Q3 X and s chart

A quality engineer collected process data for 10 subgroups with each subgroup consisting of four samples (n=4). The averages and standard deviations of samples in each subgroup are summarized in Table 3 below.

Table 3. Subgroup Data

Subgroup	1	2	3	4	5	6	7	8	9	10
Average X	13.01	12.99	13.01	12.99	12.98	12.93	12.93	13.00	13.01	13.01
Standard deviation s	0.03	0.02	0.04	0.03	0.02	0.04	0.02	0.02	0.04	0.03

(3-1) Calculate center line X of X chart.

	Answer
Center line of X chart

(3-2) Calculate average standard deviation s , which is also the center line of s chart.

	Answer
Average standard deviation s

(3-3) Calculate upper control limit (UCL) and lower control limit (LCL) of X chart.

	Answer
UCL of X chart
LCL of X chart

(3-4) Calculate upper control limit (UCL) and lower control limit (LCL) of s chart.

	Answer
UCL of s chart
LCL of s chart