Problem 5.6.1

Problem 5.6.2

Problem 5.6.3

Problem 5.6.4

1. A 2³ 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 make 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.

2. A 2² 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 of 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.

b. Calculate all the variable effects.

3. A 2³ factorial design was constructed to test the effect of three different variables on the alertness of students I an early morning class. The variables tested, the design matrix, and t responses are shown in the tables.

4. The following table are data in standard order from a 2³ factorial design. The three variables are cutting speed, depth of cut, and feed. The system response is the cutting force measured during the tests. You may notice that two individual runs were performed at each of the eight tests.

(1) Calculate the main effects and the effects of two-factor interactions

(2) estimate the standard error of an effect.

(3) The significant effects are depth of cut and feed.

(4) Derive an empirical model which describes the functional relationship between the cutting force and the three cutting parameters.