Solutions Operations management

Precision Manufacturing has a government contract to produce stainless steel rods for use in militar

Question: Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each hour, random samples of size n = 4 rods are measured to check process control. Five hours of observations yielded the following:

	Diameter
Time	Rod 1	Rod 2	Rod 3	Rod 4
9 A.M.	19.8	20.4	19.9	20.3
10 A.M.	20.1	20.2	19.9	19.8
11 A.M.	19.9	20.5	20.3	20.1
Noon	19.7	19.8	20.3	20.2
1 P.M.	19.7	20.1	19.9	19.9

Using these data and the table below, construct limits for xbar- and R-charts. Is the process in control?

Control Chart Limits Factors
Sample Size n	Mean Factor A₂	Upper Range D₄	Lower Range D₃
2	1.880	3.628	0
3	1.023	2.574	0
4	0.729	2.282	0
5	0.577	2.114	0
6	0.483	2.004	0
7	0.419	1.924	0.076
8	0.373	1.864	0.136
9	0.337	1.816	0.184
10	0.308	1.777	0.223
12	0.266	1.716	0.284