The MotoTech Manufacturing Company: Design of Experiments

Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
Vol. 10, No. 2, January 2010, pp. 95–97
issn 1532-0545 10 1002 0097
informs
®
doi 10.1287/ited.1090.0041tn-b
© 2010 INFORMS
I N F O R M S
Transactions on Education
Teaching Note
The MotoTech Manufacturing Company:
Design of Experiments/ANOVA
Prakash Mirchandani
Katz Graduate School of Business, University of Pittsburgh, 358 Mervis Hall, Pittsburgh, Pennsylvania 15260,
[email protected]
Key words: design of experiments; ANOVA; process improvement; interaction effect; main effects
History: Received: June 2009; accepted: November 2009.
Distribution. To maintain the integrity and usefulness of cases published in ITE, distribution of these
teaching notes to any other party is prohibited. Please
refer interested instructors to ITE for access to the
teaching notes.
Part A. Do you agree with Nadine’s basic approach
outlined in Figure 1? Under what conditions will this
approach work? Under what conditions will it not
work and, therefore, have to be modified?
Nadine has adopted a systematic approach for
determining whether the two factors (time and temperature in the example in Figure 1) being studied
affect the product quality. The approach first identifies an approximate location for the best combination
of the two factors and then zooms in to locate this
combination more exactly. For this approach to work,
several conditions must hold. These conditions are
described below. If these conditions do not hold, then
we might end up searching in the “wrong” neighborhood, ending up with a process setting that is a local,
but not a global, optimum.
First, the initial range of factors chosen for firststage experimentation must be wide enough. If this
is not so, then the neighborhood identified in the
first stage might not be close to the neighborhood
that does contain the best combination. Therefore, we
might end up looking in the wrong neighborhood. No
amount of fine-tuned search will help if this case. For
example, if the best combination is 40 F and 150 minutes, the approach would not work because the initial
range chosen by Nadine does not include this combination. However, the question then becomes: How
does one determine the initial range within which to
experiment? One possible way for determining the
appropriate range to use in Phase 1 is to fall back
on the extant knowledge and experience that MM’s
employees have. Also, if the optimal combination
turns out to be near a boundary of the test region,
then the boundary may need to be expanded before
one zooming in begins.
Second, the relationship between the input factors
and the output factor must satisfy some properties.
Suppose the relationship between the response variable “quality” and the input factors “time” and “temperature” is given by quality = f (time, temperature).
A necessary condition for the approach outlined by
Nadine to work is that a local maximum of f is also
a global maximum. (Loosely speaking, we want f to
be unimodal, or tent-shaped, or if it is multimodal,
each maximum solution value is identical. If f has
multiple global optima, the approach will still work
by identifying one of the optimal solutions.) If this
condition is not satisfied, then the first stage of the
investigation might identify a time-and-temperature
combination close to a local optimum, and the second stage might just identify the local optimum. For
example, for a response function in Figure TN1(a), the
approach will work, but in the case of Figure TN1(b),
the best first stage combination might be at the one of
the two corner points, and the approach will identify
the corner point as the global optimum, whereas the
global optimum is in the middle of the factor ranges
used.
For the approach to work, we also have to ensure
that the other factors that could possibly affect quality
are also considered. For example, suppose barometric
95
Mirchandani: Teaching Note: The MotoTech Manufacturing Company: Design of Experiments/ANOVA
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
96
INFORMS Transactions on Education 10(2), pp. 95–97, © 2010 INFORMS
Figure TN1
Example of Situations Where the Approach May Work
(Figure TN1(a)) and Where It May Not (Figure TN1(b))
(a) Unimodal relationship
55
60
65
1.0
0.5
0.0
115
110
105
100
(b) General relationship
1.0
0.5
0.0
55
120
115
60
110
105
106
65
pressure and supplier category are two additional factors. MM may know through prior investigation that
these factors are not important, or these factors may
not be controllable by MM, in which case MM may
want to try to keep them constant as much as possible. If this is not so, MM may want to include these
two factors and conduct a higher (four, in this case,
because we have four factors) dimensional experimental design.
Another factor to keep in mind is the measurement
scale of the input factors. The approach in Figure 1
(of the case) assumes that both factors are continuous
variables, so we can continue to successively fine tune
the settings. When the factors are categorical, one can
still do stage 1 of the analysis depicted in Figure 1,
but the stage 2 analysis may not be feasible, or may
not be needed, because factor categories may not be
further divisible.
Part B. What does John Tagole mean when he says
that some other department can become the bottleneck department?
The diffusion department has been a bottleneck
until now, because the quality problems in the diffusion stage have been limiting the quality that MM
can offer its customers. As the quality of the diffusion stage improves, and the quality of the processes
that precede diffusion or those that follow is kept
unchanged, one of these other departments might
start limiting the quality that MM can deliver to its
customers. Once this happens, the bottleneck shifts
from the diffusion stage to another stage of the process. At that point, quality issues in these other
departments would need to be addressed if MM
wants to further improve the quality of its products.
Part C. For a tangible product or service product
that you are familiar with, briefly describe three CTQ
dimensions.
Some CTQ dimensions for a call center are
Time on hold;
Accuracy of information provided;
Repeat calls for the same problem.
Some CTQ dimensions for an LCD television are:
Time to failure;
Quality of the picture;
Number of dead pixels.
Part D. Do you agree with VR4U’s recommendation that supplier and temperature do not affect thickness? If yes, why? If no, why not? What would you
recommend?
VR4U has done a univariate ANOVA analysis, analyzing the supplier and temperature factors separately. From this analysis, we conclude that neither
factor is significant. (Please see MotoTech (DOE) Solution.xls spreadsheet.) However, what we need here is
two-way ANOVA. To do this, we have to reorganize
the data first.
The null and the alternate hypotheses for checking
the interaction effect are as follows:
H0 : Supplier and temperature do not interact to
affect the thickness.
HA : Supplier and temperature do interact to affect
the thickness.
Looking at the ANOVA results, we see that the
p-value of the interaction effect is less than 0.05
(Table TN1). Therefore, we can reject the null hypothesis at a significant value of = 001 and thus conclude that supplier and temperature do interact to
affect the diffusion thickness. Because there is an
interaction effect, there is no need to do the main
effect tests.
Looking at the plot of the means (Figure TN2), we
can understand why we see the main effect is not
significant and the interaction effect is. If we average across each supplier (ignoring the temperature),
then the mean for each supplier turns out to be about
3,010 Å.1 Similarly, if we average across each temperature level (ignoring the supplier), then the mean for
each temperature level turns again out to be 3,010 Å.
The graph shows that the thickness is affected by the
1
An angstrom (Å) is a unit for measuring length and equals 10−10
meters.
Mirchandani: Teaching Note: The MotoTech Manufacturing Company: Design of Experiments/ANOVA
97
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org.
INFORMS Transactions on Education 10(2), pp. 95–97, © 2010 INFORMS
Table TN1
ANOVA: Two-Factor with Replication
Summary
High
Low
Medium
Total
Pinnacle
Count
Sum
Average
Variance
15
4523534
3015689
4.787305
15
4507834
3005223
6.163007
15
4514254
3009503
1.624787
45
1354562
3010138
22.88096
Allied
Count
Sum
Average
Variance
15
4515179
301012
2.676932
15
4514744
3009829
3.333901
15
4515075
301005
4.292004
45
135450
3010
3.293833
Premier
Count
Sum
Average
Variance
15
4507187
3004792
3.120144
15
4522643
3015095
6.922027
15
4516602
3011068
3.4528
45
1354643
3010318
22.67741
45
1354522
3010049
21.86212
45
1354593
3010207
3.411622
Total
Count
Sum
Average
Variance
45
135459
30102
23.61436
ANOVA
Source of variation
Sample
Columns
Interaction
Within
Total
SS
df
MS
F
P -value
F crit
2.297154
0.717594
1,639.559
5092207
2
2
4
126
1148577
0358797
4098896
4041434
02842
008878
1014218
0753097
0915104
1.99E−38
3.0681
3.0681
2.443591
2,151.794
134
combination of the supplier and temperature levels.
Because, there is an interaction effect, there is no need
to do the tests for the main effect.
What should John Tagole do? If the temperature
can be held steady at high, he should select Premier,
or if the temperature can be held steady at low, he
should select Pinnacle. If the temperature can be held
steady only at medium, the choice of supplier does
not significantly affect the thickness. If the temperature cannot be held steady, it makes sense to buy from
Figure TN2
Plot of Means
3,020
3,015
3,010
3,005
Low
3,000
Medium
High
2,995
Pinnacle
Allied
Premier
Allied, as the output measure when Allied is used
does not vary with temperature.
Depending on the sophistication level of the students, instructors may also want to discuss the concept
of robustness. A robustness perspective will argue for
selecting Allied because the output when Allied is the
supplier is insensitive to temperature. Even if temperature can be held relatively steady at the high or
low levels, it might exhibit some variability and thus
result in poor quality for the Premier and Pinnacle
cases respectively. Note from Table TN1 that at low
temperature, Pinnacle’s mean is closer to the target
value than Allied’s is and at high temperature Premier’s mean is closer to the target value that Allied’s.
For all three temperature levels, though, the process
mean for Allied is higher than the target value. If
Allied is chosen, MotoTech and Allied should work
together to bring the process mean closer to the target value. Generally, it is easier to change the process mean (which might simply require the operator to
be better trained) than to reduce the process variance
(which might require investments in new technology).
Supplementary Material
Files that accompany this paper can be found and
downloaded from http://ite.pubs.informs.org.