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?


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:
$MTTF = \frac{1}{\lambda}$.

| cite | improve this answer | |
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.