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Homework 8 (due April 18)
1. A machine is producing shafts with a nominal diameter 5.00 mm. The
actual shaft diameter is approximately normal with a standard deviation of
0.01 mm. A shaft is considered to be inspec if its diameter is between 4.97
and 5.03 mm. When the machine is adjusted perfectly, the mean diameter of
shafts it is producing is equal to the nominal diameter (so that the fraction
of outofspec shafts produced by the machine is negligible).
a) Now assume that the mean diameter shifts by 0.02 mm. Calculate the
proportion of outofspec shafts produced by the machine after the shift.
b) Suppose now that a statistical quality control procedure is used in
which a sample of size 5 is taken every 2 hours. Then, provided the resulting
sample mean does not fall in the interval [5
.
00

Δ
,
5
.
00+Δ], the machine is
stopped and adjusted. Shifts happen randomly, once in 50 hours on average.
The cost of stopping the machine is equal to 1000. Every outofspec shaft
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 Spring '08
 Perevalov

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