MIE 364S: Methods of Quality Control and Improvement
Tutorial 0
1.
Cartons of grommets are rated at 40 pounds. Ten sample weights were obtained as
follows:
41.7
40.6
41.0
42.5
40.4
42.4
42.7
41.2
42.6
41.5
Assume the weights are normally distributed with mean
and variance
2
0.64
a)
Test the null hypothesis
41
at significance level
0.01
. Construct a
two-tailed critical region and calculate the p-value. What is your conclusion?
b)
Assuming the error of 1 pound is important to detect, find
(40)
and
(42)
c)
Find the minimum sample size n such that the error of 1 pound is detected by
the test in 1a) with probability
0.9
9.
2.
An experiment wishes to demonstrate that, at 100
。
C, the coefficient of static
friction of steel on steel when lubricated by a newly developed graphited oil is less
than 0.13. The measurement process is assumed to be normally distributed with
standard deviation
0.005
and the sample mean corresponding to a random
sample of size 40 is
0.128
X
a)
Formulate and test the null hypothesis at significance level
0.05
. Calculate
the p value and draw conclusions.
b)
Calculate the power of the test for
1
0.128
.
c)
Find the minimum sample size n such that the power of the test for
1
0.128
is
0.95
3.
Pipe stock is automatically fed to a cutter to produce cuts of nominal length 8.05
feet. To test the accuracy of the equipment, 12 cuts are randomly selected and
their lengths measured.
a)
Assuming the population of lengths is normally distributed, do the
measurements (in feet)
8.08
8.02
8.04
8.04
8.02
8.05
8.02
8.03
8.07
8.01
8.03
8.07
yield the conclusion, at the
0.05
level, that the nominal mean length should
be rejected?
b)
Estimate the p-value.
4.
The mean time to repair (MTTR) a unit is the average time it takes to repair a unit
that has been taken out of service. As an illustration, consider a robot paint-sprayer.
Such a unit can fail for any number of reasons; however, let us suppose that the

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