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A valve used to turn on and off the flow of gases and liquids is actuated manually with a lever-style handle attached to the valve stem. If too much torque is applied to the valve stem the stem will fail which is very difficult to repair. To prevent this failure from happening, the handle is designed to fail before the stem does. The distribution of stem failure torques is normal with mean µ₁ = 120 and standard deviation o₁ = 6. The distribution of handle failure torques is normal with mean µ2 = 100 and standard deviation 02 = 6. a. Use Graph> Probability Distribution Plot> Vary Parameters to plot the two distributions. Identify the ballpark value of the torques where the stems might fail before the handles. b. Calculate the probability that a strong handle will be mated with a weak stem causing the stem to fail. (Hint: This is a normal-normal interference failure problem.)

A valve used to turn on and off the flow of gases and liquids is actuated manually with a lever-style handle attached to the valve stem. If too much torque is applied to the valve stem the stem will fail which is very difficult to repair. To prevent this failure from happening, the handle is designed to fail before the stem does. The distribution of stem failure torques is normal with mean µ₁ = 120 and standard deviation o₁ = 6. The distribution of handle failure torques is normal with mean µ2 = 100 and standard deviation 02 = 6. a. Use Graph> Probability Distribution Plot> Vary Parameters to plot the two distributions. Identify the ballpark value of the torques where the stems might fail before the handles. b. Calculate the probability that a strong handle will be mated with a weak stem causing the stem to fail. (Hint: This is a normal-normal interference failure problem.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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9. A valve used to turn on and off the flow of gases and liquids is actuated manually with a lever-style handle attached to the valve stem. If too much torque is applied to the valve stem the stem will fail which is very difficult to repair. To prevent this failure from happening, the handle is designed to fail before the stem does. The distribution of stem failure torques is normal with mean μ₁ = 120 and standard deviation o₁ = 6. The distribution of handle failure torques is normal with mean µ₂ = 100 and standard deviation 02 = 6. a. Use Graph> Probability Distribution Plot> Vary Parameters to plot the two distributions. Identify the ballpark value of the torques where the stems might fail before the handles. b. Calculate the probability that a strong handle will be mated with a weak stem causing the stem to fail. (Hint: This is a normal-normal interference failure problem.)
Transcribed Image Text:9. A valve used to turn on and off the flow of gases and liquids is actuated manually with a lever-style handle attached to the valve stem. If too much torque is applied to the valve stem the stem will fail which is very difficult to repair. To prevent this failure from happening, the handle is designed to fail before the stem does. The distribution of stem failure torques is normal with mean μ₁ = 120 and standard deviation o₁ = 6. The distribution of handle failure torques is normal with mean µ₂ = 100 and standard deviation 02 = 6. a. Use Graph> Probability Distribution Plot> Vary Parameters to plot the two distributions. Identify the ballpark value of the torques where the stems might fail before the handles. b. Calculate the probability that a strong handle will be mated with a weak stem causing the stem to fail. (Hint: This is a normal-normal interference failure problem.)
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