Probability of multi failures 1

[corus]

For the fatigue assessment of a welded component, an SN curve is given that is generally a line of best fit through data of stress (S) against the number of cycles to failure (N).
What is the probability of 2 or more welded components, subject to the same stress, failing at the same time or failing within a certain number of cycles of each other?

corus

 

[GregLocock]

Let's call the lowest failure n1 cycles, and the second n2

We can fairly confidently say that p(n1=n2)=~0 if n1>1000


You could do a Weibull analysis.

http://www.weibull.com/

for a hideously complicated explanation. Also

http://www.itl.nist.gov/div898/handbook/eda/section4/eda429.htm

shows a worked example of how you do a weibull analysis in practice

Failing that, an ad hoc approach is to say that on average the mean life is .5(n1+n2), and on average 1/3 of the population will fail before n1, 1/3 between n1 and n2, and one third above n2. The proper analysis of this actually gives 29% below n1, and 29% above n2, and obviously 42% between them.

http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm

describes how to estimate standard deviations from small sample sizes.

Cheers

Greg Locock