Problem 10-29 (Algo)

The following table contains the measurements of the key lengthdimension from a fuel injector. These samples of size five weretaken at one-hour intervals. Use three-sigma control limits. UseExhibit 10.13.

	OBSERVATIONS
SAMPLE NUMBER	1	2	3	4	5
1	0.481	0.486	0.492	0.517	0.475
2	0.485	0.505	0.527	0.491	0.528
3	0.486	0.487	0.513	0.487	0.524
4	0.481	0.505	0.468	0.486	0.486
5	0.467	0.503	0.512	0.468	0.479
6	0.468	0.493	0.502	0.491	0.508
7	0.485	0.507	0.486	0.479	0.507
8	0.532	0.504	0.485	0.480	0.483
9	0.493	0.505	0.515	0.507	0.499
10	0.492	0.507	0.509	0.517	0.481
11	0.491	0.512	0.469	0.490	0.496
12	0.484	0.441	0.521	0.507	0.525
13	0.529	0.495	0.491	0.518	0.507
14	0.482	0.497	0.507	0.491	0.503
15	0.492	0.511	0.483	0.517	0.506
16	0.461	0.502	0.480	0.478	0.525
17	0.471	0.474	0.514	0.477	0.491
18	0.521	0.512	0.491	0.475	0.480
19	0.505	0.552	0.486	0.481	0.489
20	0.502	0.482	0.481	0.507	0.507

a. Calculate the mean and range for the abovesamples. (Do not round intermediate calculations. Roundyour answers to 3 decimal places.)

b. Determine X=X= and R?R? . (Do notround intermediate calculations. Round your answers to 3 decimalplaces.)

c. Determine the UCL and LCL for a X?X? -chart.(Do not round intermediate calculations. Round your answersto 3 decimal places.)

d. Determine the UCL and LCL forR-chart. (Leave no cells blank - be certain toenter "0" wherever required. Do not round intermediatecalculations. Round your answers to 3 decimal places.)

e. What comments can you make about theprocess?

• Process is in statistical control.

• Process is out of statistical control.