Question

In order to estimate the capability of a process, measurements were made on six samples of size 4 as shown in the table below (in practice at least 25 such samples would be needed). Estimate the process capability, σ. If the target value is 50, cal- culate the positions of the action and warning lines for the Shewhart charts for the sample mean and the range.

sample	Values	Values	Values	Values
1	48.8	50.8	51.3	47.9
2	48.6	50.6	49.3	49.7
3	48.2	51.0	49.3	50.3
4	54.8	54.6	50.7	53.9
5	49.6	54.2	48.3	50.5
6	54.8	54.8	52.3	52.5

Answer 1

Average value from 6 samples = 51.12

Standard deviation of 6 samples = 2.326

Upper specification limit (USL) = 54.8 (maximum of all values)

Lower specification limit (LSL) = 47.9 (minimum of all values)

Process capability index = [USL - LSL]/ 6* Standard deviation = 0.49

Warning lines are maked at = 50 2 standard deviation

Upper warning line = 50 + 2*2.326 = 54.652

Lower warning line = 50 - 2*2.326 = 45.348

Action lines are marked at = 50 3xstandard deviation

Upper action line = 50 + 3*2.326 = 56.98

Lower action line = 50 - 3*2.326 = 43.022