Statistical Quality Control Problem Set - 7
Part 1 of 2
This part of the question is based on the following information.
When set at the standard position, Autopitch can throw hard balls toward a batter at an average speed of 60mph. Autopitch devices are made for both major- and minor-league teams to help them improve their batting averages. Autopitch executives take samples of 10 Autopitch devices at a time to monitor these devices and to maintain the highest quality. The average range is 3mph. Using control chart techniques, determine control-chart limits for averages and ranges for Autopitch.
| Sample Size, n | Mean Factor, A_2 | Upper Range, D_4 | Lower Range, D_3 |
| 2 | 1.88 | 3.268 | 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 |
| 14 | 0.235 | 1.671 | 0.329 |
| 16 | 0.212 | 1.636 | 0.364 |
| 18 | 0.194 | 1.608 | 0.392 |
| 20 | 0.18 | 1.586 | 0.414 |
| 25 | 0.153 | 1.541 | 0.459 |
Based on the table, the upper control limit for averagesis __________________ (round two decimal points and include no units)
Based on the table, the lower control limit for averagesis __________________ (round two decimal points and include no limits).
Based on the table, the upper control limit for rangesis ______________ (round two decimal points and include no units)
Based on the table, the lower control limit for rangesis ___________________ (round two decimal points and include no units.
Part 2 of 2
This part of the question is based on the following information.
Colonel Electric is a large company that produces light bulbs and other electrical products. One particular light bulb is supposed to have an average life of about 1,000 hours before it burns out. Periodically the company will test 5 of these and measure the average time before these burn out. The following table gives the results of 10 such samples.
| Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mean | 979 | 1087 | 1080 | 934 | 1072 | 1007 | 952 | 986 | 1063 | 958 |
| Range | 50 | 94 | 57 | 65 | 135 | 134 | 101 | 98 | 145 | 84 |
The overall average of these means is ________________, and the overall average range is _______________. (round it to one decimal point and include no units)
Based on the result in Question 5 and the table for part 1, the upper control limit for a 99.7% control chart for the mean/average is _______________. (Round it to two decimal points and include no units)
Based on the results in Question 5 and the table in part 1, the lower controllimit for a 99.7% control chart for the mean/average is __________________. (round it to two decimal points and include no units).
Does this process appear to be in control in terms of the mean? Yes or No
Based on the results in Question 5 and the table for Part 1, the uppercontrol limit for a 99.7% control chart for the rangeis _________________ and the lowercontrol limit is ________________. (Round it to two decimal points and include no units)
Does this process appear to be in control in terms of the range? Yes or No.
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Solution: Statistical Quality Control Problem Set - 7 Solution