Chapter 6. Design of Experiments

5.5 Assignment Problems ( Page 6-26, 6-27, 6-28 )


6-1. A factorial design was conducted to study the influence of temperature (x1), pressure (x2), and cycle time (x3) on the occurrence of splay in an injection-molding process. For each of the eight unique trials, 50 parts were made and the response observed was the number of incidences of the occurrence of splay on the part surface across all 50 parts. The design matrix and test responses are given in the table.
a. Draw the geometrical representation of this experiment and label each corner of the cube with the corresponding test conditions (e.g., +, -, +) as well as the test response.
b. Calculate the main effects of all three variables.
c. Calculate all the two- and three- factor interaction effects.
d. Write down the appropriate mathematical model, assuming that all estimated effects are to be included in the model.

6-2. A factorial experiment was conducted to determine the effects that tool surface coating (x1) and the application of cutting fluid (x2) might have on the surface finish of a turned part. The low level for each f the two variables represented the absence of the technology in question (i.e., no surface coating, no cutting fluid). The high level represented the technology at some commercially recommended level. The response is the part surface finish in microinches (Ra value).



a. Draw the geometrical representation of this experiment, labeling the corners with the corresponding test conditions (e.g., +,-).
b. Calculate all the variable effects.
c. Sketch a graphical representation of the two-factor interaction effect using a two-way diagram and explain the nature of the interaction effect in words.

6-3. A factorial design was constructed to test the effect of three different variables on the alertness of students in an early morning class. The variables tested, the design matrix, and the responses are shown in the tables.



a. Calculate all the variable effects.
b. Write down the appropriate mathematics model.