# Question

For one new product to be produced by the A plus Company, bushings will need to be drilled into a metal block and cylindrical shafts inserted into the bushings. The shafts are required to have a radius of at least 1.0000 inch, but the radius should be as little larger than this as possible. With the proposed production process for producing the shafts, the probability distribution of the radius of a shaft has a triangular distribution with a minimum of 1.0000 inch, a most likely value of 1.0010 inches, and a maximum value of 1.0020 inches. With the proposed method of drilling the bushings, the probability distribution of the radius of a bushing has a normal distribution with a mean of 1.0020 inches and a standard deviation of 0.0010 inch. The clearance between a bushing and a shaft is the difference in their radii. Because they are selected at random, there occasionally is interference (i.e., negative clearance) between a bushing and a shaft to be mated.

Management is concerned about the disruption in the production of the new product that would be caused by this occasional interference. Perhaps the production processes for the shafts and bushings should be improved (at considerable cost) to lessen the chance of interference. To evaluate the need for such improvements, management has asked you to determine how frequently interference would occur with the currently proposed production processes.

Estimate the probability of interference by using ASPE to perform 1,000 trials of a simulation on a spreadsheet.

Management is concerned about the disruption in the production of the new product that would be caused by this occasional interference. Perhaps the production processes for the shafts and bushings should be improved (at considerable cost) to lessen the chance of interference. To evaluate the need for such improvements, management has asked you to determine how frequently interference would occur with the currently proposed production processes.

Estimate the probability of interference by using ASPE to perform 1,000 trials of a simulation on a spreadsheet.

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