a) Prepare a normal probability plot of the effects. Which effects seem active?
|
|
- Gladys Shepherd
- 6 years ago
- Views:
Transcription
1 Problema 8.6: R.D. Snee ( Experimenting with a large number of variables, in experiments in Industry: Design, Analysis and Interpretation of Results, by R. D. Snee, L.B. Hare, and J. B. Trout, Editors, ASQC, 985) describes an experiment in which a 5- design with I = ABCDE was used to investigate the effects of five factors on the color of a chemical product. The factors are A= solvent/reactant, B = catalyst/reactant, C = temperature, D = reactant purity, and E = reactant ph. The results obtained were as follows: Tratamientos Resultados e -.6 a.5 b -.68 abe.66 c.6 ace. bce -.9 abc.9 d 6.79 ade 5.7 bde.5 abd 5.68 cde 5. acd.8 bcd. abcde.5 a) Prepare a normal probability plot of the effects. Which effects seem active?
2 Normal Probability Plot of the Effects (response is Results, Alpha =.5) D Effect Type Not Significant Significant Factor Name A A B B C C D D E E Effect 5 Lenth's PSE =.765 El efecto significativo es la D = pureza del reactante. b) Calculate the residuals. Construct a normal probability plot of the residuals and plot the residuals versus the fitted values. Comment on the plots. Normal Probability Plot of the s 9 5 Plots for Results s Versus the Fitted Values Fitted Value.6.8 Histogram of the s s Versus the Order of the Data Frequency Observation Order Los residuales muestran un comportamiento aproximadamente normal y al compararlos con los fitted values no se ve un cambio en la varianza poco significativo.
3 c) If any factors are negligible, collapse the 5- design into a full factorial in the active factors. Comment on the resulting design, and interpret the results. Factorial Fit: Respuesta versus D Estimated Effects and Coefficients for Respuesta (coded units) Term Effect Coef SE Coef T P Constant D S =.6556 R-Sq = 68.% R-Sq(adj) = 65.86% Analysis of Variance for Respuesta (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects Error Pure Error Total Unusual Observations for Respuesta Obs StdOrder Respuesta Fit SE Fit St Resid R R denotes an observation with a large standardized residual. Alias Structure I D Normal Probability Plot of the s 9 5 Plots for Respuesta s Versus the Fitted Values Fitted Value.6.8 Histogram of the s s Versus the Order of the Data Frequency Observation Order
4 Problema 8.8: An article in Industrial and Engineering Chemistry uses a 5- design to investigate the effect of A = condensation temperature, B = amount of material, C = solvent volume, D = condensation time, and E = amount of material on yield. The results obtained are as follows: Tratamientos e. ab 5.5 ad 6.9 bc 6. cd.8 ace. bde 6.8 abcde 8. Resultados a) Verify that the design generators used were I = ACE and I = BDE. Factors: 5 Base Design:, 8 Resolution: III Runs: 8 Replicates: Fraction: / Blocks: Center pts (total): * NOTE * Some main effects are confounded with two-way interactions. Design Generators: D = ABC, E = AC Alias Structure (up to order ) I + ACE + BDE A + CE + BCD + ABDE B + DE + ACD + ABCE C + AE + ABD + BCDE D + BE + ABC + ACDE E + AC + BD + ABCDE AB + CD + ADE + BCE AD + BC + ABE + CDE ABCD Los generadores si son ACE y BDE.
5 b) Write down the complete defining relation and the aliases for this design. A = CE = BCD = ABDE B = DE = ACD = ABCE C = AE = ABD = BCDE D = BE = ABC = ACDE E = AC = BD = ABCDE AB = CD = ADE = BCE AD = BC = ABE = CDE ABCD c) Estimate the main effects. Estimated Effects and Coefficients for Respuesta (coded units) Term Effect Coef SE Coef T P Constant A B C D E S =.66 R-Sq = 88.95% R-Sq(adj) = 6.% Normal Probability Plot of the Effects (response is Respuesta, Alpha =.5) Effect Type Not Significant Significant Factor Name A A B B C C D D E E Effect.5 5. Lenth's PSE =.775 No se ve ningun factor significativo sin embargo se verifico que factor tiene un efecto mayor sobre la respuesta con el siguiente grafico:
6 Main Effects Plot (data means) for Respuesta A B C Mean of Respuesta D - - E Se observa que B es el que mas impacta la respuesta. d) Prepare an analysis of variance table. Verify that the AB and AD interactions are available to use as error. Analysis of Variance for Respuesta (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects * * -Way Interactions * * Error * * * Total Effects Plot for Respuesta Alias Structure I + A*C*E + B*D*E + A*B*C*D A + C*E + B*C*D + A*B*D*E B + D*E + A*C*D + A*B*C*E C + A*E + A*B*D + B*C*D*E D + B*E + A*B*C + A*C*D*E E + A*C + B*D + A*B*C*D*E A*D + B*C + A*B*E + C*D*E A*B + C*D + A*D*E + B*C*E Dejando las interacciones mencionadas por fuera no se obtiene aun grados de libertad para el error. Sabiendo que B es el que mas impacta, se procedió a realizar una anova incluyendo solo el factor B:
7 Factorial Fit: Respuesta versus B Estimated Effects and Coefficients for Respuesta (coded units) Term Effect Coef SE Coef T P Constant B S =.555 R-Sq = 59.69% R-Sq(adj) = 5.97% Analysis of Variance for Respuesta (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects Error Pure Error Total Unusual Observations for Respuesta Obs StdOrder Respuesta Fit SE Fit St Resid R R denotes an observation with a large standardized residual. * NOTE * Normal and Pareto effects plots require at least terms. Alias Structure I B e) Plot the residuals versus the fitted values. Also construct a normal probability plot of the residuals. Plots for Respuesta Normal Probability Plot of the s s Versus the Fitted Values Fitted Value. Histogram of the s s Versus the Order of the Data Frequency Observation Order 7 8
8 Se observa un comportamiento aproximadamente normal, pero parece que a mayor valor en la respuesta mayor varianza en los residuales. Problema.9: An experiment was performed to investigate the capability of a measurement system. Ten parts were randomly selected, and two randomly selected operators measured each part three times. The tests were made in random order, and the data below resulted. Part number Operator Operator General Linear Model: results versus operador, Part number Factor Type Levels Values operador random, Part number random,,,, 5, 6, 7, 8, 9, Analysis of Variance for results, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P operador Part number operador*part number Error Total
9 Normal Probability Plot of the s (response is results) Según lo anterior la interacción de las partes con el operador no es significativa. b) Find point estimates of the variance components using the analysis of variance method. σ = MS E =.5 σ τβ = (MS AB MS E ) / n = ( ) / <, asumiendo σ τβ = σ τ = (MS B MS AB ) / an = ( ) / * =.7 σ β = (MS A MS AB ) / bn <, asumiendo σ τ =
STAT451/551 Homework#11 Due: April 22, 2014
STAT451/551 Homework#11 Due: April 22, 2014 1. Read Chapter 8.3 8.9. 2. 8.4. SAS code is provided. 3. 8.18. 4. 8.24. 5. 8.45. 376 Chapter 8 Two-Level Fractional Factorial Designs more detail. Sequential
More informationInstitutionen för matematik och matematisk statistik Umeå universitet November 7, Inlämningsuppgift 3. Mariam Shirdel
Institutionen för matematik och matematisk statistik Umeå universitet November 7, 2011 Inlämningsuppgift 3 Mariam Shirdel (mash0007@student.umu.se) Kvalitetsteknik och försöksplanering, 7.5 hp 1 Uppgift
More informationST3232: Design and Analysis of Experiments
Department of Statistics & Applied Probability 2:00-4:00 pm, Monday, April 8, 2013 Lecture 21: Fractional 2 p factorial designs The general principles A full 2 p factorial experiment might not be efficient
More informationAPPENDIX 1. Binodal Curve calculations
APPENDIX 1 Binodal Curve calculations The weight of salt solution necessary for the mixture to cloud and the final concentrations of the phase components were calculated based on the method given by Hatti-Kaul,
More informationCSCI 688 Homework 6. Megan Rose Bryant Department of Mathematics William and Mary
CSCI 688 Homework 6 Megan Rose Bryant Department of Mathematics William and Mary November 12, 2014 7.1 Consider the experiment described in Problem 6.1. Analyze this experiment assuming that each replicate
More informationSuppose we needed four batches of formaldehyde, and coulddoonly4runsperbatch. Thisisthena2 4 factorial in 2 2 blocks.
58 2. 2 factorials in 2 blocks Suppose we needed four batches of formaldehyde, and coulddoonly4runsperbatch. Thisisthena2 4 factorial in 2 2 blocks. Some more algebra: If two effects are confounded with
More information20g g g Analyze the residuals from this experiment and comment on the model adequacy.
3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value. One-way ANOVA Source DF SS MS F P Factor 3 36.15??? Error??? Total 19 196.04 3.11. A pharmaceutical
More information3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value.
3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value. One-way ANOVA Source DF SS MS F P Factor 3 36.15??? Error??? Total 19 196.04 Completed table is: One-way
More informationContents. TAMS38 - Lecture 8 2 k p fractional factorial design. Lecturer: Zhenxia Liu. Example 0 - continued 4. Example 0 - Glazing ceramic 3
Contents TAMS38 - Lecture 8 2 k p fractional factorial design Lecturer: Zhenxia Liu Department of Mathematics - Mathematical Statistics Example 0 2 k factorial design with blocking Example 1 2 k p fractional
More informationChapter 30 Design and Analysis of
Chapter 30 Design and Analysis of 2 k DOEs Introduction This chapter describes design alternatives and analysis techniques for conducting a DOE. Tables M1 to M5 in Appendix E can be used to create test
More informationThe One-Quarter Fraction
The One-Quarter Fraction ST 516 Need two generating relations. E.g. a 2 6 2 design, with generating relations I = ABCE and I = BCDF. Product of these is ADEF. Complete defining relation is I = ABCE = BCDF
More information23. Fractional factorials - introduction
173 3. Fractional factorials - introduction Consider a 5 factorial. Even without replicates, there are 5 = 3 obs ns required to estimate the effects - 5 main effects, 10 two factor interactions, 10 three
More information19. Blocking & confounding
146 19. Blocking & confounding Importance of blocking to control nuisance factors - day of week, batch of raw material, etc. Complete Blocks. This is the easy case. Suppose we run a 2 2 factorial experiment,
More informationStrategy of Experimentation III
LECTURE 3 Strategy of Experimentation III Comments: Homework 1. Design Resolution A design is of resolution R if no p factor effect is confounded with any other effect containing less than R p factors.
More informationChapter 11: Factorial Designs
Chapter : Factorial Designs. Two factor factorial designs ( levels factors ) This situation is similar to the randomized block design from the previous chapter. However, in addition to the effects within
More informationSession 3 Fractional Factorial Designs 4
Session 3 Fractional Factorial Designs 3 a Modification of a Bearing Example 3. Fractional Factorial Designs Two-level fractional factorial designs Confounding Blocking Two-Level Eight Run Orthogonal Array
More informationExperimental design (DOE) - Design
Experimental design (DOE) - Design Menu: QCExpert Experimental Design Design Full Factorial Fract Factorial This module designs a two-level multifactorial orthogonal plan 2 n k and perform its analysis.
More informationFractional Replications
Chapter 11 Fractional Replications Consider the set up of complete factorial experiment, say k. If there are four factors, then the total number of plots needed to conduct the experiment is 4 = 1. When
More informationHomework 04. , not a , not a 27 3 III III
Response Surface Methodology, Stat 579 Fall 2014 Homework 04 Name: Answer Key Prof. Erik B. Erhardt Part I. (130 points) I recommend reading through all the parts of the HW (with my adjustments) before
More informationAnswer Keys to Homework#10
Answer Keys to Homework#10 Problem 1 Use either restricted or unrestricted mixed models. Problem 2 (a) First, the respective means for the 8 level combinations are listed in the following table A B C Mean
More informationAssignment 9 Answer Keys
Assignment 9 Answer Keys Problem 1 (a) First, the respective means for the 8 level combinations are listed in the following table A B C Mean 26.00 + 34.67 + 39.67 + + 49.33 + 42.33 + + 37.67 + + 54.67
More informationUSE OF COMPUTER EXPERIMENTS TO STUDY THE QUALITATIVE BEHAVIOR OF SOLUTIONS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS
USE OF COMPUTER EXPERIMENTS TO STUDY THE QUALITATIVE BEHAVIOR OF SOLUTIONS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS Seshadev Padhi, Manish Trivedi and Soubhik Chakraborty* Department of Applied Mathematics
More informationHigher Order Factorial Designs. Estimated Effects: Section 4.3. Main Effects: Definition 5 on page 166.
Higher Order Factorial Designs Estimated Effects: Section 4.3 Main Effects: Definition 5 on page 166. Without A effects, we would fit values with the overall mean. The main effects are how much we need
More informationFractional Factorial Designs
Fractional Factorial Designs ST 516 Each replicate of a 2 k design requires 2 k runs. E.g. 64 runs for k = 6, or 1024 runs for k = 10. When this is infeasible, we use a fraction of the runs. As a result,
More informationTWO-LEVEL FACTORIAL EXPERIMENTS: REGULAR FRACTIONAL FACTORIALS
STAT 512 2-Level Factorial Experiments: Regular Fractions 1 TWO-LEVEL FACTORIAL EXPERIMENTS: REGULAR FRACTIONAL FACTORIALS Bottom Line: A regular fractional factorial design consists of the treatments
More informationUnit 6: Fractional Factorial Experiments at Three Levels
Unit 6: Fractional Factorial Experiments at Three Levels Larger-the-better and smaller-the-better problems. Basic concepts for 3 k full factorial designs. Analysis of 3 k designs using orthogonal components
More informationFactorial Experiments
Factorial Experiments 92 93 94 95 96 97 ack to two-factor experiment 98 99 DOE terminology main effects: Interaction effects 00 0 Three factors z z2 z3 z2 z3 z23 z23 02 03 Two-factor interaction Three-factor
More informationUnreplicated 2 k Factorial Designs
Unreplicated 2 k Factorial Designs These are 2 k factorial designs with one observation at each corner of the cube An unreplicated 2 k factorial design is also sometimes called a single replicate of the
More informationDesign and Analysis of
Design and Analysis of Multi-Factored Experiments Module Engineering 7928-2 Two-level Factorial Designs L. M. Lye DOE Course 1 The 2 k Factorial Design Special case of the general factorial design; k factors,
More informationThe 2 k Factorial Design. Dr. Mohammad Abuhaiba 1
The 2 k Factorial Design Dr. Mohammad Abuhaiba 1 HoweWork Assignment Due Tuesday 1/6/2010 6.1, 6.2, 6.17, 6.18, 6.19 Dr. Mohammad Abuhaiba 2 Design of Engineering Experiments The 2 k Factorial Design Special
More informationFractional Factorials
Fractional Factorials Bruce A Craig Department of Statistics Purdue University STAT 514 Topic 26 1 Fractional Factorials Number of runs required for full factorial grows quickly A 2 7 design requires 128
More informationMath Treibergs. Peanut Oil Data: 2 5 Factorial design with 1/2 Replication. Name: Example April 22, Data File Used in this Analysis:
Math 3080 1. Treibergs Peanut Oil Data: 2 5 Factorial design with 1/2 Replication. Name: Example April 22, 2010 Data File Used in this Analysis: # Math 3080-1 Peanut Oil Data April 22, 2010 # Treibergs
More informationCS 5014: Research Methods in Computer Science
Computer Science Clifford A. Shaffer Department of Computer Science Virginia Tech Blacksburg, Virginia Fall 2010 Copyright c 2010 by Clifford A. Shaffer Computer Science Fall 2010 1 / 254 Experimental
More informationContents. 2 2 factorial design 4
Contents TAMS38 - Lecture 10 Response surface methodology Lecturer: Zhenxia Liu Department of Mathematics - Mathematical Statistics 12 December, 2017 2 2 factorial design Polynomial Regression model First
More informationA Statistical Approach to the Study of Qualitative Behavior of Solutions of Second Order Neutral Differential Equations
Australian Journal of Basic and Applied Sciences, (4): 84-833, 007 ISSN 99-878 A Statistical Approach to the Study of Qualitative Behavior of Solutions of Second Order Neutral Differential Equations Seshadev
More informationFRACTIONAL FACTORIAL
FRACTIONAL FACTORIAL NURNABI MEHERUL ALAM M.Sc. (Agricultural Statistics), Roll No. 443 I.A.S.R.I, Library Avenue, New Delhi- Chairperson: Dr. P.K. Batra Abstract: Fractional replication can be defined
More informationESTIMATION METHODS FOR MISSING DATA IN UN-REPLICATED 2 FACTORIAL AND 2 FRACTIONAL FACTORIAL DESIGNS
Journal of Statistics: Advances in Theory and Applications Volume 5, Number 2, 2011, Pages 131-147 ESTIMATION METHODS FOR MISSING DATA IN k k p UN-REPLICATED 2 FACTORIAL AND 2 FRACTIONAL FACTORIAL DESIGNS
More informationConstruction of Mixed-Level Orthogonal Arrays for Testing in Digital Marketing
Construction of Mixed-Level Orthogonal Arrays for Testing in Digital Marketing Vladimir Brayman Webtrends October 19, 2012 Advantages of Conducting Designed Experiments in Digital Marketing Availability
More informationConfounding and fractional replication in 2 n factorial systems
Chapter 20 Confounding and fractional replication in 2 n factorial systems Confounding is a method of designing a factorial experiment that allows incomplete blocks, i.e., blocks of smaller size than the
More information2 k, 2 k r and 2 k-p Factorial Designs
2 k, 2 k r and 2 k-p Factorial Designs 1 Types of Experimental Designs! Full Factorial Design: " Uses all possible combinations of all levels of all factors. n=3*2*2=12 Too costly! 2 Types of Experimental
More informationFRACTIONAL REPLICATION
FRACTIONAL REPLICATION M.L.Agarwal Department of Statistics, University of Delhi, Delhi -. In a factorial experiment, when the number of treatment combinations is very large, it will be beyond the resources
More informationConfidence Interval for the mean response
Week 3: Prediction and Confidence Intervals at specified x. Testing lack of fit with replicates at some x's. Inference for the correlation. Introduction to regression with several explanatory variables.
More informationLECTURE 10: LINEAR MODEL SELECTION PT. 1. October 16, 2017 SDS 293: Machine Learning
LECTURE 10: LINEAR MODEL SELECTION PT. 1 October 16, 2017 SDS 293: Machine Learning Outline Model selection: alternatives to least-squares Subset selection - Best subset - Stepwise selection (forward and
More informationSoo King Lim Figure 1: Figure 2: Figure 3: Figure 4: Figure 5: Figure 6: Figure 7: Figure 8: Figure 9: Figure 10: Figure 11: Figure 12: Figure 13:
1.0 ial Experiment Design by Block... 3 1.1 ial Experiment in Incomplete Block... 3 1. ial Experiment with Two Blocks... 3 1.3 ial Experiment with Four Blocks... 5 Example 1... 6.0 Fractional ial Experiment....1
More informationChapter 13 Experiments with Random Factors Solutions
Solutions from Montgomery, D. C. (01) Design and Analysis of Experiments, Wiley, NY Chapter 13 Experiments with Random Factors Solutions 13.. An article by Hoof and Berman ( Statistical Analysis of Power
More informationStatistics GIDP Ph.D. Qualifying Exam Methodology May 26 9:00am-1:00pm
Statistics GIDP Ph.D. Qualifying Exam Methodology May 26 9:00am-1:00pm Instructions: Put your ID (not name) on each sheet. Complete exactly 5 of 6 problems; turn in only those sheets you wish to have graded.
More informationDesign and Analysis of Multi-Factored Experiments
Design and Analysis of Multi-Factored Experiments Two-level Factorial Designs L. M. Lye DOE Course 1 The 2 k Factorial Design Special case of the general factorial design; k factors, all at two levels
More informationLecture 12: 2 k p Fractional Factorial Design
Lecture 12: 2 k p Fractional Factorial Design Montgomery: Chapter 8 Page 1 Fundamental Principles Regarding Factorial Effects Suppose there are k factors (A,B,...,J,K) in an experiment. All possible factorial
More information2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationTMA4267 Linear Statistical Models V2017 (L19)
TMA4267 Linear Statistical Models V2017 (L19) Part 4: Design of Experiments Blocking Fractional factorial designs Mette Langaas Department of Mathematical Sciences, NTNU To be lectured: March 28, 2017
More informationReference: Chapter 8 of Montgomery (8e)
Reference: Chapter 8 of Montgomery (8e) 69 Maghsoodloo Fractional Factorials (or Replicates) For Base 2 Designs As the number of factors in a 2 k factorial experiment increases, the number of runs (or
More informationReference: Chapter 6 of Montgomery(8e) Maghsoodloo
Reference: Chapter 6 of Montgomery(8e) Maghsoodloo 51 DOE (or DOX) FOR BASE BALANCED FACTORIALS The notation k is used to denote a factorial experiment involving k factors (A, B, C, D,..., K) each at levels.
More informationMATH 251 MATH 251: Multivariate Calculus MATH 251 FALL 2006 EXAM-II FALL 2006 EXAM-II EXAMINATION COVER PAGE Professor Moseley
MATH 251 MATH 251: Multivariate Calculus MATH 251 FALL 2006 EXAM-II FALL 2006 EXAM-II EXAMINATION COVER PAGE Professor Moseley PRINT NAME ( ) Last Name, First Name MI (What you wish to be called) ID #
More informationLEARNING WITH MINITAB Chapter 12 SESSION FIVE: DESIGNING AN EXPERIMENT
LEARNING WITH MINITAB Chapter 12 SESSION FIVE: DESIGNING AN EXPERIMENT Laura M Williams, RN, CLNC, MSN MOREHEAD STATE UNIVERSITY IET603: STATISTICAL QUALITY ASSURANCE IN SCIENCE AND TECHNOLOGY DR. AHMAD
More informationProbability Distribution
Probability Distribution 1. In scenario 2, the particle size distribution from the mill is: Counts 81
More informationCS 5014: Research Methods in Computer Science. Experimental Design. Potential Pitfalls. One-Factor (Again) Clifford A. Shaffer.
Department of Computer Science Virginia Tech Blacksburg, Virginia Copyright c 2015 by Clifford A. Shaffer Computer Science Title page Computer Science Clifford A. Shaffer Fall 2015 Clifford A. Shaffer
More informationDesign of Experiments SUTD - 21/4/2015 1
Design of Experiments SUTD - 21/4/2015 1 Outline 1. Introduction 2. 2 k Factorial Design Exercise 3. Choice of Sample Size Exercise 4. 2 k p Fractional Factorial Design Exercise 5. Follow-up experimentation
More informationStatistics GIDP Ph.D. Qualifying Exam Methodology May 26 9:00am-1:00pm
Statistics GIDP Ph.D. Qualifying Exam Methodology May 26 9:00am-1:00pm Instructions: Put your ID (not name) on each sheet. Complete exactly 5 of 6 problems; turn in only those sheets you wish to have graded.
More informationDesign and Analysis of Multi-Factored Experiments
Design and Analysis of Multi-Factored Experiments Fractional Factorial Designs L. M. Lye DOE Course 1 Design of Engineering Experiments The 2 k-p Fractional Factorial Design Motivation for fractional factorials
More informationThe hypergeometric distribution - theoretical basic for the deviation between replicates in one germination test?
Doubt is the beginning, not the end, of wisdom. ANONYMOUS The hypergeometric distribution - theoretical basic for the deviation between replicates in one germination test? Winfried Jackisch 7 th ISTA Seminar
More informationMATH 251 MATH 251: Multivariate Calculus MATH 251 FALL 2005 EXAM-I FALL 2005 EXAM-I EXAMINATION COVER PAGE Professor Moseley
MATH 251 MATH 251: Multivariate Calculus MATH 251 FALL 2005 EXAM-I FALL 2005 EXAM-I EXAMINATION COVER PAGE Professor Moseley PRINT NAME ( ) Last Name, First Name MI (What you wish to be called) ID # EXAM
More informationContents. TAMS38 - Lecture 6 Factorial design, Latin Square Design. Lecturer: Zhenxia Liu. Factorial design 3. Complete three factor design 4
Contents Factorial design TAMS38 - Lecture 6 Factorial design, Latin Square Design Lecturer: Zhenxia Liu Department of Mathematics - Mathematical Statistics 28 November, 2017 Complete three factor design
More informationCS 484 Data Mining. Association Rule Mining 2
CS 484 Data Mining Association Rule Mining 2 Review: Reducing Number of Candidates Apriori principle: If an itemset is frequent, then all of its subsets must also be frequent Apriori principle holds due
More informationStrategy of Experimentation II
LECTURE 2 Strategy of Experimentation II Comments Computer Code. Last week s homework Interaction plots Helicopter project +1 1 1 +1 [4I 2A 2B 2AB] = [µ 1) µ A µ B µ AB ] +1 +1 1 1 +1 1 +1 1 +1 +1 +1 +1
More informationMATH 251 MATH 251: Multivariate Calculus MATH 251 FALL 2005 EXAM-3 FALL 2005 EXAM-III EXAMINATION COVER PAGE Professor Moseley
MATH 251 MATH 251: Multivariate Calculus MATH 251 FALL 2005 EXAM-3 FALL 2005 EXAM-III EXAMINATION COVER PAGE Professor Moseley PRINT NAME ( ) Last Name, First Name MI (What you wish to be called) ID #
More informationA note on inertial motion
Atmósfera (24) 183-19 A note on inertial motion A. WIIN-NIELSEN The Collstrop Foundation, H. C. Andersens Blvd. 37, 5th, DK 1553, Copenhagen V, Denmark Received January 13, 23; accepted January 1, 24 RESUMEN
More informationReference: CHAPTER 7 of Montgomery(8e)
Reference: CHAPTER 7 of Montgomery(8e) 60 Maghsoodloo BLOCK CONFOUNDING IN 2 k FACTORIALS (k factors each at 2 levels) It is often impossible to run all the 2 k observations in a 2 k factorial design (or
More informationUnit 5: Fractional Factorial Experiments at Two Levels
Unit 5: Fractional Factorial Experiments at Two Levels Source : Chapter 4 (sections 4.1-4.3, 4.4.1, 4.4.3, 4.5, part of 4.6). Effect aliasing, resolution, minimum aberration criteria. Analysis. Techniques
More informationStatistical Design and Analysis of Experiments Part Two
0.1 Statistical Design and Analysis of Experiments Part Two Lecture notes Fall semester 2007 Henrik Spliid nformatics and Mathematical Modelling Technical University of Denmark List of contents, cont.
More informationTWO-LEVEL FACTORIAL EXPERIMENTS: BLOCKING. Upper-case letters are associated with factors, or regressors of factorial effects, e.g.
STAT 512 2-Level Factorial Experiments: Blocking 1 TWO-LEVEL FACTORIAL EXPERIMENTS: BLOCKING Some Traditional Notation: Upper-case letters are associated with factors, or regressors of factorial effects,
More informationContents. TAMS38 - Lecture 10 Response surface. Lecturer: Jolanta Pielaszkiewicz. Response surface 3. Response surface, cont. 4
Contents TAMS38 - Lecture 10 Response surface Lecturer: Jolanta Pielaszkiewicz Matematisk statistik - Matematiska institutionen Linköpings universitet Look beneath the surface; let not the several quality
More informationFractional Factorial Designs
k-p Fractional Factorial Designs Fractional Factorial Designs If we have 7 factors, a 7 factorial design will require 8 experiments How much information can we obtain from fewer experiments, e.g. 7-4 =
More informationUnit 9: Confounding and Fractional Factorial Designs
Unit 9: Confounding and Fractional Factorial Designs STA 643: Advanced Experimental Design Derek S. Young 1 Learning Objectives Understand what it means for a treatment to be confounded with blocks Know
More informationModel Building Chap 5 p251
Model Building Chap 5 p251 Models with one qualitative variable, 5.7 p277 Example 4 Colours : Blue, Green, Lemon Yellow and white Row Blue Green Lemon Insects trapped 1 0 0 1 45 2 0 0 1 59 3 0 0 1 48 4
More informationCHAPTER 12 DESIGN OF EXPERIMENTS
1 Sections CHAPTER 12 DESIGN OF EXPERIMENTS Introduction Designs Based on Level of Process Knowledge Some Flawed Experimental Designs One-Factor Designs Two-Factor Factorial Designs Factorial Designs Involving
More informationUNIT 3 BOOLEAN ALGEBRA (CONT D)
UNIT 3 BOOLEAN ALGEBRA (CONT D) Spring 2011 Boolean Algebra (cont d) 2 Contents Multiplying out and factoring expressions Exclusive-OR and Exclusive-NOR operations The consensus theorem Summary of algebraic
More informationDesign of Experiments SUTD 06/04/2016 1
Design of Experiments SUTD 06/04/2016 1 Outline 1. Introduction 2. 2 k Factorial Design 3. Choice of Sample Size 4. 2 k p Fractional Factorial Design 5. Follow-up experimentation (folding over) with factorial
More informationCHAPTER 5 KARNAUGH MAPS
CHAPTER 5 1/36 KARNAUGH MAPS This chapter in the book includes: Objectives Study Guide 5.1 Minimum Forms of Switching Functions 5.2 Two- and Three-Variable Karnaugh Maps 5.3 Four-Variable Karnaugh Maps
More informationGeometry Problem Solving Drill 08: Congruent Triangles
Geometry Problem Solving Drill 08: Congruent Triangles Question No. 1 of 10 Question 1. The following triangles are congruent. What is the value of x? Question #01 (A) 13.33 (B) 10 (C) 31 (D) 18 You set
More informationExercise 1. min_sup = 0.3. Items support Type a 0.5 C b 0.7 C c 0.5 C d 0.9 C e 0.6 F
Exercise 1 min_sup = 0.3 Items support Type a 0.5 C b 0.7 C c 0.5 C d 0.9 C e 0.6 F Items support Type ab 0.3 M ac 0.2 I ad 0.4 F ae 0.4 F bc 0.3 M bd 0.6 C be 0.4 F cd 0.4 C ce 0.2 I de 0.6 C Items support
More informationMATH 251 MATH 251: Multivariate Calculus MATH 251 FALL 2005 EXAM-IV FALL 2005 EXAM-IV EXAMINATION COVER PAGE Professor Moseley
MATH 5 MATH 5: Multivariate Calculus MATH 5 FALL 5 EXAM-IV FALL 5 EXAM-IV EXAMINATION COVER PAGE Professor Moseley PRINT NAME ( ) Last Name, First Name MI (What you wish to be called) ID # EXAM DATE Thursday,
More informationLecture 11: Blocking and Confounding in 2 k design
Lecture 11: Blocking and Confounding in 2 k design Montgomery: Chapter 7 Page 1 There are n blocks Randomized Complete Block 2 k Design Within each block, all treatments (level combinations) are conducted.
More informationMATH602: APPLIED STATISTICS
MATH602: APPLIED STATISTICS Dr. Srinivas R. Chakravarthy Department of Science and Mathematics KETTERING UNIVERSITY Flint, MI 48504-4898 Lecture 10 1 FRACTIONAL FACTORIAL DESIGNS Complete factorial designs
More informationMultiple Regression Examples
Multiple Regression Examples Example: Tree data. we have seen that a simple linear regression of usable volume on diameter at chest height is not suitable, but that a quadratic model y = β 0 + β 1 x +
More informationOn the Compounds of Hat Matrix for Six-Factor Central Composite Design with Fractional Replicates of the Factorial Portion
American Journal of Computational and Applied Mathematics 017, 7(4): 95-114 DOI: 10.593/j.ajcam.0170704.0 On the Compounds of Hat Matrix for Six-Factor Central Composite Design with Fractional Replicates
More informationAnalysis of Covariance. The following example illustrates a case where the covariate is affected by the treatments.
Analysis of Covariance In some experiments, the experimental units (subjects) are nonhomogeneous or there is variation in the experimental conditions that are not due to the treatments. For example, a
More informationIE 361 Exam 3 (Form A)
December 15, 005 IE 361 Exam 3 (Form A) Prof. Vardeman This exam consists of 0 multiple choice questions. Write (in pencil) the letter for the single best response for each question in the corresponding
More informationLec 10: Fractions of 2 k Factorial Design
December 5, 2011 Fraction of 2 k experiments Screening: Some of the factors may influence the results. We want to figure out which. The number of combinations, 2 k, is too large for a complete investigation.
More informationKarnaugh Map & Boolean Expression Simplification
Karnaugh Map & Boolean Expression Simplification Mapping a Standard POS Expression For a Standard POS expression, a 0 is placed in the cell corresponding to the product term (maxterm) present in the expression.
More informationWritten Exam (2 hours)
M. Müller Applied Analysis of Variance and Experimental Design Summer 2015 Written Exam (2 hours) General remarks: Open book exam. Switch off your mobile phone! Do not stay too long on a part where you
More information2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationConfounding and Fractional Replication in Factorial Design
ISSN -580 (Paper) ISSN 5-05 (Online) Vol.6, No.3, 016 onfounding and Fractional Replication in Factorial esign Layla. hmed epartment of Mathematics, ollege of Education, University of Garmian, Kurdistan
More informationChapter 6 The 2 k Factorial Design Solutions
Solutions from Montgomery, D. C. (004) Design and Analysis of Experiments, Wiley, NY Chapter 6 The k Factorial Design Solutions 6.. A router is used to cut locating notches on a printed circuit board.
More informationSolutions to Exercises
1 c Atkinson et al 2007, Optimum Experimental Designs, with SAS Solutions to Exercises 1. and 2. Certainly, the solutions to these questions will be different for every reader. Examples of the techniques
More informationDesign of Engineering Experiments Chapter 5 Introduction to Factorials
Design of Engineering Experiments Chapter 5 Introduction to Factorials Text reference, Chapter 5 page 170 General principles of factorial experiments The two-factor factorial with fixed effects The ANOVA
More informationLecture 14: 2 k p Fractional Factorial Design
Lecture 14: 2 k p Fractional Factorial Design Montgomery: Chapter 8 1 Lecture 14 Page 1 Fundamental Principles Regarding Factorial Effects Suppose there arek factors (A,B,...,J,K) in an experiment. All
More informationDesign and Analysis of Experiments
Design and Analysis of Experiments Part VII: Fractional Factorial Designs Prof. Dr. Anselmo E de Oliveira anselmo.quimica.ufg.br anselmo.disciplinas@gmail.com 2 k : increasing k the number of runs required
More informationLecture 10: 2 k Factorial Design Montgomery: Chapter 6
Lecture 10: 2 k Factorial Design Montgomery: Chapter 6 Page 1 2 k Factorial Design Involving k factors Each factor has two levels (often labeled + and ) Factor screening experiment (preliminary study)
More informationDesign & Analysis of Experiments 7E 2009 Montgomery
Chapter 5 1 Introduction to Factorial Design Study the effects of 2 or more factors All possible combinations of factor levels are investigated For example, if there are a levels of factor A and b levels
More informationSMAM 314 Computer Assignment 5 due Nov 8,2012 Data Set 1. For each of the following data sets use Minitab to 1. Make a scatterplot.
SMAM 314 Computer Assignment 5 due Nov 8,2012 Data Set 1. For each of the following data sets use Minitab to 1. Make a scatterplot. 2. Fit the linear regression line. Regression Analysis: y versus x y
More information