# ATM transaction times for a specific bank branch are being monitored and the following data has been collected. Each sample contained 17 items. Sample Mean Range 1 4.06 .42 2 4.15 .50 3 4.11 .41 4 4.13 .46 5 4.06 .46 6 4.20 .45 Calculate the lower and upper control limits for the mean

ATM transaction times for a specific bank branch are being monitored and the following data has been collected. Each sample contained 17 items.

Sample Mean Range
1 4.06 .42
2 4.15 .50
3 4.11 .41
4 4.13 .46
5 4.06 .46
6 4.20 .45
Calculate the lower and upper control limits for the mean

## Solution

Using the table:

Tabular values for X-bar and range charts
Subgroup Size A2 d2 D3 D4
2 1.88 1.128 —– 3.268
3 1.023 1.693 —– 2.574
4 0.729 2.059 —– 2.282
5 0.577 2.326 —– 2.114
6 0.483 2.534 —– 2.004
7 0.419 2.704 0.076 1.924
8 0.373 2.847 0.136 1.864
9 0.337 2.97 0.184 1.816
10 0.308 3.078 0.223 1.777
11 0.285 3.173 0.256 1.744
12 0.266 3.258 0.283 1.717
13 0.249 3.336 0.307 1.693
14 0.235 3.407 0.328 1.672
15 0.223 3.472 0.347 1.653
16 0.212 3.532 0.363 1.637
17 0.203 3.588 0.378 1.622
18 0.194 3.64 0.391 1.608
Sample Mean Range n= 17
1 4.06 0.42 UCL (R) = R-bar x D4 0.7299
2 4.15 0.5 LCL(R) = R-bar x D3 0.1701
3 4.11 0.41 UCL (X-bar) = X-bar-bar + (A2 x R-bar) 4.209683
4 4.13 0.46 LCL(X-bar) = X-bar-bar – (A2 x R-bar) 4.026983
5 4.06 0.46
6 4.2 0.45
4.118333 0.45
X bar bar R bar

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