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實驗設計與統計. 胡子陵 立德管理學院資環所副教授 Leader University. 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)

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slide1

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

slide2
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--------

design and analysis of experiments

slide3
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----------

design and analysis of experiments

part 1 chapter 1
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

design and analysis of experiments

slide5
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”

design and analysis of experiments

slide6
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。

design and analysis of experiments

slide7
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.

design and analysis of experiments

slide8
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

design and analysis of experiments

the meaning of blocking
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。

design and analysis of experiments

slide10
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 designedexperiments
    • Based on Fisher’s factorial concept

design and analysis of experiments

slide11
因子設計
  • In a factorial experiment, allpossiblecombinations 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…

design and analysis of experiments

one factor at a time
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

design and analysis of experiments

slide13
因子設計

design and analysis of experiments

slide14
多因子之因子設計

design and analysis of experiments

slide15
多因子之因子設計-部份因子

design and analysis of experiments

slide16
實驗設計指南
  • 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

design and analysis of experiments

slide17
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

design and analysis of experiments

slide18
實驗中使用統計技術
  • Get statisticalthinking 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)

design and analysis of experiments

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