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Xbar and R charts, Is the process in control?

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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:

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.

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Solution Summary

Limits of xbar and Rcharts constructed. Also process control explained.

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See Also This Related BrainMass Solution

Question about Xbar and R Charts: Weight of boxes of cereal, control limits, trends, and process control.

As a quality analyst you are also responsible for controlling the weight of a box of cereal. The Operations Manager asks you to identify the ways in which statistical quality control methods can be applied to the weights of the boxes. Provide your recommendations to the Operations Manager in a two-page report. Using the data provided in the Doc Sharing area, create Xbar and R charts.

Your report should indicate the following along with valid justifications of your answers:

The control limits of the weights of the boxes.
Nonrandom patterns or trends, if any.
If the process is in control.
The appropriate action if the process is not in control.

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