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統 計 學 ( 二 ) 朝陽科技大學工業工程與管理系副教授 洪弘祈 89.02.28 企業與統計之關係 品質管制 預測統計與市場調查 績效與人事管理 例行報告之方案評估與決策參考 製程改善 研發能力之提昇 產品可靠度 生產管制 Statistics II 2 分段主題 統計之基礎理論與觀念 基礎統計在品管與製程上之應用(含可靠度) 進階統計之一 ~ 實驗計劃法與田口式品質工程 進階統計之二 ~ 反應曲面技術 進階統計之三 ~ 迴歸分析 進階統計之四 ~ 時間序列 進階統計之五 ~ 多變量分析 Statistics II 3 數學 Vs. 統計 數 學 統計之基礎理論與觀念 統 計 社會 科學 1 100 5 500 在統計上未必為真 24 1 50 2 在統計上未必為假 Statistics II 4 THE ENGINEERING METHOD AND STATISTICAL THINKING Engineering or Scientific Method Develop a clear and concise description of the problem. Identify, at least tentatively, the important factors that affect this problem or that may play a role in its solution. Propose a model for the problem, using scientific or engineering knowledge of the phenomenon being studied. State any limitations or assumptions of the model. II Conduct appropriate Statistics experiments and collect data to 5 THE ENGINEERING METHOD AND STATISTICAL THINKING Refine the model on the basis of the observed data. Manipulate the model to assist in developing a solution to the problem. Conduct an appropriate experiment to confirm that the proposed solution to the problem is both effective and efficient. Draw conclusions or make recommendations based on the problem solution. Statistics II 6 The Engineering or Scientific Method Statistics II 7 Statistics Deals with the collection, presentation, analysis, and the use of data to make decisions, solve problems, and design products and processes. Describe and understand variability Apply statistical thinking Find out the sources of variability Statistics II 8 機率 Vs. 統計 母體 母體參數 統計之基礎理論與觀念 抽樣 推論 Statistics II 樣本 樣本統計量 9 統計之專有名詞 母體(Population) 樣本(Sample) 抽樣(Sampling) 隨機變數(Random Variable) 參數(Parameter) 統計量(Statistics) Examples Statistics II 統計之基礎理論與觀念 10 Dot Diagram Location and variability Statistics II 11 Sample Mean Statistics II 12 Statistics II 13 Some Statistical Terms Sample and Sampling Population Population Mean Sample Variance Sample Standard Deviation Statistics II 14 Sample Variance and Standard Deviation Statistics II 15 Statistics II 16 Statistics II 17 Computation of s2 n n 2 2 x x x nx i i s2 i 1 i 1 n 1 n 1 n 2 xi x s2 i 1 n 1 n x n 2 i 1 xi n i 1 Statistics II 2 n 1 18 Some Statistical Terms Population Variance Population Standard Deviation Degrees of Freedom • independent terms in the equation • unknown population mean (m), using sample mean instead Statistics II 19 Statistical Thinking Which one has the smaller variation? Statistics II 20 Statistics II 21 Statistics II 22 Collecting Engineering Data observational study designed experiment hypothesis testing Statistics II 23 Mechanistic and Empirical Model Mechanistic Model: built from our underlying knowledge of the basic physical mechanism. Empirical Model: adding the nature variability, or built from observed data. Statistics II 24 Statistics II 25 Statistics II 26 Statistics II 27 Designing Experimental Investigation factorial experiment replicates interaction fractional factorial experiment Statistics II 28 Statistics II 29 Statistics II 30 Statistics II 31 Statistics II 32 ~ Observing Processes Over Time Statistics II 33 Statistics II 34 Statistics II 35 Statistics II 36 Statistics II 37 Statistics II 38 Statistics II 39 Statistics II 40