基於操作上的便利，斯華特管制圖成為品質管制中最常被使用的管制圖之一。由於科技的進步，產品的壽命愈來愈長，所以廠商在檢驗產品壽命是否符合規格時，基於成本考量，常常會收集到設限的資料(不完整資料)，而無法得知所有受測產品真正的壽命。在此情況下，如果仍採用傳統的斯華特管制圖來監控製程是不恰當的。Steiner & Mackay(2000)提出了CEV X-bar管制圖，來代替原本的X-bar管制圖，CEV X-bar管制圖在型I右設限資料下的偵測效果比傳統的X-bar管制圖來的好，而且更具有其理論價值。根據這些原因，本文討論當產品壽命時間服從Gompertz分配且為型I右設限資料時，利用Zhang & Chen(2004)所提出的上界EWMA CEV管制圖和下界EWMA CEV管制圖之概念及張毓芳(2005)所提出的一個新統計量來建立單一管制圖以偵測受限的Gompertz壽命資料下之製程平均壽命遞增或遞減的情況，文中並利用模擬方式討論在各種參數條件下，EWMA CEV管制圖的績效。

Shewhart control charts are popular in practical SPC applications due to the simplicity of operation.Over the past years,long lifetime products are designed and manufactured based on the rapid development of high technology.Consider the limitations of cost and the test time,the manufactures often collect censored data to detect if the mean lifetime of products reaches the required specification.Hence,Shewhart control charts are inadequate to be used in such situations due to the normality assumption is violated.Steiner & Mackay(2000) established a CEV X-bar control chart to monitor the mean lifetime of products with censored data.They conclude that the CEV X-bar control chart performs better than Shewhart X-bar control chart bases on the Type I right censored data.In this thesis,I develop an EWMA CEV control chart based on a new statistic proposed by Zhang (2005) and the one side EWMA CEV control chart established by Zhang & Chen(2004).The proposed control chart can detect the mean lifetime of products increase or decrease,simultaneously.A numerical study is conducted to evaluate the performance of the proposed method.

目錄 

第一章 緒論 1 
1.1 研究背景 1
1.2 研究動機與目的 3
1.3 研究架構與流程 5
第二章 文獻回顧 6
2.1 管制圖介紹 6
2.2 X-bar管制圖介紹8
2.3 CEV X-bar管制圖介紹 9
2.4 下界與上界EWMA CEV管制圖介紹 11
2.4.1 下界EWMA CEV管制圖介紹 11
2.4.2 上界EWMA CEV管制圖介紹 13
2.5 指數EWMA CEV管制圖介紹 14
第三章 數值分析 17
3.1 管制圖之比較準則 17
3.2 Gompertz分配之介紹 18
3.3 模擬過程 20
3.4 模擬結果評估 23
3.5 數值例子 24
第四章 結論 30
4.1 結論 30
4.2 未來展望 31
參考文獻 32 

圖形目錄
3.1 平均數下降之EWMA CEV管制圖 29
3.2 平均數上升之EWMA CEV管制圖 29

表格目錄
3.1 不同的設限率p_c下，對應的CE(X)值 21
3.2 λ=0.05，管制界限K1的模擬值 25
3.3 λ=0.1，管制界限K1的模擬值 26
3.4 λ=0.2，管制界限K1的模擬值 27

參考文獻

Crowder,S.V. and Hamilton,M.D.(1992),An EWMA for Monitoring Process Standard Deviation.Journal of Quality Technology,24,12-21

Gan,F.F.(1993),Exponentially Weighted Moving Average Control Charts with Reflecting Boundaries.Journal of Statistical Computation and Simulation.46,45-67.

Keats,J.B.,Lawrence,F.P.and Wang,F.K.(1997),Weibull Maximum Likelihood Parameter Estimates with Censored Data.Journal of Quality Technology,29,105-110.

Montgomery,D.C.(2005),Introduction to Statistical Quality Control,5th edn,John Wiley & Sons,New York.

Page,E.S.(1954),Continuous Inspection Schemes Biometrika,41,100-115.

Roberts,S.W.(1959),Control Chart Tests Based on Geometric Moving Averages.Technometrics,1,239-250.

Ryan,T.P.(2000),Statistical Methods for Quality Improvement,2nd edn,John Wiley & Sons,New York.

Steiner,S.H. and Mackay,R.J.(2000),Monitoring Processes with Highly Censored Data.Journal of Quality Technology,32,199-208.

Steiner,S.H. and Mackay,R.J.(2001),Detecting Changes in the Mean from Censored Lifetime Data.Frontiers in statistical Quality Control 6,Lenz,H.J. and Wilrich,P.T.,275-289.

Zhang,L. and Chen,G.(2004),EWMA Chart for Monitoring the Mean of Censored Weibull Lifetimes.Journal of Quality Technology,36,321-328.

張毓芳(2005),偵測設限資料之EWMA管制方法,國立中央大學統計研究所碩士論文.