Details of Assignment (W4): Complete problems 6.12, S6.11, S6.20, S6.23, S6.27, and S6.35 in the textbook.Submit one Excel file. Put each problem result on a separate sheet in your file. (also uploaded problems)
S6.11Twelve samples, each containing five parts, were taken
from a process that produces steel rods. The length of each rod in
the samples was determined. The results were tabulated and sample
means and ranges were computed. The results were:
|
SAMPLE |
SAMPLE MEAN (in.) |
RANGE (in.) |
|
1 |
10.002 |
0.011 |
|
2 |
10.002 |
0.014 |
|
3 |
9.991 |
0.007 |
|
4 |
10.006 |
0.022 |
|
5 |
9.997 |
0.013 |
|
6 |
9.999 |
0.012 |
|
7 |
10.001 |
0.008 |
|
8 |
10.005 |
0.013 |
|
9 |
9.995 |
0.004 |
|
10 |
10.001 |
0.011 |
|
11 |
10.001 |
0.014 |
|
12 |
10.006 |
0.009 |
a) Determine the upper and lower control limits and the overall
means for x-charts and R-charts.
b) Draw the charts and plot the values of the sample means and
ranges.
c) Do the data indicate a process that is in control?
d) Why or why not?
S6.12Eagletrons are all-electric automobiles produced by
Mogul Motors, Inc. One of the concerns of Mogul Motors is that the
Eagletrons be capable of achieving appropriate maximum speeds.
To monitor this, Mogul executives take samples of eight Eagletrons
at a time. For each sample, they determine the average maximum
speed and the range of the maximum speeds within the sample.
They repeat this with 35 samples to obtain 35 sample means and
35 ranges. They find that the average sample mean is 88.50 miles
per hour, and the average range is 3.25 miles per hour. Using these
results, the executives decide to establish an R chart. They would
like this chart to be established so that when it shows that the range
of a sample is not within the control limits, there is only approximately
a 0.0027 probability that this is due to natural variation.
What will be the upper control limit (UCL) and the lower control
limit (LCL) in this chart?
S6.20Jamison Kovach Supply Company manufactures paper
clips and other office products. Although inexpensive, paper clips
have provided the firm with a high margin of profitability. Sample
size is 200. Results are given for the last 10 samples:
|
SAMPLES |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
DEFECTIVES |
5 |
7 |
4 |
4 |
6 |
3 |
5 |
6 |
2 |
8 |
a) Establish upper and lower control limits for the control chart and
graph the data.
b) Is the process in control?
c) If the sample size were 100 instead, how would your limits and
conclusions change?
S6.23The school board is trying to evaluate a new math
program introduced to second-graders in five elementary schools
across the county this year. A sample of the student scores on
standardized math tests in each elementary school yielded the following
data:
|
SCHOOL |
NO. OF TEST ERRORS |
|
A |
52 |
|
B |
27 |
|
C |
35 |
|
D |
44 |
|
E |
55 |
Construct a c-chart for test errors, and set the control limits
to contain 99.73% of the random variation in test scores.
What does the chart tell you? Has the new math program been
effective?
S6.27Meena Chavan Corp.’s computer chip production process
yields DRAM chips with an average life of 1,800 hours and
s = 100 hours. The tolerance upper and lower specification limits
are 2,400 hours and 1,600 hours, respectively. Is this process capable
of producing DRAM chips to specification.
S6.35One of New England Air’s top competitive priorities
is on-time arrivals. Quality VP Clair Bond decided to personally
monitor New England Air’s performance. Each week for the past
30 weeks, Bond checked a random sample of 100 flight arrivals for
on-time performance. The table that follows contains the number of
flights that did not meet New England Air’s definition of “on time”:
|
SAMPLE (WEEK) |
LATE FLIGHTS |
SAMPLE (WEEK) |
LATE FLIGHTS |
|
11 |
2 |
16 |
2 |
|
221 |
4 |
17 |
3 |
|
13 |
10 |
18 |
7
|
|
44 |
4 |
19 |
3 |
|
15 |
1 |
20 |
2 |
|
6666666 |
1 |
21 |
3
|
|
1 7 |
13 |
22 |
7
|
|
8 |
9 |
23 |
4 |
|
1 9 |
11 |
24 |
3 |
|
110 |
0 |
25 |
2
|
|
111 |
3 |
26 |
2 |
|
112 |
4 |
27 |
0
|
|
113 |
2 |
28 |
1 |
|
1144 |
2 |
29 |
3 |
|
1155 |
8 |
30 |
4
|
(WEEK)
a) Using a 95% confidence level, plot the overall percentage of late
flights (p) and the upper and lower control limits on a control
chart.
b) Assume that the airline industry’s upper and lower control limits
for flights that are not on time are .1000 and .0400, respectively.
Draw them on your control chart.
c) Plot the percentage of late flights in each sample. Do all samples
fall within New England Air’s control limits? When one falls outside
the control limits, what should be done?
d) What can Clair Bond report about the quality of service?
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