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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:
DiameterTime Rod 1 Rod 2 Rod 3 Rod 49 A.M. 19.8 20.4 19.9 20.310 A.M. 20.1 20.2 19.9 19.811 A.M. 19.9 20.5 20.3 20.1Noon 19.7 19.8 20.3 20.21 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 FactorsSample Sizen Mean Factor(A2) Upper Range(D4) Lower Range (D5)2 1.880 3.628 03 1.023 2.574 04 0.729 2.282 05 0.577 2.114 06 0.483 2.004 07 0.419 1.924 0.0768 0.373 1.864 0.1369 0.337 1.816 0.18410 0.308 1.777 0.22312 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.
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