1. ISE 352: Design of Experiments
Dr. Laura Moody
Course Objectives:
Upon successful completion of this course, you should be able to do the following:
Plan an experiment.
Identify the appropriate experimental method.
Develop a detailed experimental design.
Conduct and analyze the results of an experiment.
Draw appropriate conclusions and specific recommendations.
ISE Ch. 1&2

2. Experimentation What is an experiment?
Give an example of an experiment you have conducted …
Experiment: a test or series of tests in which purposeful changes are made to the input variables of a product or system so that we may observe and identify the reasons for changes we may observe in the output variables.
ISE Ch. 1&2

3. Why experiment? Process improvement Engineering design
improve productivity & safety
reduce variability / improve quality
reduce development time
reduce overall costs
Engineering design
evaluation / comparison of design configurations
evaluation of alternatives
select design parameters for robust design / performance
explore product ideas
ISE Ch. 1&2

4. Basic Principles randomization replication blocking ISE 352 - Ch. 1&2
replication vs repeated measures- taking the same measurement repeatedly is not the same as replicating the trial
ISE Ch. 1&2

5. Guidelines … with an example
Example: can you improve the range of a remote car key?
Recognition and statement of the problem:
Selection of the response variable:
Choice of factors, levels, and range:
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6. Guidelines … with an example (cont.)
Choice of experimental design:
Performing the experiment:
Statistical analysis of the data:
Conclusions & recommendations:
ISE Ch. 1&2

7. Some basic statistical concepts
Describing sample data
Random samples
Sample mean, variance, standard deviation
Populations versus samples
Population mean, variance, standard deviation
Estimating parameters
Simple comparative experiments
The hypothesis testing framework
The two-sample t-test
Checking assumptions, validity
ISE Ch. 1&2

8. Homework
Problem 1.4, pg. 22
Read chapters 1 & 2 and review the remaining slides in this slideshow.
Be prepared to solve the following in class on Friday:
2.4, 2.15, 2.19, 2.25
Helpful hints:
An Excel data set is available through the textbook website (
ISE Ch. 1&2

9. An Example: Portland cement formulation See data, page 24
ch 2 examples.xls
ISE Ch. 1&2

10. Graphical view of the data
Dot diagram
fig. 2.1, pp. 24
What do you see?
Use minitab to find this …
Unmodified appears to be stronger than modified
- see this both in the distribution of dots and in the means …
ISE Ch. 1&2

11. If you have a large sample, a histogram may be useful
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12. Another graphical comparison
Box plots
Fig. 2.3, pp. 26
What do you see here?
Explain the plot … rule of thumb (lower quartile above median  difference)
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13. The hypothesis testing framework
Statistical hypothesis testing is a useful framework for many experimental situations
Origins of the methodology date from the early 1900s
For the Portland cement example, we will use the two-sample t-test
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14. The hypothesis testing framework
Sampling from a normal distribution
Statistical hypotheses:
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15. Estimation of parameters
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16. Portland cement example …
Summary statistics (see pg. 36)
Can get these from Minitab, as well …
Modified Mortar
Unmodified Mortar
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17. The two-sample t-test:
Use the sample mean to draw inferences about the population means …
Comparison is …
This suggests a statistic, =
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18. The two-sample t-test:
Note: to use the first ratio, must calculate the pooled degrees of freedom (see pg. 45)
ISE Ch. 1&2

19. The two-sample t-test:
Values of t0 that are near zero are consistent with the null hypothesis
Values of t0 that are very different from zero are consistent with the alternative hypothesis
t0 is a “distance” measure-how far apart the averages are expressed in standard deviation units
Note: this is an interpretation of t0 as a signal-to-noise ratio
ISE Ch. 1&2

20. For the Portland cement example
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21. The two-sample (pooled) t-test
So far, we haven’t really done any “statistics”
We need an objective basis for deciding how large the test statistic t0 really is
In 1908, W. S. Gosset derived the reference distribution for t0 … called the t distribution
Tables of the t distribution – see Appendix II, pg. 614
In Excel, use the function
________________________________________
OR …
In Minitab, …
ISE Ch. 1&2

22. The two-sample (pooled) t-test
The P-value is the area (probability) in the tails of the t-distribution beyond the probability beyond (it’s a two-sided test)
The P-value is a measure of how unusual the value of the test statistic is given that the null hypothesis is true
The P-value the risk of wrongly rejecting the null hypothesis of equal means (it measures rareness of the event)
The P-value in our problem is P = 0.042
(Note the values for tcrit used in the traditional approach)
ISE Ch. 1&2

23. Computer two-sample t-test results
t-Test: Two-Sample Assuming Equal Variances
Modified
Unmodified
Mean
16.764
17.042
Variance
Observations 10
Pooled Variance
0.0808
Hypothesized Mean Difference df 18
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
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24. Checking assumptions – the normal probability plot
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25. Normality testing in Minitab
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26. Importance of the t-Test
Provides an objective framework for simple comparative experiments
Could be used to test all relevant hypotheses in a two-level factorial design, because all of these hypotheses involve the mean response at one “side” of the cube versus the mean response at the opposite “side” of the cube
ISE Ch. 1&2

27. Confidence intervals (See pg. 44)
Hypothesis testing gives an objective statement concerning the difference in means, but it doesn’t specify “how different” they are
General form of a confidence interval
The 100(1- α)% confidence interval on the difference in two means:
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28. The Portland cement example
(see pg. 45)
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29. Other chapter topics Hypothesis testing when the variances are known
One sample inference
Hypothesis tests on variances
Paired experiments
ISE Ch. 1&2

30. Homework (due Monday, Aug. 27)
Finish and format the results of the problems you solved in class on Friday.
Read Chapter 3 and review the PowerPoint slides.
Be prepared to solve the following in class:
3.3
3.8, part a only (use Minitab or Excel)
Bring your solutions to class on Monday.
ISE Ch. 1&2