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?