Transcript Design and Analysis of Engineering Experiments

實驗設計與統計
胡子陵
立德管理學院資環所副教授
Leader University
design and analysis of experiments
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實驗設計與統計課程綱要及進度
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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
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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
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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
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“All experiments are designed experiments,
some are poorly designed, some are welldesigned”
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解釋名詞
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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
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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
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Randomization
 Running
the trials in an experiment in random order
 Notion of balancing out effects of “lurking” variables
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Replication
 Sample
size (improving precision of effect estimation,
estimation of error or background noise)
 Replication versus repeat measurements?
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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
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“Best-guess” experiments
 Having
a lot of technical or theoretical knowledge
 More successful than you might suspect, but there
are disadvantages…
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One-factor-at-a-time (OFAT) experiments
associated with the “scientific” or
“engineering” method
 Devastated by interaction, also very inefficient
 Sometimes
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Statistically designed experiments
 Based
on Fisher’s factorial concept
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因子設計
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In a factorial experiment,
all possible
combinations of factor
levels are tested
The golf experiment:
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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
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Recognition of & statement of problem
Choice of factors, levels, and ranges
Selection of the response variable(s)
Choice of design
Conducting the experiment
Statistical analysis
Drawing conclusions, recommendations
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實驗設計歷史發展的四個時期
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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
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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)
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