Pareto diagrams, control charts, x charts, R charts, s charts, p charts, and c charts

13-36. The number of blemishes in rolls of Scotch brand tape coming out of a production process at a plant of the 3M Company in Minnesota is as follows: 17, 12, 13, 18, 12, 13, 14, 11, 18, 29, 13, 13, 15, 16. Is there evidence that the production process is out of control?

13-37. The number of defective items out of random samples of 100 windshield wipers selected at the end of each production shift at a factory is as follows: 4, 4, 5, 4, 4, 6, 6, 3, 3, 3, 3, 2, 2, 4, 5, 3, 4, 6, 4, 12, 2, 2, 0, 1, 1, 1, 2, 3, 1. Is there evidence that the production process is out of control?

13-38. Weights of pieces of tile made in Arizona in April 2007 (in ounces) are as follows: 2.5, 2.66, 2.8, 2.3, 2.5, 2.33, 2.41, 2.88, 2.54, 2.11, 2.26, 2.3, 2.41, 2.44, 2.17, 2.52, 2.55, 2.38, 2.89, 2.9, 2.11, 2.12, 2.13, 2.16. Create an R chart for these data, using subgroups of size 4. Is the process variation under control?

13-39. Use the data in problem 13-38 to create an chart to test whether the process mean is under control.

13-41. The weight of a connecting rod used in a diesel engine made at a plant of the General Motors Corporation needs to be strictly uniform to minimize vibrations in the engine. The connecting rod is produced by a forging process. Every day, five rods coming out of the process are selected at random and weighed. The data for 10 days' samples in early 2007 are given below.

1 2 3 4 5 6 7 8 9 10
1 577 579 576 579 577 579 579 577 577 584
2 577 580 580 580 580 576 578 579 579 580
3 579 578 580 580 578 578 580 578 579 582
4 580 580 579 578 580 577 578 579 577 579
5 578 580 576 577 578 578 577 580 576 580

On the 10th day, the supervisor stopped the process, declaring it out of control. Prepare one or more appropriate control charts and test whether the process is indeed out of control.