的，管制圖已被大量且廣泛的應用在統計製程管制(Statistical Process Control, SPC)中，Shewhart首先在1920年提出了管制圖的概念與想法，用以減少生產流程之變異，為了要因應製程中不同的狀況，許多改良過後的適應性管制圖也被提出與採用，像是兩階段(Two-Stage)管制圖、累積和(CUSUM)管制圖和指數加權移動平均(Exponential Weighted Moving Average, EWMA)管制圖等。
傳統的管制圖中只對績效變數(Performance Variable)進行監控，但某些情況下，需耗費較高的成本來進行製程的監測，利用與績效變數高度相關的代理變數(Surrogate Variable)進行監測是比較經濟且有效率的。在本篇論文中，我們利用一個用於兩階段管制圖之經濟設計的健全模型，並且以交替的方式監測績效變數和代理變數。 我們透過使用最大期望淨利和參數設定的最佳值，將該健全模型的監測過程的效率和監測的成本降低與參考模型的效率進行比較。

It is important to improve the stability of the process and the quality of the product in the production process. Control charts have been widely used in statistical process control because of their operational simplicity. In order to reduce the variation in the process, Shewhart proposed the concept of the control chart in 1920. Many adaptive charts have been proposed to improve the performance of control charts, such as two-stage control chart, CUSUM chart and EWMA control chart.
Traditional control charts are only monitored with a performance variable. However, it takes a higher cost to monitor the process in some cases. It is more economical and efficient to use surrogate variables which are highly correlated with performance variables. In this thesis, we consider a robust model for economic design of two-stage control charts that using performance variable and surrogate variable in alternating fashion. We will compare the efficiency of the process and the cost reduction of monitoring of this robust model with that of the model in the reference by using the maximum expected net income and the optimum values of design parameters.

Contents
1 Introduction 1
2 Two-stage skew normal control chart 3
2.1 Properties of two-stage skew normal control chart . . . 3
2.2 Control limits of two-stage skew normal control chart . 11
2.3 The operating procedure of two-stage skew normal control chart . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Markov chain approach and economic design 15
3.1 Markov chain approach . . . . . . . . . . . . . . . . . 15
3.2 Economic design of control charts . . . . . . . . . . . 18
4 Simulation study 20
4.1 Process parameter setting . . . . . . . . . . . . . . . . 20
4.2 Comparison of different designs . . . . . . . . . . . . . 23
5 Conclusion 27
References 28

List of Figures
2.1 Scatter plot of λx and λy (ζ~N δ,ε~SN) . . . . 7
2.2 Scatter plot of λx and λy (ζ~SN δ,ε~N) . . . . 7
2.3 Scatter plot of λx and λy with ζ~N δ,ε~SN(0.5 < ρx,y < 0.9) . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Scatter plot of λx and λy with ζ~SN δ,ε~N(0.5 < ρx,y < 0.9) . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 Density/Contour plot of X and Y (X~N & Y~SN) 9
2.6 Density/Contour plot of X and Y (X~SN & Y~N) 10
2.7 Density/Contour plot of X and Y (X~SN & Y~SN) 10
2.8 Flowchart of the two-stage control chart . . . . . . . . 14

List of Tables
2.1 The calculation of ρx,y with given (αδ,αε) . . . . . . 5
2.2 Parameter setting of X and Y . . . . . . . . . . . . . 6
4.1 Cost and process parameters for test examples . . . . 20
4.2 Process parameter settings of X and Y . . . . . . . . 21
4.3 Process parameters with fixed ρx,y (X~N, Y~SN) 21
4.4 Process parameters with fixed ρx,y (X~SN, Y~N) 22
4.5 Process parameters with fixed ρx,y (X~SN, Y~SN) 22
4.6 E(A) and optimal value of (nX; nY ; hX; hY ) with various
c (X~N; Y~SN) . . . . . . . . . . . . . . . . 24
4.7 E(A) and optimal value of (nX; nY ; hX; hY ) with various
c (X~SN; Y~N) . . . . . . . . . . . . . . . . 25
4.8 E(A) and optimal value of (nX; nY ; hX; hY ) with various
c (X~SN; Y~SN) . . . . . . . . . . . . . . . 26

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