IE341 Problems

1. Nuisance effects can be known or unknown. If they are known, what are the ways you can deal with them?

What happens if they are unknown?

2. If you have an uncontrollable nuisance variable that you suspect affects the response variable, what kind of analysis should you do?

What happens if you don’t do this type of analysis?

3. We are testing 3 different types of glue for tensile strength when joining parts together. But the tensile strength is also affected by the thickness of the glue applied. Our data are:

(a) What kind of analysis should you do? (b) Explain what role each of the following plays

in the design: - glue type - tensile strength - glue thickness

Glue Type 1 Glue Type 2 Glue Type 3Strengt

hThickne

ssStreng

thThickne

ssStreng

thThickne

ss46.5 13 48.7 12 46.3 1545.9 14 49.0 10 47.1 1449.8 12 50.1 11 48.9 1146.1 12 48.5 12 48.2 1144.3 14 45.2 14 50.3 10

4. The surface finish on parts made by 3 machines is being studied. Each machine has three operators, and each operator tests two specimens. Because the machines are in different locations, different operators are used for each machine. The data are:

What kind of design is this? What makes it this kind of design?

Operator

Machine 1 Machine 2 Machine 31 2 3 1 2 3 1 2 3

Rep 1 79 94 46 92 85 76 88 53 46Rep 2 62 74 57 99 79 68 75 56 57

5. An experiment is performed to test the effect of temperature (2 levels) and heating time (3 levels) on the strength of steel. During the experiment, the oven is heated to one of the two temperatures and 3 specimens are placed in the oven. After 10 minutes, one specimen is removed. After 20 minutes, a second specimen is removed. After 30 minutes, the third specimen is removed. Then the temperature is changed to the other level and the process is repeated. Three shifts were used to collect the data, shown in the next slide.

(a) What kind of experiment is this? Why? (b) What role does each of the following

variables play in this design: shift temperature time (c) Which variables can you test for significance?

5 (continued)

Set up the ANOVA table for this kind of design. (no computations)

1500˚F 1600˚FShift 1 10 min 63 89

20 min 54 9130 min 61 62

Shift 2 10 min 50 8020 min 52 7230 min 59 69

Shift 3 10 min 48 7320 min 74 8130 min 71 69

6. Four different feed rates were studied in a test of a machine to produce parts for aircraft. From prior experience, the engineer has learned that changing the feed rate will not change the average dimension of the parts, but it might change the variability. He makes 4 production runs at each of 4 feed rates, measures the standard deviation, and these are his data.

What must he do to analyze these data? Why?

Production RunFeed

rateRun 1 Run 2 Run 3 Run

410 0.09 0.10 0.13 0.08

12 0.06 0.09 0.12 0.07

14 0.11 0.08 0.08 0.05

16 0.19 0.13 0.15 0.20

7. Four different designs are being studied for a computer circuit to see which has the least noise. There are 4 replicates. The data are

What type of analysis would you suggest? Why?

Do the first step of the analysis.

Design Noise observed

1 39 27 29 8

2 80 61 73 80

3 47 39 25 50

4 95 47 80 107

8. An engineer trying to optimize his process has run a first-order model in two variables with the following results.

Source SS df MS p Regression 5.00 2 2.50 Residual 21.20 6 3.53 Interaction 5.24 1 5.24 0.1101 Pure Quad 10.76 1 10.76 0.0426 Error 5.00 4 1.25 Total 26.20 8

(a) What would you recommend that he do next? (b) What kind of design would you suggest?

9. Show a central composite design for two variables.

Explain under what circumstances it is useful.

10.If the canonical form of the fitted RSM model is , what do you know about the stationary point?

What do you know about the sensitivity of the response to the two variables?

22

21 307.29762.035.80ˆ wwY

11. What makes mixture experiments different from other RSM experiments?

12.Describe the kind of design that is ordinarily used for mixture experiments.

What are its disadvantages and how do you overcome them?

13. What are two ways of determining whether the response at the stationary point is a maximum, a minimum, or a saddle point?

14. A mixture experiment has resulted in the following polynomial that is a good fit to the data.

If you are looking for a maximum response, what would you choose? Why?

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15. A textile mill has a problem. The strength of the cloth produced has too much variability. They wonder if it’s due mostly to the looms or to the operators, so they decide to study it. From the large number of looms they have, 3 looms are chosen randomly. Also 3 operators are chosen at random from all the operators in the plant. 3 replicates are run for each combination of loom and operator. The ANOVA table is

Source SS df MS p Looms 94 2 47 0.089 Operators 220 2 110 0.007 AB 80 4 20 0.354 Error 306 18 17 Total 700 26

15. (continued) (a) What type of ANOVA is this?

(b) Given the E(MS) table below, what proportion of variance is due to looms, to operators, to interaction, and to error?

22

222

222

2

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nMSE

JnnMSE

KnnMSE

MSE

AB

B

A

E

16. Four factors are to be used in a manufacturing process for integrated circuits to improve yield.

A is aperture setting (small, large), B is exposure time (20 sec, 30 sec), C is development time (30 sec, 45 sec), D is mask dimension (small, large). You are the statistical consultant for the firm

and you are asked to design the experiment. You’d better do it or the boss will be angry and you know what that means.

What kind of design did you create?