Factors for Calculating Three-Sigma Limits for the X-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

Cooling motors are subjected to rigorous testing before they are shipped to air conditioning manufacturers around the world. Results from the last five samples are shown in the table. Create control charts that will fully monitor the process and indicate the result of X-bar and R chart analysis. (Algebraic solutions only, DO NOT INCLUDE GRAPH)

a. X-bar upper and lower control limits (15pts)

b. According to X-bar limits is the process in statistical control? (5pts)

c. R chart upper and lower control limits (15 pts)

d. According to R chart limits is the process in statistical control?(5pts)

Unit #	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5
1	74	71	72	74	71
2	71	71	73	73	72
3	70	73	72	72	73
4	71	71	70	74	74
5	72	70	71	74	71
6	75	72	73	73	74