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# Control Charts

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A) A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each lot of tablets is measured in order to control the compression process. The process has been operating in control with mean at the target value = 11.5 kilograms (kg) and estimated standard deviation = 0.2 kg. The table below gives three sets of data, each representing x for 20 successive samples. One set remains in control at the target value. In a second set, the process mean shifts suddenly to a new value. In a third the process mean drifts gradually.
(1) What are the center line and control limits for an x chart for this process?
(2) Construct a separate x chart for each of the three data sets. Identify any points that are beyond the control limits.

Sample Data with N=20
Data Set A Data Set B Data Set C
1 11.602 11.627 11.495
2 11.547 11.613 11.475
3 11.312 11.493 11.465
4 11.449 11.602 11.497
5 11.401 11.360 11.573
6 11.608 11.374 11.563
7 11.471 11.592 11.321
8 11.453 11.458 11.533
9 11.446 11.552 11.486
10 11.522 11.463 11.502
11 11.664 11.383 11.534
12 11.823 11.715 11.624
13 11.629 11.485 11.629
14 11.602 11.509 11.575
15 11.756 11.429 11.730
16 11.707 11.477 11.680
17 11.612 11.570 11.729
18 11.628 11.623 11.704
19 11.603 11.472 12.052
20 11.816 11.531 11.905