Table 1:

Factors for Calculating Three-Sigma Limits for thex-bar 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

Source: 1950ASTM Manual on Quality Control of Materials, copyright American Society for Testing Materials. Reprinted with permission.

Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Calculate control limits for a chart that will monitor performance to target. The correct control limits as (LCL,UCL) are:

Unit #	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5
1	73.5	70.8	72.2	73.6	71.0
2	71.3	71.0	73.1	72.7	72.2
3	70.0	72.6	71.9	72.4	73.3
4	71.1	70.6	70.3	74.2	73.6
5	70.8	70.7	70.7	73.5	71.1

ANSWERS:

a. (69.71,74.14).

b. (69.80,74.05).

c. (68.94,74.89).

d. (70.46, 73.39).