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Let's say I have 4 pipes that have been testes for 150 000 cycles each and one of them broke at 120 000. How can I estimate the probability of failure from this sample?

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It seems that what you describe fits the exponential distribution.

First you calculate the failure rate $\lambda$. There was one failure in $3 * 150000 + 1 * 120000 = 570000$ cycles, thus:
$\lambda = \frac{failures}{\Delta t} = 1 / 570000$.

The reliability in time is then:
$R(t) = e^{-\lambda t} = e^{\frac{-t}{570000}}$,
where t is the number of cycles.

You can look at the mean time to failure (MTTF) of a piece, given by:
$MTTF = \frac{1}{\lambda}$.

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  • $\begingroup$ Thanks. So t here would also be 570 000 which then gives me e^(-1) which is 0.36787944117. How do I interpret this number? $\endgroup$ – Maja Aug 13 '19 at 7:51
  • $\begingroup$ That means that at time t=570000 cycles the probability that all your pieces are still functioning is 36.787..%. In other words, by then, expect a bit less than two thirds (63.2%) of the pieces to be broken. You can also take a look at the mean time to failure (MTTF). I will add to the answer. $\endgroup$ – rambo Aug 13 '19 at 8:12

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