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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.

A First Course in Probability (10th Edition)
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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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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