Solutions

1. a. Use the p chart. This is attribute data with the categories of satisfactory and defective bushings.

b. .

c. .

d.

Sample No.

Statistic (p)

Sample No.

Statistic (p)

1 16/125 = 12%

6 11.2%

2

3

4

5

10.4

12.8

8.8

10.4

7

8

9

10

16.0

20.0

24.0

36.0

e.

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26.03 UCL

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·

-- 16.16

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· ·

· · ·

·

6.29

LCL

0 5 10

f. No. Sample #10 falls above the UCL. g. He should look for an assignable cause for sample #10.

2. a. The revised centerline will be obtained by deleting sample #10 and

recalculating the value of on the basis of the remaining nine samples.

revised

b. Revised

Revised

Revised c. The revised control limits have lower values than the original control limits, and they are slightly closer to the centerline.

3. a. Use the x-bar chart; this is measurement data.

b. v. (k = the number of samples)

c. Because the value of the population standard deviation is unknown, use and the A2 control chart factor.

v.

v.

v. d. The sample mean. e.

·

UCL

·

· ·

· ·

--

· ·

· · ·

· ·

· · ·

LCL

0 5 10 15

f. No, sample #11 is out of control. g. He should look for an assignable cause for sample #11.

4. a. Because s is unknown, use and the factors, D3 and D4 from the Table of Control Chart Factors.

v.

v. b. The sample ranges. c. UCL

·

· ·

· ·

--

· · · · ·

· · ·

· ·

·

LCL

0 5 10 15

d. Yes. e. No action is needed.

5. a. v.

b. LCL = 5.03 - .48(.53) = 4.78 v. UCL = 5.03 + .48(.53) = 5.28 v. c. The new control limits are lower but are still the same distance from the centerline.