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Demonstrating MTBF with a small sample size

Demonstrating MTBF with a small sample size

Demonstrating MTBF with a small sample size

(OP)
Hello,
To preface I have never done any reliability engineering before so, this is written from the point of view of someone who knows nearly nothing about the subject. Sorry
A customer has specified targets/requirements for the life of and MTBF (mean time between failure?) of an engine system we are developing.  I am trying to figure out what kind of a test program we need to plan on to demonstrate that we have met this requirement and hopefully claim we have exceeded these objectives.   Lets say 100 hrs life and 3000 hours mtbf.  We know from our previous development( using an agreed upon duty cycle) that the system is capable of operating for much longer than the required life before the units starts to have wear out related failures,  250 hrs.   
The cost driver for testing the system is the price of the units themselves, running them is relatively cheap.  We usually end up with a small sample size ≈3 and running them for long durations.  There is a time constraint on the program so even test time is limited.
Traditionally on our other products we run time terminated test programs with aggressive duty cycles running the units beyond their normal life but stopping short of failures from just wearing out.  
Back to MTBF, to demonstrate a 90% confidence of 3000 hours  assuming an exponential failure distribution (might be ok if the engines service life is short of wearing out and systems  are "burned in" prior to being put into the field?) it would take 7000 hours of testing without failure.  With a small # of units we would end up having to run the systems for very long durations running the risk of wear out failures.  Is there some way around this?
 

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