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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 0.004 centimeter per piece. The process has a natural variation, o, of O.010 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. 30 Wear rate 30 Starting Ending Lower specification process mean process mean Upper specification Number of shafts How many shafts can the process turn out before tool replacement becomes necessary? (See diagram.) (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Number of shafts pieces

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 0.004 centimeter per piece. The process has a natural variation, o, of O.010 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. 30 Wear rate 30 Starting Ending Lower specification process mean process mean Upper specification Number of shafts How many shafts can the process turn out before tool replacement becomes necessary? (See diagram.) (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Number of shafts pieces

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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 0.004 centimeter per piece. The process has a natural variation, o, of 0.010 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. Wear rate 3σ 1 30 Starting Ending Lower specification process Upper specification process mean mean Number of shafts How many shafts can the process turn out before tool replacement becomes necessary? (See diagram.) (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Number of shafts pieces
Transcribed Image Text: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 0.004 centimeter per piece. The process has a natural variation, o, of 0.010 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. Wear rate 3σ 1 30 Starting Ending Lower specification process Upper specification process mean mean Number of shafts How many shafts can the process turn out before tool replacement becomes necessary? (See diagram.) (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Number of shafts pieces
Expert Solution
Step 1

Given data 

The rate at which the tools wears is 0.004 

Natural variation of a process (σ)= 0.010 and is normally distributed 

Upper Specification LImits (USL) = 15.2 

Lower Specification Limits (LSL) =15.0

3σ=3×variation =3×0.010=0.03

 

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