Answered: wwwww Wear rate = .004/p | 3ơ 3σ1 15.2…

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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Question

Specifications for a metal shaft are much wider than the machine used to make the 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?

wwwww
Wear rate = .004/p
| 3ơ
3σ1
15.2
15.0
Lower
specification i
Starting
process
mean
Ending
process
mean
Upper
i specification
Number of shafts

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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