Question

Checkout times at a drug store are being monitored and the following data has been collected. Each sample contained 18 items.

Sample Mean Range
1 3.06 .42
2 3.15 .50
3 3.11 .41
4 3.13 .46
5 3.06 .46
6 3.09 .45

Calculate the lower and upper control limits for the mean. (Keep three decimal places)

Question 44 options:

Lower = 3.019

Upper = 3.181

Lower = 3.255

Upper = 3.000

Lower = 3.015

Upper = 3.186

Lower = 3.000

Upper = 3.255

Answer 1

Solution:

From the above table;

X-bar = 3.1

R-bar = 0.45

From the three-sigma control limits for X-bar and R-charts,

For n = 18 (Number of items in each sample = 18)

A2 = 0.19

D3 = 0.39

D4 = 1.61

The lower and upper control limits for the mean (X-bar chart) is calculated as;

Lower limit, LCLx = X-bar - (A2 x R-bar)

Lower limit, LCLx = 3.1 - (0.19 x 0.45)

Lower limit, LCLx = 3.015

Upper limit, UCLx = X-bar + (A2 x R-bar)

Upper limit, UCLx = 3.1 + (0.19 x 0.45)

Upper limit, UCLx = 3.186