1. Statistical Process Control 統計製程管制

3. Process 製程 Variation 變異 Data 資料 Statistical Tools 統計方法 Statistical Thinking 統計思維 Statistical Methods 統計方法 Statistical Thinking and Statistical Methods 統計思維與統計方法

11. Depends on levels of activity and job responsibility. 依據活動的層級與工作執掌 Where we're headed 我們朝何方 Managerial processes to guide us 用管理的程序來指導我們 Where the work gets Done 讓所需的工作被執行完成 Strategic 策略上的 Managerial 管理上的 Operational 作業性的 Executives 高階決策層 Managers 經理階層 Workers 現場員工 Use of Statistical Thinking 運用統計思維

25. Grams (a) Location Average ( 平均值 ) Common Causes 共同原因

26. (a) Location Grams Average Assignable Causes 特殊原因

28. Mean 平均值 Central Limit Theorem Standard deviation 樣本標準差 Theoretical Basis of Control Charts

29. UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限 1 2 3 Samples Control Charts 管制圖

30. 1 2 3 Samples Control Charts 管制圖 UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限

31. Assignable causes likely 可能的特殊原因 1 2 3 Samples Control Charts 管制圖 UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限

33. The Relationship Between Population and Sampling Distributions 群體與樣本間之關係 Uniform Normal Beta Distribution of sample means 樣本平均值分配 Standard deviation of the sample means (mean) Three population distributions 群體分配

34. Visualizing Chance Causes 機遇原因之觀察 Target At a fixed point in time 固定時間 Time Target Over time 連續時間 Think of a manufacturing process producing distinct parts with measurable characteristics. These measurements vary because of materials, machines, operators, etc. These sources make up chance causes of variation. 製造各零件之量測特性會因 4M 等機遇原因而發生變異

35. Process Control Charts 製程管制圖

36. Control Chart Types 管制圖型態 計量 計數 Control Charts Variables Charts Attributes Charts Continuous 連續的 Numerical Data Categorical or Discrete 離散的 Numerical Data

37. Control Chart Selection 管制圖的選定 Quality Characteristic variable attribute n>1? n>=10 or computer? x and MR no yes x and s x and R no yes defective defect constant sample size? p-chart with variable sample size no p or np yes constant sampling unit? c u yes no

38. Produce Good Provide Service Stop Process Yes No Assign. Causes? Take Sample Inspect Sample Find Out Why Create Control Chart Start Statistical Process Control Steps 統計製程管制控制步驟

40. Using Control Charts 如何使用管制圖 1) Select the process to be charted 選擇需要被圖表化之製程 2) Get 20 - 25 groups of samples 選擇樣組及樣本大小 (usually 5-20 per group for X and R-chart or n≥50 for p-chart) 3) Construct the Control Chart 建立管制圖 4) Analyze the data relative to the control limits. Points outside of the limits should be explained 分析關聯於管制界線之資料 , 點超出界限需能被解釋 5) Once they are explained, eliminate them from the data and recalculate the control chart 一旦澄清 , 消除異常點及原因 , 並重算管制圖資料 6) Use the chart for new data, but DO NOT recalculate the control limits 利用此新資料 , 但無須重算管制界限

42. Basic Probabilities Concerning the Distribution of Sample Means 有關樣本平均數之機率分佈 Std. dev. of the sample means 樣本平均數標準差 :

45. How to Construct a Control Chart 如何建立管制圖 1. Take samples and measure them. 取樣量測 2. For each subgroup, calculate the sample average and range. 每個群組 , 計算平均值與全距 3. Set trial center line and control limits. 製作解析用管制圖之中心線與管制界限 4. Plot the R chart. Remove out-of-control points and revise control limits. 畫 R 圖 , 移除異常點 , 再修正管制界限 5. Plot x-bar chart. Remove out-of-control points and revise control limits. 畫 R 圖 , 移除異常點 , 再修正管制界限 6. Implement - sample and plot points at standard intervals. Monitor the chart. 管制用管制圖 , 於標準間隔時間取樣 , 監控此管制圖

46. Type 1 and Type 2 Error 第一種與第二種錯誤 Alarm No Alarm In-Control 管制內 Out-of-Control 失控

48. Type 1 Errors for these Tests 第一種錯誤 Test Probability Type 1 Error 2/3 7/7 10/11 16/20 1/1 2(0.00135) 0.0027 0.0052 (0.5) 7 0.0078 0.00586 0.0059

50.  X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i From Table

51. Factors for Computing Control Chart Limits 管制圖之係數表 Table

53. Sample Range at Time i 某時間間隔之全距 Samples size 樣本大小 From Table 查表 R Chart Control Limits R 管制圖管制界限公式

56. Example: The first 20 days samples are as follows:

59. Ex: Control “Commuting times” Step 1 Commuting Times (min.) - A.M. WEEK Minutes Xbar = R = Step 2 Step 3 X = 74.6 R = 36 n = 5 UCL L = X + A 2 *R = 74.6 + (.58)*(36) = 95.48 LCL L = X - A 2 *R = 74.6 - 20.88 = 53.72 UCL R = D 4 *R = (2.11)*(36.0) = 75.96 LCL R = D 3 *R = 0

60. Control “Commuting times” (cont.) step 4 Commuting times - A.M. UCL = 95.48 Xbarbar = 74.6 LCL = 53.72 Xbar Chart 1 10 2 3 4 5 6 7 8 9 50 100 75 R Chart UCL = 75.96 Rbar = 36.0 LCL = 0 1 10 2 3 4 5 6 7 8 9 75 5 35

61. Figure

74. Figure

75. 425 Grams Mean 平均值 Process Distribution 製程分配 Distribution of sample means 樣本平均值分配 Sample Means and the Process Distribution 樣本平均值與製程分配

76. Process Capability 製程能力 µ , Nominal value 800 1000 1200 Hours Upper specification Lower specification Process distribution (a) Process is capable

77. Process Capability 製程能力 Lower specification Mean Upper specification Two sigma µ , Nominal value

78. Process Capability 製程能力 Lower specification Mean Upper specification Four sigma Two sigma µ , Nominal value

79. Process Capability 製程能力 Lower specification Mean Upper specification Six sigma Four sigma Two sigma µ , Nominal value

82. Meanings of C pk Measures C pk 量測之意義 C pk = negative number C pk = zero C pk = between 0 and 1 C pk = 1 C pk > 1

83. Statistical Process Control – Identify and Reduce Process Variability 統計製程管制 - 確認並降低製程變異 Lower specification limit Upper specification limit (a) Acceptance sampling (b) Statistical process control (c) c pk >1

91. Operating Characteristic Curve OC 曲線 允 收 機 率 AQL LTPD  = 0.10  = 0.05 Probability of acceptance, P a { 0.60 0.40 0.20 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.80 { Proportion defective 不良比例 1.00 OC curve for n and c 樣本大小與 c 允收數

93. AOQ Curve 平均出廠品質曲線 0.015 0.010 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 AOQL Average Outgoing Quality (Incoming) Percent Defective AQL LTPD