Experimental Design Course Outline

8/12/2019 Experimental Design Course Outline

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Lesson Outline: Design and Analysis of Experiments and Observational Studies (c21) Part 2

Introduction to Chapter 4, Two Level Factorial Experiments, Testing 123 by Ledolter and Swersey:

Experimental design methods have roots in agriculture, and we use an example from that held to introduce the material we will cover. Suppose we are experimenting with ways to improve the yield of corn, and we identify three factors that seem importanttype of fertilizer, variety of seed, and type of pesticide. We decide to test two fertilizer formulations, two kinds of seed, and two different pesticides. As we discussed in Chapter 1, the traditional method for testing multiple factors is to test one factor at a time. But Fisher (1935) showed that a factorial design that tests all factors simultaneously is a much better approach. Using Fishers method, we test the 2 X 2 X 2 = 8 possible combinations of fertilizers, seeds, and pesticides. We divide our experimental field into 32 equal sized plots and randomly assign each of the eight combinations to four plots. For each of the 32 plots* we measure the number of bushels of corn produced. This factorial arrangement would allow us to compare the two fertilizers, the two kinds of seeds, and the two pesticides. It would also allow us to un cover any interactions between factors. For example, it may turn out that seed variety I is better than variety 2 when fertilizer 1 is used for both, but that the opposite is true when fertilizer 2 is used with both seeds.

Consider another

example.

An

advertising

agency

is

designing

an

online ad. It identifies three factors to test, with the response being the fraction of ad viewers who sign up for the advertised service. One factor is the ad copya traditional version or a more modern one. The second factor is the fonta traditional font or a fancier one, while the third factor is the background colorwhite or blue. In a factorial design, one of the eight possible ads would randomly be sent to each viewer. The question is what is important here? Is it the copy, the font, or the background color that matters? Do the factors interact in the sense that the fancier font works better with the blue background? These are the kinds of issues we will address in this chapter.


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Direct_Mail.jmp


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Add main effects (factors) to Construct Model Effects

Select both Envelope and Miles in the Select Columns > then select Cross to create the interaction effect (seen as Envelope*Miles)

Model Results

Indicates the overall model is significant

Effect Tests

Indicates the interaction is not significant


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To see the interaction plot:

Factor Profiling > Interaction Plots

This plot can be rescaled to more easily interpret the results


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Since interaction is not significant, return to model dialog, remove interaction term and re run analysis


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To Examine Main Effect Plots

Select Effect Details > Factor (choose one) Hot Spot > LSMeans Plot

The LSMeans Plot is the Main Effect Plot: this shows the average effect of the levels a main effect factor.

You can examine the main effect plots for each factor to interpret the best levels


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Analyzing the Results of a 2k Experiment

Cracked Pots Experiment

Example: Reducing the Number of Cracked Pots, Section 4.2, Chapter 4: Two Level Factorial Experiments, Testing 123 , Ledolter and Swersey, Stanford Business Books.

The following example illustrates some basic, important concepts. A company manufac tures clay pots that are used to hold plants. For one of their newest products, the company has been experiencing an unacceptably high percentage of pots that crack during the man ufacturing process. Company production engineers have identified three key factors they believe will affect cracking, and they decide to run an experiment to learn about the most important factor(s). The factors studied are the peak temperature in the kiln, the rate at which pots are cooled after being heated to the peak temperature, and a coefficient that describes the expansion of the clay pot. A higher peak temperature can be expected to reduce the percentage of cracks, but the higher temperature also increases operating costs. Cooling the pots at a faster rate would mean an increase in the number of pots produced per hour, but it could also increase the percentage of cracked pots. The coefficient of expansion depends on the composition of the clay. A supplier has offered the company a new clay mix that it asserts has a lower coefficient of expansion. The mix is being offered at the same price as the raw material that is currently used. A lower coefficient of expansion should decrease the incidence of cracks.

LEVEL

Factors +

Rate of cooling Temperature Coefficient of expansion

Slow 2000F Low

Fast 2060F High

Results entered in a JMP table (Cracked Pots Tbl 4.3 w Results)

(single replicate of experiment)


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Run Screening

Screening Hot Spot > Run Script

Make Model

> Select Run Model


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Examine and Interpret Results

The Effect Tests tell us there is a significant interaction. Since there are only 2 factors in the model and there is a significant interaction, we use the interaction to interpret the best settings for this experiment.


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Select Factor Profiling > Interaction Plot

The prediction model will be:

Estimates > Show Prediction Expression

(of course, the prediction formula can also be saved to the table| Save Columns > Prediction Formula and/or Predicted Values)


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Also useful to use the Profiler to explore the relationships

Factor Profiling > Profiler


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Creating an experiment, entering data, and analyzing the results:

Problem 3-2, DOE Simplif ied: Practical Tools for Effective Experimentation by

Mark J. Anderson and Patrick J. Whitcomb

Modern cars are built with such precision that they become hermetically sealed when locked. As a result, the interior becomes unbearably hot in cars parked outdoors on warm, sunny days. A variety of window covers can be purchased to alleviate the heat. The materials vary, but generally the covers present either a white or shiny, metallic surface that reflects solar radiation. In some cases, they can be flipped to one side or the other. The white variety of cover usually displays some sort of printed pattern, such as a smiling sun or the logo of a local sports team. These patterns look good, but they may detract from the heat shielding effect. A two level factorial design was conducted to quantify the effects of

several potential variables: cover (shiny versus white), direction of the parked car (east versus west), and location (close by the office in an open lot versus far away from the office under a shade tree).

The resulting eight run, two level DOE was performed during a period of stable weather in Minneapolis during early September. However, just in case variations did occur, the experimenter recorded temperature, cloudiness, wind speed, and other ambient conditions. Outside temperatures ranged from 66 to 76 degrees Fahrenheit under generally clear skies. Randomization of the run order provided insurance against the minor variations in weather. The response shown in Table 314 is the difference in temperature from inside to outside, as measured by a digital thermometer.

Even in this relatively mild late summer season, the inside temperatures of the automobile often exceeded 100 degrees Fahrenheit. It's not hard to imagine how hot it could get under extreme midsummer weather

Analyze this data to see what, if any, factors prove to be significant. Make a recommendation on how to shade the car and how and where to park it.


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pg. 14

Table 3-14. Results from car-shade experiment

Standard A: Cover B: Orientation C: Location Temp Increase (Deg F)

1 White East Close/Open 42.12 Shiny East Close/Open 20.83 White West Close/Open 5434 Shiny West Close/Open 23.25 White East Far/Shaded 17.46 Shiny East Far/Shaded 10.47 White West Far/Shaded 11.78 Shiny West Far/Shaded 16.0

Identify Design Response and Factors

DOE > Full Factorial Design

Generate design by identifying characteristics of response and factors (number, type, levels)


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pg. 15

Create table by identifying run order and number of replicates.

Make Table

Enter response values in table

Select screening designs on top left dialog | Run Script


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pg. 16

Evaluate screening results. This output indicates the factors Location and Cover are significant as well as the Location * Cover interaction. This can be seen in the effects as well as the half normal plot.

If satisfied with this assessment, select Make Model

Verify the model to run, then select Run


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pg. 17

Model Results of the Selected Model

Check residuals for assumptions Inspect the Summary of Fit and ANOVA table results. Inspect the parameter for final model

Inspect the half normal plot


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pg. 18

Interpret application results using the interaction plot


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pg. 19

Additional Problem Sets

Cracked Pots with Replication

Run a full

factorial

experiment

with

the

replicated

data

(all

main

effects,

all

2

way

interactions

and

one

3way interaction) using Fit Model

Machine Tool Life [61] (Montgomery, Design and Analysis of Experiments, 5e, Wiley )

An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results follow:

Treatment Replicate

A B C Combination 1 II III (1) 22 31 25

+ a 32 43 29 + b 35 34 50

+ + ab 55 47 46 + c 44 45 38

+ + ac 40 37 36 + + bc 60 50 54

+ + + abc 39 41 47

1. Estimate the factor effects. 2. Write down the regression model for predicting tool life based on the results of this experiment. 3. Based on an analysis of main effect and interaction plots, what levels of A, B and C would you

recommend?

Experimental Design Course Outline

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