HVAC Manufacturing produces parts and materials for the heating, ventilation, and air conditioning industry. One of its facilities produces metal ductwork in various sizes for the home construction market. One particular product is 6-inch diameter round metal ducting. It is a simple product, but the diameter of the i nished ducting is critical. If it is too small or large, contractors will have difi culty i tting the ducting into other parts of the system. The target diameter is 6 inches exactly, with an acceptable tolerance of 6.03 inches. Anything produced outside of specii cations is considered defective. The line supervisor for this product has data showing that the actual diameter of i nished product is 5.99 inches with a standard deviation of .01 inches. a. What is the current capability index of this process? What is the probability of producing a defective unit in this process? b. The line supervisor thinks he will be able to adjust the process so that the mean diameter of output is the same as the target diameter, without any change in the process variation. What would the capability index be if he is successful? What would be the probability of producing a defective unit in this adjusted process? c. Through better training of employees and investment in equipment upgrades, the company could produce output with a mean diameter equal to the target and a standard deviation of .005 inches. What would the capability index be if this were to happen? What would be the probability of producing a defective unit in this case?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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HVAC Manufacturing produces parts and materials for the heating, ventilation, and air
conditioning industry. One of its facilities produces metal ductwork in various sizes for the
home construction market. One particular product is 6-inch diameter round metal ducting. It is
a simple product, but the diameter of the i nished ducting is critical. If it is too small or large,
contractors will have difi culty i tting the ducting into other parts of the system. The target
diameter is 6 inches exactly, with an acceptable tolerance of 6.03 inches. Anything produced
outside of specii cations is considered defective. The line supervisor for this product has data
showing that the actual diameter of i nished product is 5.99 inches with a standard deviation
of .01 inches.
a. What is the current capability index of this process? What is the probability of producing a
defective unit in this process?
b. The line supervisor thinks he will be able to adjust the process so that the mean diameter
of output is the same as the target diameter, without any change in the process variation.
What would the capability index be if he is successful? What would be the probability of
producing a defective unit in this adjusted process?
c. Through better training of employees and investment in equipment upgrades, the company
could produce output with a mean diameter equal to the target and a standard deviation of
.005 inches. What would the capability index be if this were to happen? What would be the
probability of producing a defective unit in this case?

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