Question

Question 4

By utilising Annexure A, answer the following questions:

(a) 15 samples of n = 8 have been taken from a cleaning operation. The average sample range for the 20 samples was 0.016 minute, and the average mean was 3 minutes. Determine the three-sigma control limits for this process.

(b) 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.

(c) 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

ANNEXURE A:

Table 1: Control Chart Parameters

Number 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