Doing Optimization with MTBF or Number of Failures goals

[Frank]

I have a bunch of component in series. I am given a goal expressed in terms of:

- Number of failures (which could be caused by any of the components) during a defined number of warranty hours
- I am also given an MTBF goal.

I am trying to optimize the system to meet my goals. The optimization tool you have in BlockSim asks for reliability goal at a certain time (which is not the kind of goals I have defined), and returns reliability values! Instead, I'm interested in MTBF values or max number of failures to be allocated for each component. What do you suggest?

[Pantelis]

Well if you have a reliability value, i.e. 98% at 100 hrs, you expect 2% to fail by 100 hours… so if you have 100 units then this is 2 failures by 100 hours… Given this, transforming your failures to reliability is trivial.

Now with respect to the MTBF, this gets harder. In general (and have said this many times), the MTBF is not necessarily the best metric since it does not tell you what percent will fail by the mean (if assuming a complex distribution). Now if you want to make the simplifying assumption of an exponential then the reliability value is (1-0.632) while if you assume normality this is 50% - or if you don’t want to assume a distribution, then 50% will give you the median time to failure.

Hope this helps