# probability of failure estimation when only one piece broke

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

• 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? – Maja Aug 13 '19 at 7:51
• 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. – rambo Aug 13 '19 at 8:12