Question

Boxes of cereals are supposed to weigh exactly 14 oz. Inspectors want to develop process control charts. They take ten samples of six boxes per sample and weigh them. Based on the following computations of the sample means X-bar and the sample ranges,
compute the lower and upper control limits and determine whether the process is in control. Use TABLE 10.2 on page 204 of your textbook to find the parameters for control chart limits.

Sample	X-Bar	Range
1	13.8	1
2	14.4	0.3
3	14.5	0.5
4	14.1	0.7
5	14.2	0.2
6	14.3	0.4
7	13.9	0.5
8	14.0	0.8
9	13.8	0.3
10	14.0	0.3

A. What are the control limits for the X-bar chart?
a. 4.83; 1.0
b. 14.254; 13.946
c. 13.86; 0
d. 13.86; 12.97
e. 14.34; 13.86

B.What are the control limits for the R chart? a. 2.004; 0
b. .8885; .1115
c. 1.00; 1.00
d. 2.004; 1.002
e. 1.00; 0

C. The process is
a. in statistical control and should be continued.
b. not in statistical control because the R chart shows lack of statistical control.
c. not in statistical control and assignable causes should be investigated and eliminated. d. the process is in statistical control but not capable.

Answer 1

Sample	X-Bar	Range
1	13.8	1
2	14.4	0.3
3	14.5	0.5
4	14.1	0.7
5	14.2	0.2
6	14.3	0.4
7	13.9	0.5
8	14	0.8
9	13.8	0.3
10	14	0.3
Average =	14.1	0.5
A2 =	0.483
D3 =	0
D4 =	2.004

A.

Correct Answer:

E

working note:

For X-bar chart:

LCL = X bar - A2*R bar = 14.1 - .483*.5 = 13.86

UCL = X bar + A2*R bar = 14.1 + .483*.5 = 14.34

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B.

Correct Answer:

E

Working note:

For Range Chart:

LCL = D3*Rbar = 0*.5 = 0

UCL = D4*Rbar = 2.004*.5 = 1.00

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C

Correct Answer:

C

Xbar chart shows that the process is not in statistical control. values are going outside of the UCL ans well as LCL.