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Problem 103
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 

Factors for threesigma control limits for and R charts 
FACTORS FOR R CHARTS 

Number
of Observations in Subgroup, 
Factor
for 
Lower 
Upper 
2 
1.88 
0 
3.27 
3 
1.02 
0 
2.57 
4 
0.73 
0 
2.28 
5 
0.58 
0 
2.11 
6 
0.48 
0 
2.00 
7 
0.42 
0.08 
1.92 
8 
0.37 
0.14 
1.86 
9 
0.34 
0.18 
1.82 
10 
0.31 
0.22 
1.78 
11 
0.29 
0.26 
1.74 
12 
0.27 
0.28 
1.72 
13 
0.25 
0.31 
1.69 
14 
0.24 
0.33 
1.67 
15 
0.22 
0.35 
1.65 
16 
0.21 
0.36 
1.64 
17 
0.20 
0.38 
1.62 
18 
0.19 
0.39 
1.61 
19 
0.19 
0.40 
1.60 
20 
0.18 
0.41 
1.59 

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.) 
Upper limit for mean 

Lower limit for mean 

Upper limit for range 

Lower limit for range 


b. 
Is the process in control? 


Problem 104
Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed. 
SAMPLE 

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 

Factors for threesigma control limits for and R charts 
FACTORS FOR R CHARTS 

Number
of Observations in Subgroup, 
Factor
for 
Lower 
Upper 
2 
1.88 
0 
3.27 
3 
1.02 
0 
2.57 
4 
0.73 
0 
2.28 
5 
0.58 
0 
2.11 
6 
0.48 
0 
2.00 
7 
0.42 
0.08 
1.92 
8 
0.37 
0.14 
1.86 
9 
0.34 
0.18 
1.82 
10 
0.31 
0.22 
1.78 
11 
0.29 
0.26 
1.74 
12 
0.27 
0.28 
1.72 
13 
0.25 
0.31 
1.69 
14 
0.24 
0.33 
1.67 
15 
0.22 
0.35 
1.65 
16 
0.21 
0.36 
1.64 
17 
0.20 
0.38 
1.62 
18 
0.19 
0.39 
1.61 
19 
0.19 
0.40 
1.60 
20 
0.18 
0.41 
1.59 

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.) 
Mean Chart 
Range Chart 

UCL 

LCL 


b. 
Decide if the process is in control. 


Problem 106
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. 
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 

a. 
Determine the upper and lower control limits for the fraction of retests using twosigma 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.) 
UCL 

LCL 


b. 
Is the process in control? 


Problem 107
The postmaster of a small western town receives a certain number of complaints each day about mail delivery. 
DAY 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

Number of complaints 
4 
12 
15 
8 
9 
6 
5 
13 
14 
7 
6 
4 
2 
10 

a. 
Determine twosigma 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.) 
UCL 

LCL 


b. 
Is the process in control? 


Problem 108
Given the following data for the number of defects per spool of cable. 
OBSERVATION 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

Number of defects 
1 
3 
1 
0 
1 
3 
2 
0 
2 
4 
3 
1 
2 
0 

a. 
Determine threesigma 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.) 
UCL 

LCL 


b. 
Is the process in control? 


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