# How to calculate number of cycles in twenty year from a daily distribution

I am asked to determine a distribution of the number of cycles a component is expected to do during its entire lifetime. What is do have now is a distribution of cycles the component makes per day.

I am not very familiar with component lifetime calculations. So what I am wondering is, can I simply multiply the number of cycles shown in the daily distibution by number of days in twenty years (7305)? This creates the distribution below.

I have the feeling that this will make an extreme case, for example the 99 percentile, even more extreme.

Another way might be to use the daily distribution and draw 7305 random samples and then sum up these random samples. I have done this a large number of times such that a gaussian distribution is created. But now the spread is way smaller than that of the distribution above.

Does anybody know what is the right way to go?

• It doesn't look like you summed the variables: that appears to be a plot of the mean. That's why its spread looks too narrow. – whuber Mar 20 at 20:23
• @whuber: he did not take the mean, he multiplied one draw by 7305! – kjetil b halvorsen Apr 8 at 4:00

You have the distribution of cycles per day, and want the distribution of cycles in 20 years. Then you ask

So what I am wondering is, can I simply multiply the number of cycles shown in the daily distribution by number of days in twenty years (7305)?

That would be correct only if each of the components have a constant daily number of cycles, each day for twenty years. That's probably not the case. If you assume independence between the days (which also is doubtful, but you have not given enough specifics), you can simulate the distribution by summing 7305 independent draws. An analytic soultion is difficult, see this stored search, but approximations is possible.

Ask yourself questions like:

• Might the distribution change as the component ages?

• Might there be some latent quality or oyher characteristic of the component that has a distribution in the pool of components, and influences the distribution?

• ...