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The annual maximum load (in tons) on a structure is normal distributed with mean and standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure (R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13 tons, with probabilities 0.3, 0.6, and 0.1, respectively. a) Compute the failure probability of the system in any year. b) Determine the reliability of the structure over its 30-year life span. c) Compute the expected number of failure events over the lifetime. d) Compute the safety margin and safety factor for the structure.

The annual maximum load (in tons) on a structure is normal distributed with mean and standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure (R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13 tons, with probabilities 0.3, 0.6, and 0.1, respectively. a) Compute the failure probability of the system in any year. b) Determine the reliability of the structure over its 30-year life span. c) Compute the expected number of failure events over the lifetime. d) Compute the safety margin and safety factor for the structure.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 8CR
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The annual maximum load (in tons) on a structure is normal distributed with mean and standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure (R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13 tons, with probabilities 0.3, 0.6, and 0.1, respectively. a) Compute the failure probability of the system in any year. b) Determine the reliability of the structure over its 30-year life span. c) Compute the expected number of failure events over the lifetime. d) Compute the safety margin and safety factor for the structure.
Transcribed Image Text:The annual maximum load (in tons) on a structure is normal distributed with mean and standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure (R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13 tons, with probabilities 0.3, 0.6, and 0.1, respectively. a) Compute the failure probability of the system in any year. b) Determine the reliability of the structure over its 30-year life span. c) Compute the expected number of failure events over the lifetime. d) Compute the safety margin and safety factor for the structure.
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