Question

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 range. (Keep three decimal places)

Answer 1

The first step is to calculate Rbar which is the average value of the range.

R bar = (0.42 + 0.50 + 0.41 + 0.46 + 0.46 + 0.45) / 6

= 0.45

For n = 17, i.e. sample size equal to 17,

D3 = 0.378

D4 = 1.622

For the R-chart:

UCL_R = D4 * Rbar

= 1.622 * 0.45

= 0.730

LCL_R = D3 * Rbar

= 0.378 * 0.45

= 0.170

Hence the lower control limit is 0.170 and the upper control limit is 0.730