Factors for Calculating Three-Sigma Limits for the Chart and R-Chart

Size of Sample (n)	Factor for UCL and LCL for x-bar-Charts A2	Factor for LCL for R-Charts D3	Factor for UCL for R-Charts D4
2	1.880	0	3.267
3	1.023	0	2.575
4	0.729	0	2.282
5	0.577	0	2.115
6	0.483	0	2.004
7	0.419	0.076	1.924
8	0.373	0.136	1.864
9	0.337	0.184	1.816
10	0.308	0.223	1.777

Construct a 3-sigma x-bar chart and R-chart for the length in centimeters of a part from the following table. (Must calculate UCL and LCL, drawing the chart is optional) What's your conclusion, is the process under control?

(Ten samples in total, and each sample has 4 observations)

Sample #	Observation 1	Observation 2	Observation 3	Observation 4
1	0.486	0.499	0.493	0.511
2	0.499	0.506	0.516	0.494
3	0.496	0.5	0.515	0.488
4	0.495	0.506	0.483	0.487
5	0.472	0.502	0.526	0.469
6	0.473	0.495	0.507	0.493
7	0.495	0.512	0.49	0.471
8	0.525	0.501	0.498	0.474
9	0.497	0.501	0.517	0.506
10	0.495	0.505	0.516	0.511