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# Autopitch Control Charts with Control Limits

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17- 9. When set at the standard position, Autopitch can throw hard balls toward a batter at an average speed of 60 mph. 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 aver-age range is 3 mph. Using control- chart techniques; determine control- chart limits for averages and ranges for Autopitch.

17- 16. Colonel Electric is a large company that produces lightbulbs and other electrical products. One particular lightbulb 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

(a) What is the overall average of these means? What is the average range?
(b) What does the upper and lower control limits for a 99.7% control chart for the mean?
(c) Does this process appear to be in control? Explain.

17- 17. For Problem 17-16 develop upper and lower control limits for the range. Do these samples indicate that the process is in control?

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Solutions are on the attached Excel spreadsheet with forumlas and explanations.

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17-9 ] To calculate LCL and UCL based on sample size 10, we use A2, D3, and D4 from ...

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