I want to generate failure times over, say, a 10 year period for a piece of equipment that fails with a mean time to failure (MTTF) of, say 0.45 years -- that is about 11 failures over the 10 year period. The distribution of failures is of the Exponential type.

How best to set this up? Any advice would be most helpful. Thanks.

Nazim Nathoo

Hi,

Just so I understand, are you talking about mean time to failure or mean time between failure? In the former case, typically that's a single event. At least as I understand it, MTBF is used in the case where you have a repeating failure (and repair) condition.

Alex Edwards
alex@riskamp.com

The difference between MTTF and MTBF is negligible in terms of numeric value if the Mean Time To Repair (MTTR) is small. Else, both refer to failures that are repairable. The idea is, for example, if there are 11 random failures in 10 years (MTTF=0.45 yr) that follow the exponential distribtion, each of which will have a repair time associated with it, then how does one create that ith the functions in this Monte Carlo add-in.

Hope this clarifies your question.

Thanks.

My apologies - that should have been 22 failures over 10 years not 11 as indicated. I believe I have answered my own query using INT(-0.45*LN(RAND()) and some additional logic.

Thanks.

Hi,

No worries. I'll answer your question anyway, just so it's on the record.

Using our function the answer would be essentially the same. The function takes two parameters, location and shape. Ignoring location for the moment, the shape represents the inverse rate, so the shape parameter in your case would be 10/22, or the inverse of the rate (22/10).

This would look like

=ExponentialValue( 0, 10/22 )

The mean of that should be the same as the shape, or (10/22) = .4545.

Location is a shift applied after the distribution, so if location is zero, then it has no effect. If you have a location of 1, then

=ExponentialValue( 1, 10/22 )

would have a mean of 1.4545. Internally, the function looks like

location - shape * log( uniform( 0, 1 ) )


As long as you're using Excel 2003 or higher, your function should be fine. If you're using an earlier version of Excel, then I wouldn't recommend using RAND(), because it had a really weak generator algorithm.

I hope that's helpful.

Alex Edwards
alex@riskamp.com

Thank you, Alex. Appreciate your feedback.