# Consider Exercise 10.2. (a) Give an estimate of the process variance as a function of x 1 , the…

Consider Exercise 10.2.

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Consider Exercise 10.2. (a) Give an estimate of the process variance as a function of x 1 , the…
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(a) Give an estimate of the process variance as a function
of x1, the implant dose.

(b) What assumptions were made in constructing this variance
function? Discuss the variance–mean trade off here. If we use ^ as
a criterion, give optimal values of implant dose and time.

Exercise 10.2

Consider Example 4.2 in Chapter 4. Suppose, in this process
for manufacture of integrated circuits, that the temperature is very difficult
to control. There is some concern over variability in wafer resistivity due to
uncontrolled variability in temperature. Consider the other factors as control
variables.

(a) From the analysis given in Chapter 4, can any of the
control variables be used to exert some influence over this variability?
Explain.

(b) It is of interest to maximize wafer resistivity and
still minimize variability produced by changes in temperature. Can this be
done? Explain.

Example 4.2

A 25-1 Design Five factors in a manufacturing
process for an integrated circuit were investigated in a 25-1 design
with the objective of learning how these factors affect the resistivity of the
wafer. The five factors were A = implant dose, B = temperature, C = time, D =
oxide thickness, and E = furnace position. Each factor was run at two levels.
The construction of the 25-1 design is shown in Table 4.5. Notice
that the design was constructed by writing down the basic design having 16 runs
(a 24 design in A, B, C, and D), selecting ABCDE as the generator, and then
setting the levels of the fifth factor E = ABCD. Figure 4.5 gives a pictorial
representation of the design.  