實驗設計 design of experiments 洪弘祈, ph.d....

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

&One DOE_Class 90a 2

實驗目的 :

&1 DOE 簡介

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？


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)


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


最佳因子水準組合為？ Driver: Regular Mode of travel: Ride Beverage: Water

But what if…………………

Results of the one-factor-a-time strategy for the golf experiment


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


The two-factor factorial design for the golf experiment (II)

Ball Effect = ？ Ball-Driver Interaction Effect = ？


Other Designs for the Golf Experiment

Four-factor factorial design

Three-factor factorial design


Other Designs for the Golf Experiment

Four-factor fractional factorial design


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


Example:Optimizing a Process


基本原則複製 (Replication)

隨機化 (Randomization)

區隔化 (Blocking)

增進實驗之精確度

估計自然誤差中央極限定理

“Averaging out” the effects from uncontrollable variables


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 invest

ed in the first experiment


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


Master Guide Sheet (I)

1. Experimenter's Name and Organization: Brief Title of Experiment:2. Objectives of the experiment (should be unbiased, specif

ic, measurable, and of practical consequence):3. Relevant background on response and control variables: (a) theoretical relationships; (b) expert knowledge/experie

nce; (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):


Master Guide Sheet (II)5. List: (a) each control variable, (b) the normal control variable le

vel 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:


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?


Blank Sheet (I)_Response Variables

responsevariable(units)

normaloperating level& range

meas. precision,accuracyHow known?

relationship ofresponse variable toobjective


Blank Sheet (II)_Control Variables

controlvariable(units)

normal level& range

meas. precision& setting errorHow known?

Proposed settings,based on predictedEffects

Predicted Effects (for various Responses)


Blank Sheet (III)_”Held Constant” Variables

factor(units)

Desired experimentallevel & allowable range

measurementprecisionHow known?

how tocontrol (inexperiment)

anticipatedeffects


Blank Sheet (IV)_Nuisance Factors

nuisancefactor (units)

measurementprecisionHow known?

strategy (e.g., randomization,blocking, etc.)

anticipated effects


Blank Sheet (V)_Interactions

Control Variables

1 2 3 4 5 6 7

1

2

3

4

5

6

7


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


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

實驗設計之種類 (Another Prospect)

實 驗 設 計 design of experiments 洪弘祈, ph.d....

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實驗設計 design of experiments 洪弘祈, ph.d....