實 驗 設 計 Design of Experiments 洪弘祈, Ph.D. 朝陽科技大學工業工程與管理系副教授

&1 DOE簡介 實驗目的: 對y影響最大的變數為何？ 如何設定x1, x2, …, xp使y值趨近最佳值？ 如何設定x1, x2, …, xp使不可控制因素z1, z2, …, zp之影響最小？ &One DOE_Class 90a

An Example：Play Golf Objective: Lower score without much practicing. Response Variable: Score (per round) Possible Factors: The type of driver used (oversized or regular-sized) The type of ball used (balata or three-piece) Walking or riding in a golf cart Beverage Type (water or beer) Time (in the morning or afternoon) Weather (cool or hot, windy or calm) The type of golf shoe spike (metal or soft) &One DOE_Class 90a

一般實驗進行方式 Best-guess approach On-factor-at-a-time No Good, Guess Again Switching the levels of one (perhaps two) factors for the next test based on the outcome of the current test Good Enough, Stop! On-factor-at-a-time Selecting a baseline starting point Varying each factor over its range with the other factors held constant at the baseline level Interactions ruin everything &One DOE_Class 90a

Results of the one-factor-a-time strategy for the golf experiment 最佳因子水準組合為？ Driver: Regular Mode of travel: Ride Beverage: Water But what if………………… &One DOE_Class 90a

The two-factor factorial design for the golf experiment (I) &One DOE_Class 90a

The two-factor factorial design for the golf experiment (II) Ball Effect = ？ Ball-Driver Interaction Effect = ？ &One DOE_Class 90a

Other Designs for the Golf Experiment Three-factor factorial design Four-factor factorial design &One DOE_Class 90a

Other Designs for the Golf Experiment Four-factor fractional factorial design &One DOE_Class 90a

實驗計劃法(DOE) 在一個或連串的試驗中刻意地改變製程輸入參數值, 以便觀察並找出影響製程輸出變數之因素. 應用: 改進製程產出率 降低製程變異, 改善產品品質 降低研發時間 降低總體成本 評估各種可行之設定值 評估各替代原料 確定影響產品特性之因素 &One DOE_Class 90a

Example: Optimizing a Process &One DOE_Class 90a

基本原則 複製(Replication) 區隔化(Blocking) 隨機化(Randomization) 估計自然誤差 中央極限定理 “Averaging out” the effects from uncontrollable variables 隨機化(Randomization) 增進實驗之精確度 &One DOE_Class 90a

DOE之程序 問題之認知與陳述 選擇因子與其水準 選擇反應變數 選擇適當之實驗設計 執行實驗 資料分析 結論與建議 Follow-up run and confirmation test Iterative No more than 25% of available resources should be invested in the first experiment &One DOE_Class 90a

Notes 使用統計以外之專業知識 實驗之設計與分析應愈簡單愈好 實驗之統計分析結果與現實上之差異 實驗通常是遞迴式的 成本 技術 時間 前幾次實驗通常只是學習經驗而已 &One DOE_Class 90a

Master Guide Sheet (I) 1. Experimenter's Name and Organization: Brief Title of Experiment: 2. Objectives of the experiment (should be unbiased, specific, measurable, and of practical consequence): 3. Relevant background on response and control variables: (a) theoretical relationships; (b) expert knowledge/experience; (c) previous experiments. Where does this experiment fit into the study of the process or system?: 4. List: (a) each response variable, (b) the normal response variable level at which the process runs, the distribution or range of normal operation, (c) the precision or range to which it can be measured (and how): &One DOE_Class 90a

Master Guide Sheet (II) 5. List: (a) each control variable, (b) the normal control variable level at which the process is run, and the distribution or range of normal operation, (c) the precision (s) or range to which it can be set (for the experiment, not ordinary plant operations) and the precision to which it can be measured, (d) the proposed control variable settings, and (e) the predicted effect (at least qualitative) that the settings will have on each response variable: 6. List: (a) each factor to be "held constant" in the experiment, (b) its desired level and allowable s or range of variation, (c) the precision or range to which it can measured (and how), (d) how it can be controlled, and (e) its expected impact, if any, on each of the responses: 7. List: (a) each nuisance factor (perhaps time-varying), (b) measurement precision, (c)strategy (e.g., blocking, randomization, or selection), and (d) anticipated effect: 8. List and label known or suspected interactions: &One DOE_Class 90a

Master Guide Sheet (III) 9. List restrictions on the experiment, e.g., ease of changing control variables, methods of data acquisition, materials, duration, number of runs, type of experimental unit (need for a split-plot design), “illegal” or irrelevant experimental regions, limits to randomization, run order, cost of changing a control variable setting, etc.: 10. Give current design preferences, if any, and reasons for preference, including blocking and randomization: 11. If possible, propose analysis and presentation techniques, e.g., plots, ANOVA, regression, plots, t tests, etc.: 12. Who will be responsible for the coordination of the experiment? 13. Should trial runs be conducted? Why / why not? &One DOE_Class 90a

Blank Sheet (I)_Response Variables (units) normal operating level & range meas. precision, accuracy How known? relationship of response variable to objective &One DOE_Class 90a

Blank Sheet (II)_Control Variables (units) normal level & range meas. precision & setting error How known? Proposed settings, based on predicted Effects Predicted Effects (for various Responses) &One DOE_Class 90a

Blank Sheet (III)_”Held Constant” Variables factor (units) Desired experimental level & allowable range measurement precision How known? how to control (in experiment) anticipated effects &One DOE_Class 90a

Blank Sheet (IV)_Nuisance Factors factor (units) measurement precision How known? strategy (e.g., randomization, blocking, etc.) anticipated effects &One DOE_Class 90a

Blank Sheet (V)_Interactions Control Variables 1 2 3 4 5 6 7 &One DOE_Class 90a

實驗設計之種類 單因子實驗設計 Variance Model 單因子區隔設計 二因子實驗設計 二水準階層實驗設計 二水準部分階層實驗設計 三水準階層實驗設計 三水準部分階層實驗設計 反應曲面技術 &One DOE_Class 90a

實驗設計之種類(Another Prospect) 因子篩選(Screening Experiments) 二水準部分階層實驗設計 Plackett-Burman Design Group-Screening Designs 特定區間 二水準階層實驗設計 三水準階層實驗設計 三水準部分階層實驗設計 混合設計 最佳化(Optimizing) 反應曲面技術 &One DOE_Class 90a