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# Looking for a reliability-type formula

## Looking for a reliability-type formula

(OP)
Hi guys
I'm working on a project and I'm trying to put together a cost analysis for some items. I remember in University handling similar problems, but I don't remember the methodology.

Here is what I'm trying to do. Given:
- The age of the unit (say, 1989, so 18 yrs)
- The expected useful life (say 30 yrs)
- The number of units (say 10 units)
- Some accuracy percentage (say 95%),
- some time interval (say, the next 5 years)

I'd like to be able to CALCULATE that X number of units of my 10 are 95% likely to fail within the next 5 years.

thanks everyone.

dan

### RE: Looking for a reliability-type formula

Hi Dan,

Not sure about your question but perhaps a life cycle costing analysis will provide a better financial picture.

+R

### RE: Looking for a reliability-type formula

Do you have the MTBF?  How are you going to do the analysis without that?

But, in any case, without some additional data, I don't see that you can your desired answer.  Prognostication is horrifically non-deterministic.  You need to know hours-on, operating temperature, vibration environment, etc, to come up with a mean value, but even then, you'd need statistic history to know how much variance there is in the actual times to fail.

### RE: Looking for a reliability-type formula

(OP)
What if you used the number of units that have failed since 1989 to estimate a failure rate (say, 2 units over 18 yrs = 0.111 units per year)?

And we'll make up a confidence interval, say 99% of units have an expected useful life of 30 years.

My gut says that Poisson can be modified to solve for this type of problem, but its been 8 years since I did any real probability problems.

With regards to accuracy, we have some flexibility since this is not a life safety issue. If we say that we are 95% confident that 4 units will fail, and instead, 5 fail, it is acceptable to attribute the variance to a poor maintenance program.

### RE: Looking for a reliability-type formula

Is that 2 units out of 10?  If so, then it's more like 2 fails/180 system*yr.

### RE: Looking for a reliability-type formula

(OP)
With the added information, can this type of problem be modeled with a single formula?

If so, what is it?

### RE: Looking for a reliability-type formula

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