Specifications for a metal shaft are much wider than the machine used to make shafts is capable of.

Consequently, the decision has been made to allow the cutting tool to wear a certain amount before replacement. The tool wears at the rate of .004 centimeter per piece. The process has a natural variation,

σ, of .02 centimeter and is normally distributed. Specifications are 15.0 to 15.2 centimeters. A three-sigma cushion is set at each end to minimize the risk of output outside of the specifications. How many shafts can the process turn out before tool replacement becomes necessary? (See diagram.) LO.1

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30 | Wear rate = .004/p | 30 15.0 Lower Starting Ending specification process mean process mean 15.2 Upper specification 0 Number of shafts