design and analysis of experiments 1

實驗設計與統計

胡子陵立德管理學院資環所副教授Leader University

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實驗設計與統計課程綱要及進度 Week1 ： Statistics (Review) Week2 ： Simple Comparative Experiments Week3 ： Experiments with a Single Factor ： The Analysis of

Variance(1) Week4 ： Experiments with a Single Factor ： The Analysis of

Variance(2) Week5 ： Introduction to Factorial Designs (1) Week6 ： Introduction to Factorial Designs (2) Week7 ： The 2K Factorial Design(1) Week8 ： The 2K Factorial Design(2) Week9 ： -----Mid-Term Report--------

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實驗設計與統計課程綱要及進度 Week10 ： Blocking and Confounding in the 2k Factorial Design(1) Week11 ： Blocking and Confounding in the 2k Factorial Design(2) Week12 ： Two-Level Fractional Factorial Design(1) Week13 ： Two-Level Fractional Factorial Design(2) Week14 ： Fitting Regression Models(1) Week15 ： Fitting Regression Models(2) Week16 ： Response Surface Methods and Other Approaches to

Process Optimization(1) Week17 ： Response Surface Methods and Other Approaches to

Process Optimization (2) Week18 ： ----Final Examination----------

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實驗設計與統計Part 1 – 前言Chapter 1課程目的歷史回顧一些基本原理 ( 原則 ) 和術語實驗的策略規畫、進行和分析實驗的方針

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實驗設計介紹 An experiment is a test or a series of tests Experiments are used widely in the

engineering world Process characterization & optimization Evaluation of material properties Product design & development Component & system tolerance determination

“All experiments are designed experiments, some are poorly designed, some are well-designed”

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解釋名詞 Response variable Explanatory variable Treatment Lurking variable Confounded Statistical significance：我們的結論有統計顯著性，即證據或結果強到很少會光靠機遇 (chance)而發生。

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工程上之實驗要求 Reduce time to

design/develop new products & processes

Improve performance of existing processes

Improve reliability and performance of products

Achieve product & process robustness

Evaluation of materials, design alternatives, setting component & system tolerances, etc.

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實驗設計歷史發展的基本原則 Randomization

Running the trials in an experiment in random order Notion of balancing out effects of “lurking” variables

Replication Sample size (improving precision of effect estimation,

estimation of error or background noise) Replication versus repeat measurements?

Blocking Dealing with nuisance factors

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The meaning of Blocking

Blocking( 區集 ) ：一組實驗個體，這些個體在實驗之前，就被認為在會影響反應的某些地方很近似；與抽樣中的分層樣本具有相同類似的功用。

Blocking design ：將個體隨機分派到各處理的此一步驟，是在每個 Blocking裡個別執行的。

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實驗策略 “Best-guess” experiments

Having a lot of technical or theoretical knowledge More successful than you might suspect, but there are

disadvantages… One-factor-at-a-time (OFAT) experiments

Sometimes associated with the “scientific” or “engineering” method

Devastated by interaction, also very inefficient Statistically designed experiments

Based on Fisher’s factorial concept

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因子設計 In a factorial experiment,

all possible combinations of factor levels are tested

The golf experiment: Type of driver Type of ball Walking vs. riding Type of beverage Time of round Weather Type of golf spike Etc, etc, etc…

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One-factor-at-a-time設計Using the oversized driver, balata ball, walking, and drinking water levels of the four factors as the baseline.

Optimal combination: regular-sized driver, riding, and drinking water

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因子設計

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多因子之因子設計

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多因子之因子設計－部份因子

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實驗設計指南

1. Recognition of & statement of problem

2. Choice of factors, levels, and ranges

3. Selection of the response variable(s)

4. Choice of design

5. Conducting the experiment

6. Statistical analysis

7. Drawing conclusions, recommendations

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實驗設計歷史發展的四個時期 The agricultural origins, 1918 – 1940s

R. A. Fisher & his co-workers Profound impact on agricultural science Factorial designs, ANOVA (analysis of variance)

The first industrial era, 1951 – late 1970s Box & Wilson, response surfaces Applications in the chemical & process industries

The second industrial era, late 1970s – 1990 Quality improvement initiatives in many companies Taguchi and robust parameter design, process

robustness The modern era, beginning circa 1990

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實驗中使用統計技術 Get statistical thinking involved early Your non-statistical knowledge is crucial to

success Pre-experimental planning (steps 1-3) vital Think and experiment sequentially (use the

KISS principle)