I have a statistics/math problem that I can’t figure out for a piece of equipment. I have the following known data:

Failure Rate in failures per million hours.
Mean Time Between Failure.
Mission/Operating time.

What I need to calculate is the probability of success for the equipment to complete a mission of T hours. Does anyone have suggestions? I know this is a weird request, but I am at my wits end.

Where:
Reliability is R(t)
UnReliability is F(t)

R(t) + F(t) = 1

Failure rate is lamda
Mean Time Between Failures is MTBF = 1 / lamda
Or Operational Time / # of errors

Mission operational time is the Operational Time.

It appears that you only need to express show an equation of just R(t), solving out F(t).
Since the failure rate is constant, F(t)=1-e^(-lamda*t)

Since R(t) + F(t) = 1, R(t) = 1 - F(t), R(t) = e^(-lamda*t)

Replace lamda with the failure rate, and R(t) will approach zero as t approaches infinity.

I truly hope this is only the first portion of a larger question.

domcintosh is that poisson?

domcintosh,

That is the formula I came up with as well, but I wanted to get some verification from the masses. I appreciate it.

The requirement for my effort is a probability of .91 and the equipment significantly exceeds that in a good way. There are other analytical stuff associated with it, but this was the last piece of the puzzle.

Thanks again.

quote:

Originally posted by Underworld2086:
domcintosh is that poisson?

As modeled, because the failure rate is constant, yes.

F(t), over time, resembles the cumulative distribution graph.

Of course, that’s for the hardware. Factor in rebooting software, if there is any, 5 times during a mission, then it’s not so rosey.

Sorry, couldn’t resist.