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 |
.37 |
5 |
3.06 |
.46 |
| 3 |
3.11 |
.41 |
6 |
3.09 |
.45 |
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| Factors for three-sigma control limits for X and R charts |
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FACTORS FOR R CHARTS
|
Number of Observations in Subgroup,
n |
Factor for
X Chart,
A2 |
Lower
Control Limit,
D3 |
Upper
Control Limit,
D4 |
| 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 |
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| 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.)
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