A company has just negotiated a contract to produce a part for another firm. In the process of manufacturing the part, the inside diameter of successive parts becomes smaller and smaller as the cut-ting tool wears. However, the specs are so wide relative to machine capabilities that it is possible to set the diameter initially at a large value and let the process run for a while before replacing the cutting tool. The inside diameter decreases at an average rate of .001 cm per part, and the process has a standard deviation of .05 cm.

The variability is approximately normal. Assuming a three- sigma buffer at each end, how frequently must the tool be replaced if the process specs are 3 cm and 3.5 cm?

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30 I 1 30 3 3.5 Lower specification process process Upper i specification mean mean Number of shafts 0.