A manufacturing company produces rods. 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 (D5)
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
Part 2:
A p-chart has been developed for a particular item. In the past, 3% of such items have been found to be defective. If a sample of 100 is taken, and 9 of these are found to be defective, should the process be considered out of control? Explain.