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Unformatted text preview: 8.32. . _—.— v  Consider the situation in Example 8.7. A new gauge is being evaluated for this process. The same opera tor measures the same 20 parts twice using the new _ gauge and obtains the data shown in Table 8E.6. (a) What can you say about the performance of the
new gauge relative to the old one? (b) If speciﬁcations are at 25 i 15, what is the P/T
ratio for the new gauge? Three parts are assembled in series so that their crit—
ical dimensions x1, x2, and x3 add. The dimensions of
each part are normally distributed with the following
parameters: 11, = 100, a, = 4, “2 = 75, 02 = 4, ‘13 =
75, and 0'3 = 2. What is the probability that an assem
bly chosen at random will have a combined dimen
sion in excess of 262? A product is packaged by ﬁlling a container com
pletely full. This container is shaped as shown in the
ﬁgure. The process that produces these containers is
examined, and the following information collected on the three critical dimensions:
Variable Mean Variance
L—Length 6.0 0.01
H—Height 3.0 0.01
w—Wldth 4.0 0.01 I"
i’.’ ’0: ‘.‘/1’ Assuming the variables to be independent, what are approximate values for the mean and variance of
container volume? Two mating parts have critical dimensions x1 and :2
as shown in the ﬁgure. Assume that x] and x2 are nor
mally distributed with means ,ttl and ya and standard
deviations o] = 0.400 and 0': = 0.300. If it is desired
that the probability of a smaller clearanee (Le, x] — x2)
than 0.09 should be 0.006. what distance between the average dimension of the two parts (i.e., u.  pa)
should be speciﬁed by the designer? T r
J“1 J"2
I .1 .v_ ...
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 Spring '12
 Richard

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