MIE364H1S
Methods of Quality Control and Improvement
Course Instructor: Prof. V. Makis
Tutorial #6
1.
A process that produces titanium forgings for automobile turbocharger wheels is
to be controlled through use of a fraction nonconforming chart. Initially, one
sample of size 150 is taken each day for 18 days and the process average has been
shown to be 0.0185.
a.
Construct the p chart with probability limits,
α
= 0.002.
b.
Find the
β
risk when the true value of p is 0.04.
c.
What sample size is required if we wish to detect a shift in the process
fraction non conforming to 0.03 with probability 0.5?
2.
A control chart for the number nonconforming is to be established, based on
samples of size 400. To start the control chart, 30 samples were selected and the
number nonconforming in each sample determined, yielding
.
1200
30
1
=
∑
=
i
i
D
a.
What are the parameters of the np chart?
b.
Suppose the process average fraction nonconforming shifted to 0.15. What
is the probability that the shift would be detected on the first subsequent
sample?
c.
Find the average run length to detect a shift to a fraction nonconforming of 0.15.
3.
The data below represents the number of nonconformities observed in an
inspection unit of printed circuit boards. Twentysix samples, each consisting of
one inspection unit, are used to obtain the data. Set up a control chart for
nonconformities using these data. Does the process appear to be in statistical
control?
Sample
Number
Number of
Nonconformities
Sample
Number
Number of
Nonconformities
1
21
14
19
2
24
15
10
3
16
16
17
4
12
17
13
5
15
18
22
6
5
19
18
7
28
20
39
8
20
21
30
9
31
22
24
10
25
23
16
11
20
24
19
12
24
25
17
13
16
26
15
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Past examination of the process that produces automobile quarterpanels has
demonstrated that scratches are responsible for the majority of defective panels.
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 Spring '10
 Makis
 Control Chart, Harshad number, UCL

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