實驗設計 Design of Experiments

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y值得變異最小？ • 如何設定x1, x2, …, xp使不可控制因素z1, z2, …, zp之影響最小？ 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) DOE_Class 90a

一般實驗進行方式 • Best-guess approach • 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 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………………… DOE_Class 90a

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

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

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

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

Example: Optimizing a Process DOE_Class 90a

基本原則 • 複製(Replication) • 估計自然誤差 • 中央極限定理 • 區隔化(Blocking) • “Averaging out” the effects from uncontrollable variables • 隨機化(Randomization) • 增進實驗之精確度 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 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 • 成本 • 技術 • 時間 • 實驗通常是遞迴式的 • 前幾次實驗通常只是學習經驗而已 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): 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: 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? DOE_Class 90a

Blank Sheet (I)_Response Variables DOE_Class 90a

Blank Sheet (II)_Control Variables DOE_Class 90a

Blank Sheet (III)_”Held Constant” Variables DOE_Class 90a

Blank Sheet (IV)_Nuisance Factors DOE_Class 90a

Blank Sheet (V)_Interactions 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 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 • 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 • 混合設計 • 最佳化(Optimizing) • 反應曲面技術 DOE_Class 90a

實驗設計 Design of Experiments