Question

By utilising Annexure A, answer the following questions:

1. 15 samples of n = 8 have been taken from a cleaning operation. The average sample range for the 20 samples was 0.016 minutes, and the average mean was 3 minutes. Determine the three-sigma control limits for this process.
2. 15 samples of n = 10 observations have been taken from a milling process. The average sample range is 0.01 centimetres. Determine upper and lower control limits for sample ranges
3. Determine which of these three processes are capable
   

Process	Mean	Standard Deviation	Lower Specification	Upper Specification
1	6.0	0.14	5.5	6.7
2	7.5	0.10	7.0	8.0
3	4.6	0.12	4.3	4.9

Numbers of observations in subgroup n	Factor for X- bar Chart A2	Factors for R Charts Lower control limit D3	Factors for R Charts Upper control limit D4
2	1.88	0	3.27
3	1.02	0	2.57
4	0.73	0	2.28
5	0.58	0	2.11
6	0.48	0	2.00
7	0.42	0.08	1.92
8	0.37	0.14	1.86
9	0.34	0.18	1.82
10	0.31	0.22	1.78
11	0.29	0.26	1.74
12	0.27	0.28	1.72
13	0.25	0.31	1.69
14	0.24	0.33	1.67
15	0.22	0.35	1.65
16	0.21	0.36	1.64
17	0.20	0.38	1.62
18	0.19	0.39	1.61
19	0.19	0.40	1.60
20	0.18	0.41	1.59

Answer 1