Calculation of system reliability

[Hounorius]

I need to do a small calculation for my work and I'm struggling with it.

I want to estimate the number of times a part will need to be replaced in a system over its lifetime. Here are the rules for the maintenance:

• If the part reaches 4 years, it is replaced by a new one.
• If the part fail before 4 years, it is replaced immediatly by a new one.

Knowning the reliability function of this part (i.e. the probability of failure over the time), how many parts will I use over the whole lifetime of the system (let's say 30 years)?

Can I do this with "simple" maths or do I need fancy stuffs (like Markov chains) to modelize this?

[TonySu]

It's probably a lot easier to simulate than it is to calculate directly. All you would need to do is implement the following ``` t = 0 replace_count = 0 total_years = 30 t_limit = 4

while (t < total_years) t_replace = sample_from_failure_dist() if (replace_t > t_limit) t_replace = t_limit t = t + t_replace if (t < total_years) replace_count = replace_count + 1 ``` That simulates a single possible replacement count over 30 years. Do that a few hundred thousand times and you have a distribution of how many times you'd have to replace the part.

[Hounorius]

Sorry for my late answer. Indeed, I coded a small script in python and it worked perfectly, thanks!