Quality Improvement Chapter 13 Experimental Design Power Point

Outline 1. Introduction 2. Basic Statistics 3. Hypotheses 4. t Test 5. F Test

Outline 8. Point and Interval Design 9. Two Factors 10. Full Factorials 11. Fractional

Learning Objectives When you complete this chapter, you are expected to: q Know the

Introduction o Experimental design is a systematic manipulation of variables to make conclusions and

Introduction (Continued) o Experimental design can be used to: n n n Improve a

Definitions (Continued) n n Repetition—multiple results of a TC Random—TC are run in a

Basic Statistics o See Chapter 5 o Variance is square of standard deviation &

Hypotheses o Hypotheses (Ho) testing is a statistical decision where inferences are made about

Hypotheses (Continued) o Therefore, we use alternate hypothesis: n μ ǂ μ 2 Both

t Test It is used when the sample size is small. The distribution is

t Test (Continued) Figure 13 -2 shows the critical region where t is the

t Test (Continued) o One sample t test uses the equation: The calculated t

t Test (Continued) o Two sample test Where: Quality Improvement, 9 e Dale H.

F Test o For more than 2 factors or levels the F test using

F Test (Continued) o Analysis of Variance (ANOVA) o Mathematical model of an experiment

ANOVA (Continued) o Normal and independent distributed with same variance in each factor/level o

Once you calculate the SS values the remaining calculations easy. Critical F value is

One Factor at a Time Design o Is not balanced (only one 2 in

Orthogonal Design o Orthogonal means balanced. Average factor/level. o A 1 = Results of

Orthogonal Design (Continued) o Design is statistically independent o Effect of A = A

Point and Interval Estimate o True value of a factor is rarely known, so

t Reference Distribution o t Reference Distribution uses the concept of interval estimate to

Example 13 -8 Data from Example 13 -4 Quality Improvement, 9 e Dale H.

Two Factors q A simple experimental design has two factors and can have many

Two Factors (Continued) ANOVA is the decision method and once the SS are calculated,

Full Factorials A 3 factor/2 level, with a + for the high level and

Full Factorials (Continued) o Signs for the 2 factor and 3 factor interactions are

Full Factorials (Continued) o ANOVA is the decision method and once the SS are

Full Factorials (Continued) The number of TC is determined by Thus for a 2

Fractional Factorials q. The number of TC’s can become quite large. q. Use Engineering

Examples o Evans Clay o John Deere o Nabisco o Wilkes-Barre Hospital o Eastman

Implementation o Set good factor/levels and response variable o Replicate and random o Block

Computer Program o Microsoft EXCEL will calculate t distribution, F distribution, confidence and SS.

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Quality Improvement Chapter 13 - Experimental Design Power. Point presentation to accompany Besterfield, Quality Improvement, 9 e

Outline 1. Introduction 2. Basic Statistics 3. Hypotheses 4. t Test 5. F Test 6. One factor at a time 7. Orthogonal Design Quality Improvement, 9 e Dale H. Besterfield 2 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Outline 8. Point and Interval Design 9. Two Factors 10. Full Factorials 11. Fractional Factorials 12. Examples 13. Final Considerations Quality Improvement, 9 e Dale H. Besterfield 3 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Learning Objectives When you complete this chapter, you are expected to: q Know the applicable terminology; q Understand the concept of hypothesis testing; q Be able to determine significant factors using the t test; q Know the concept of point and interval estimate and be able to calculate them; q Be able to determine significant factors and their levels using the F test; q Understand the concept of fraction factorials. Quality Improvement, 9 e Dale H. Besterfield 4 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

Introduction o Experimental design is a systematic manipulation of variables to make conclusions and implement results. o Goals are to determine : n n n The variable(s) and their magnitude that influences the response. The levels for these variables. How to manipulate these variables to control the response. o Experimental design should precede SPC Quality Improvement, 9 e Dale H. Besterfield 5 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Introduction (Continued) o Experimental design can be used to: n n n Improve a process by increasing performance Establish statistical control of a process Improve a product or develop a new product o Definitions for this chapter and next n n Factor– variable such as time, temp. , operator, etc Level—value assigned to a factor (50°F for temp) Treatment Condition (TC)—set of conditions (factor/levels) Replicate—repeat of TC with change in set up Quality Improvement, 9 e Dale H. Besterfield 6 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Definitions (Continued) n n Repetition—multiple results of a TC Random—TC are run in a random order Orthogonal Array—TC are put together so the design is balanced and factor/levels can be analyzed singly or in combination. Interaction—two or more factors that together produce results different than their separate effects Quality Improvement, 9 e Dale H. Besterfield 7 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Basic Statistics o See Chapter 5 o Variance is square of standard deviation & is also called the mean square MS, which is the sum or squares (SS) divided by the degrees of freedom (v) MS = SS/v SS = Ʃ (x – x)² v=n-1 Quality Improvement, 9 e Dale H. Besterfield 8 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Hypotheses o Hypotheses (Ho) testing is a statistical decision where inferences are made about the population from a sample. o Does or doesn’t the means of two samples from identical populations differ. Null hypothesis. Ho: μ 1 = μ 2 OR μ 1 - μ 2 = 0 Because, we are dealing with samples there is the risk of a Type I error (Null hypothesis is rejected when it is actually true) OR a Type II error (Null hypothesis is accepted when it is actually false). See Table 13 -1. Quality Improvement, 9 e Dale H. Besterfield 9 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Hypotheses (Continued) o Therefore, we use alternate hypothesis: n μ ǂ μ 2 Both tails of distribution n μ 1 > μ 2 Right tail of distribution n μ 1 < μ 2 Left tail of distribution o The consequences or risk (α) of making a decision are given in Table 13 -2. For example an α of 0. 01 is used where there might be a few lives lost Quality Improvement, 9 e Dale H. Besterfield 10 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

t Test It is used when the sample size is small. The distribution is unimodal and will almost be identical with the normal at n = 30 Quality Improvement, 9 e Dale H. Besterfield 11 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

t Test (Continued) Figure 13 -2 shows the critical region where t is the critical value, which is found in Appendix F for risk α and degrees of freedom v Quality Improvement, 9 e Dale H. Besterfield 12 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

t Test (Continued) o One sample t test uses the equation: The calculated t value is compared to the critical t value. If the calculated value is in the critical region, the alternate hypothesis can not be rejected. See example problem Quality Improvement, 9 e Dale H. Besterfield 13 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

F Test o For more than 2 factors or levels the F test using the F distribution and ANOVA are used. Same analysis as for the t test. If the calculated F is larger than the critical F value the test is significant Quality Improvement, 9 e Dale H. Besterfield 15 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

F Test (Continued) o Analysis of Variance (ANOVA) o Mathematical model of an experiment Quality Improvement, 9 e Dale H. Besterfield 16 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

ANOVA (Continued) o Normal and independent distributed with same variance in each factor/level o Initial calculation equations for a spreadsheet are: Quality Improvement, 9 e Dale H. Besterfield 17 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Once you calculate the SS values the remaining calculations easy. Critical F value is obtained from Appendix C and if it is smaller than the F value the test is significant Quality Improvement, 9 e Dale H. Besterfield 18 © 2013, 2008 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 • All Rights Reserved

One Factor at a Time Design o Is not balanced (only one 2 in each column) o Effects Quality Improvement, 9 e Dale H. Besterfield 19 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Orthogonal Design o Orthogonal means balanced. Average factor/level. o A 1 = Results of TC, s (1+3+5+7)/4 o A 2 = Results of TC, s (2+4+6+8)/4 o B 1 = Results of TC, s (1+2+5+6)/4 o Etc. Quality Improvement, 9 e Dale H. Besterfield 20 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Orthogonal Design (Continued) o Design is statistically independent o Effect of A = A 2 - A 1 o Effect of B = B 2 - B 1 o Etc. o It is much more efficient. o Compare results of Ex 13 -5 (One Factor at a Time) to Ex 13 -6 Quality Improvement, 9 e Dale H. Besterfield 21 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Point and Interval Estimate o True value of a factor is rarely known, so an interval or range about a value is given. Quality Improvement, 9 e Dale H. Besterfield 22 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

t Reference Distribution o t Reference Distribution uses the concept of interval estimate to determine which factor/levels are significant. Quality Improvement, 9 e Dale H. Besterfield 23 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Two Factors q A simple experimental design has two factors and can have many levels as shown below; however, two levels are common and sometimes three levels. Each factor/level can have replications. Quality Improvement, 9 e Dale H. Besterfield 25 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Two Factors (Continued) ANOVA is the decision method and once the SS are calculated, the process leads to a decision using the F test. Quality Improvement, 9 e Dale H. Besterfield 26 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Full Factorials A 3 factor/2 level, with a + for the high level and a – for the low level is shown below. Signs for the 3 factors is as shown. Quality Improvement, 9 e Dale H. Besterfield 27 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Full Factorials (Continued) o Signs for the 2 factor and 3 factor interactions are based on the signs of the 3 factors in each TC. o Two factor nteraction signs are (- x - = +) (- x + = -) (+ x - = -) (+ x + = +) o Three factor interaction signs are (- x – x - = -) (- x + x - = +) (+ x + = +) (+ x - x + = -) Quality Improvement, 9 e Dale H. Besterfield 28 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Full Factorials (Continued) o ANOVA is the decision method and once the SS are calculated, the process leads to a decision using the F test. Quality Improvement, 9 e Dale H. Besterfield 29 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Full Factorials (Continued) The number of TC is determined by Thus for a 2 level design 2² = 4; 2³ = 8; 4 -16; 5 -32; etc for a 3 level design 3² = 9; 3³ = 27; 4 -81; etc Quality Improvement, 9 e Dale H. Besterfield 30 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Fractional Factorials q. The number of TC’s can become quite large. q. Use Engineering judgment to eliminate some interactions and substitute a factor Quality Improvement, 9 e Dale H. Besterfield 31 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Examples o Evans Clay o John Deere o Nabisco o Wilkes-Barre Hospital o Eastman Kodak o Farmington High School o K 2 Corporation o Hercules Corporation Quality Improvement, 9 e Dale H. Besterfield 32 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Implementation o Set good factor/levels and response variable o Replicate and random o Block out known or unwanted sources of variation such as environment o Evaluate interactions and make adjustments o Transfer lessons learned to other experiments o Confirm results with another experiment Quality Improvement, 9 e Dale H. Besterfield 33 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved

Computer Program o Microsoft EXCEL will calculate t distribution, F distribution, confidence and SS. Quality Improvement, 9 e Dale H. Besterfield 34 Inc © 2013, 2008 by Pearson Higher Education, Upper Saddle River, New Jersey 07458 • All Rights Reserved