Page 26 - Applied Statistics And Probability For Engineers

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12 CHAPTER 1 THE ROLE OF STATISTICS IN ENGINEERING

where the ’s are unknown parameters. Now just as in Ohm’s law, this model will not exactly
describe the phenomenon, so we should account for the other sources of variability that may
affect the molecular weight by adding another term to the model; therefore
M V C T (1-6)
1
n
2
3
0
is the model that we will use to relate molecular weight to the other three variables. This type of
model is called an empirical model; that is, it uses our engineering and scientific knowledge of
the phenomenon, but it is not directly developed from our theoretical or first-principles under-
standing of the underlying mechanism.
To illustrate these ideas with a specific example, consider the data in Table 1-2. This table
contains data on three variables that were collected in an observational study in a semicon-
ductor manufacturing plant. In this plant, the finished semiconductor is wire bonded to a
frame. The variables reported are pull strength (a measure of the amount of force required to
break the bond), the wire length, and the height of the die. We would like to find a model
relating pull strength to wire length and die height. Unfortunately, there is no physical mech-
anism that we can easily apply here, so it doesn’t seem likely that a mechanistic modeling
approach will be successful.

Table 1-2 Wire Bond Pull Strength Data
Observation Pull Strength Wire Length Die Height
Number y x 1 x 2
1 9.95 2 50
2 24.45 8 110
3 31.75 11 120
4 35.00 10 550
5 25.02 8 295
6 16.86 4 200
7 14.38 2 375
8 9.60 2 52
9 24.35 9 100
10 27.50 8 300
11 17.08 4 412
12 37.00 11 400
13 41.95 12 500
14 11.66 2 360
15 21.65 4 205
16 17.89 4 400
17 69.00 20 600
18 10.30 1 585
19 34.93 10 540
20 46.59 15 250
21 44.88 15 290
22 54.12 16 510
23 56.63 17 590
24 22.13 6 100
25 21.15 5 400