Suppose that a structural component subjected to environmental corrosion has the potential to fail by a two-step process: First, a crack may initiate with a nominal depth of 5 mils; subsequently, the crack may grow to a sufficient depth that the component fractures. If the initiation time distribution is Lognormal(u = 6.91,0 = 0.06), the crack growth rate has a Weibull(a = 0.4 mils/hr, ß = 1.9) distribution, and failure occurs when the crack depth reaches twenty mils, find the component failure probability after 1100 hours of operation.
Suppose that a structural component subjected to environmental corrosion has the potential to fail by a two-step process: First, a crack may initiate with a nominal depth of 5 mils; subsequently, the crack may grow to a sufficient depth that the component fractures. If the initiation time distribution is Lognormal(u = 6.91,0 = 0.06), the crack growth rate has a Weibull(a = 0.4 mils/hr, ß = 1.9) distribution, and failure occurs when the crack depth reaches twenty mils, find the component failure probability after 1100 hours of operation.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:Suppose that a structural component subjected to environmental corrosion has the potential to fail by a two-step
process: First, a crack may initiate with a nominal depth of 5 mils; subsequently, the crack may grow to a sufficient
depth that the component fractures. If the initiation time distribution is Lognormal(u = 6.91, o = 0.06), the crack
growth rate has a Weibull(a = 0.4 mils/hr, ß = 1.9) distribution, and failure occurs when the crack depth
reaches twenty mils, find the component failure probability after 1100 hours of operation.
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