實驗設計與統計
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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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實驗設計與統計

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6846843

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

  • 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


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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----------

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


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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”

design and analysis of experiments


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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。

design and analysis of experiments


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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.

design and analysis of experiments


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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

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


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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 designedexperiments

    • Based on Fisher’s factorial concept

design and analysis of experiments


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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


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因子設計

design and analysis of experiments


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多因子之因子設計

design and analysis of experiments


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多因子之因子設計-部份因子

design and analysis of experiments


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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


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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

design and analysis of experiments


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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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