The following table contains the sampled measured (in centimeters) of a special rod used in a high-tech product. These samples were taken at one-hour intervals. The plant manager has some concerns about the capability of the machine that produces this rod.
Observation Observation
Sample Number 1 2 3 4 5 Sample Number 1 2 3 4 5
1 1.714 1.964 1.794 1.524 1.604 11 1.954 0.484 0.574 0.524 0.474
2 2.314 0.634 0.614 0.634 0.514 12 2.394 0.434 0.454 0.514 0.514
3 1.464 0.674 0.384 0.504 0.514 13 2.014 0.494 0.604 0.674 0.544
4 1.914 0.424 0.704 0.574 0.584 14 1.924 0.394 0.624 0.494 0.634
5 2.174 0.504 0.564 0.434 0.514 15 1.484 0.394 0.514 0.474 0.574
6 2.224 0.504 0.614 0.704 0.594 16 1.964 0.674 0.574 0.424 0.584
7 2.091 0.914 0.684 0.714 0.694 17 1.654 0.674 0.714 0.624 0.614
8 2.254 0.484 0.484 0.494 0.524 18 2.084 0.544 0.684 0.494 0.544
9 1.774 0.534 0.444 0.484 0.454 19 1.514 0.604 0.614 0.394 0.484
10 2.354 0.664 0.434 0.444 0.634 20 1.684 0.684 0.674 0.444 0.544
Develop and show the corresponding 3-sigma chart(s) for the length of the fuel injector. Based on your results, is the Plant Manager's concern reasonable?