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| Teaching Since: | May 2017 |
| Last Sign in: | 352 Weeks Ago, 4 Days Ago |
| Questions Answered: | 20103 |
| Tutorials Posted: | 20155 |
MBA, PHD
Phoniex
Jul-2007 - Jun-2012
Corportae Manager
ChevronTexaco Corporation
Feb-2009 - Nov-2016
Question description
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Problem 10-3
|
Checkout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed: |
|
Sample |
Mean |
Range |
Sample |
Mean |
Range |
|
1 |
3.06 |
.42 |
4 |
3.13 |
.46 |
|
2 |
3.15 |
.38 |
5 |
3.06 |
.46 |
|
3 |
3.11 |
.41 |
6 |
3.09 |
.45 |
| Â |
|
Factors for three-sigma control limits for and R charts |
| Â |
FACTORS FOR R CHARTS Â |
||
|
Number of Observations in Subgroup, |
Factor for |
Lower |
Upper |
|
2 Â |
1.88 |
 0 |
3.27 |
|
3 Â |
1.02 |
 0 |
2.57 |
|
4 Â |
0.73 |
 0 |
2.28 |
|
5 Â |
0.58 |
 0 |
2.11 |
|
6 Â |
0.48 |
 0 |
2.00 |
|
7 Â |
0.42 |
 0.08 |
1.92 |
|
8 Â |
0.37 |
 0.14 |
1.86 |
|
9 Â |
0.34 |
 0.18 |
1.82 |
|
10 Â |
0.31 |
 0.22 |
1.78 |
|
11 Â |
0.29 |
 0.26 |
1.74 |
|
12 Â |
0.27 |
 0.28 |
1.72 |
|
13 Â |
0.25 |
 0.31 |
1.69 |
|
14 Â |
0.24 |
 0.33 |
1.67 |
|
15 Â |
0.22 |
 0.35 |
1.65 |
|
16 Â |
0.21 |
 0.36 |
1.64 |
|
17 Â |
0.20 |
 0.38 |
1.62 |
|
18 Â |
0.19 |
 0.39 |
1.61 |
|
19 Â |
0.19 |
 0.40 |
1.60 |
|
20 Â |
0.18 |
 0.41 |
1.59 |
| Â |
|
a. |
Using the factors in the above table, determine upper and lower limits for mean and range charts.(Round your intermediate calculations and final answers to 4 decimal places.) |
| Â | Â |
|
 Upper limit for mean |
 |
|
 Lower limit for mean |
 |
|
 Upper limit for range |
 |
|
 Lower limit for range |
 |
| Â |
|
b. |
Is the process in control? |
||||
| Â | Â | ||||
| Â |
|
Problem 10-4
|
Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed. |
|
SAMPLE Â |
|||||
|
1 |
2 |
3 |
4 |
5 |
6 |
|
79.2 |
80.5 |
79.6 |
78.9 |
80.5 |
79.7 |
|
78.8 |
78.7 |
79.6 |
79.4 |
79.6 |
80.6 |
|
80.0 |
81.0 |
80.4 |
79.7 |
80.4 |
80.5 |
|
78.4 |
80.4 |
80.3 |
79.4 |
80.8 |
80.0 |
|
80.2 |
80.1 |
80.8 |
80.6 |
78.8 |
81.1 |
| Â |
|
Factors for three-sigma control limits for and R charts |
| Â | Â |
FACTORS FORÂ RÂ CHARTS Â |
|
|
Number of Observations in Subgroup, |
Factor for |
Lower |
Upper |
|
2 Â |
1.88 |
 0 |
3.27 |
|
3 Â |
1.02 |
 0 |
2.57 |
|
4 Â |
0.73 |
 0 |
2.28 |
|
5 Â |
0.58 |
 0 |
2.11 |
|
6 Â |
0.48 |
 0 |
2.00 |
|
7 Â |
0.42 |
 0.08 |
1.92 |
|
8 Â |
0.37 |
 0.14 |
1.86 |
|
9 Â |
0.34 |
 0.18 |
1.82 |
|
10 Â |
0.31 |
 0.22 |
1.78 |
|
11 Â |
0.29 |
 0.26 |
1.74 |
|
12 Â |
0.27 |
 0.28 |
1.72 |
|
13 Â |
0.25 |
 0.31 |
1.69 |
|
14 Â |
0.24 |
 0.33 |
1.67 |
|
15 Â |
0.22 |
 0.35 |
1.65 |
|
16 Â |
0.21 |
 0.36 |
1.64 |
|
17 Â |
0.20 |
 0.38 |
1.62 |
|
18 Â |
0.19 |
 0.39 |
1.61 |
|
19 Â |
0.19 |
 0.40 |
1.60 |
|
20 Â |
0.18 |
 0.41 |
1.59 |
| Â |
|
a. |
Using factors from above table, determine upper and lower control limits for mean and range charts.(Round your intermediate calculations and final answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.) |
| Â |
 Mean Chart |
 Range Chart |
|
 UCL |
 |  |
|
 LCL |
 |  |
| Â |
|
b. |
Decide if the process is in control. |
||||
| Â | Â | ||||
| Â |
|
Problem 10-6
|
A medical facility does MRIs for sports injuries. Occasionally a test yields inconclusive results and must be repeated. Using the following sample data and n = 192. |
Â
Â
| Â |
SAMPLE |
||||||||||||
|
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
|
 Number of retests |
1 |
1 |
2 |
0 |
2 |
1 |
1 |
0 |
2 |
9 |
4 |
2 |
1 |
| Â |
Â
|
a. |
Determine the upper and lower control limits for the fraction of retests using two-sigma limits. (Do not round intermediate calculations. Round your final answers to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.) |
Â
| Â | Â |
|
 UCL |
 |
|
 LCL |
 |
| Â |
Â
|
b. |
Is the process in control? |
||||
| Â | Â | ||||
| Â |
|
Problem 10-7
|
The postmaster of a small western town receives a certain number of complaints each day about mail delivery. |
| Â |
DAY Â |
|||||||||||||
| Â |
1 Â |
2 Â |
3 Â |
4 Â |
5 Â |
6 Â |
7 Â |
8 Â |
9 Â |
10 Â |
11 Â |
12 Â |
13 Â |
14 Â |
|
 Number of complaints |
4 Â |
12 Â |
15 Â |
8 Â |
9 Â |
6 Â |
5 Â |
13 Â |
14 Â |
7 Â |
6 Â |
4 Â |
2 Â |
10 Â |
| Â |
|
a. |
Determine two-sigma control limits using the above data. (Round your intermediate calculations to 4 decimal places and final answers to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required.) |
| Â | Â |
|
 UCL |
 |
|
 LCL |
 |
| Â |
|
b. |
Is the process in control? |
||||
| Â | Â | ||||
| Â |
|
Problem 10-8
|
Given the following data for the number of defects per spool of cable. |
| Â |
OBSERVATION Â |
|||||||||||||
| Â |
1 Â |
2 Â |
3 Â |
4 Â |
5 Â |
6 Â |
7 Â |
8 Â |
9 Â |
10 Â |
11 Â |
12 Â |
13 Â |
14 Â |
|
 Number of defects |
1 Â |
3 Â |
1 Â |
0 Â |
1 Â |
3 Â |
2 Â |
0 Â |
2 Â |
4 Â |
3 Â |
1 Â |
2 Â |
0 Â |
| Â |
|
a. |
Determine three-sigma control limits using the above data. (Do not round intermediate calculations. Round your final answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.) |
| Â | Â |
|
 UCL |
 |
|
 LCL |
 |
| Â |
|
b. |
Is the process in control? |
||||
| Â | Â | ||||
| Â |
|
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