ENSE 627 Quality Management in Systems
Homework Assignment 6
Chapter 5. Design of Experiments
5.6 Assignment Problems ( Page 5-26 ~5-27 )
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.
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).
3. A 23 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.
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.
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.
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.
a. Calculate all the variable effects.
b. Write down the appropriate mathematic model.
(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.