Question

Luggage weighing scales are subjected to rigorous testing before they are shipped to airport check-in counters around the world. Results from weighing the last five luggage samples are shown in the table. Calculate control limits for a chart that will monitor performance to target.

	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5
1	73.5	70.8	72.2	73.6	71.0
2	71.3	71.0	73.1	72.7	72.2
3	70.0	72.6	71.9	72.4	73.3
4	71.1	70.6	70.3	74.2	73.6
5	70.8	70.7	70.7	73.5	71.1

The correct control limits are:

LCL ______

UCL ______

please show the work

Answer 1

STEP 1

The process consistency can be depicted from R chart.

Hence, measuring range values of each subgroup:

Sample 1 R = 73.5 - 70 = 3.5

Sample 2 R = 72.6 - 70.6 = 2

Sample 3 R = 73.1 - 70.3 = 2.8

Sample 4 R = 74.2 - 72.4 = 1.8

Sample 5 R = 73.6 - 71 = 2.6

mean value of R(R bar) = 3.5+ 2 + 2.8 + 1.8 + 2.6 /5 = 2.54

STEP 2

now, UCL R = D₄ * R bar

LCL R = D₃ * R bar

As subgroup size is 5, using control chart table we get for n=5 : D₄=2.114 and D₃ =0

STEP 3

Hence,

UCL = 2.114 * 2.54 = 5.37

LCL =0

the correct control limits are : (0.00 , 5.37)