Bono,
You have incomplete information posted in your question.
MTBF/MTTF = 300,000 hours;
Failures ‘f’ = 5;
Confidence Level (%) = 90 %.
How many units do you have? OR How many units you would like to be tested? This is also required to get the “Test time – t”.
Secondly, in order to design and conduct such a test, something about the behaviour of the product will need to be known. For example, the shape parameter of the chip’s life distribution. You need to study the financial trade-offs between the no. of units and how much test hours is needed to demonstrate the desired goal (MTBF=300,000 hours). Use cumulative binomial distribution and find out the test hours required. But you will require the no. of units also in addition to the above data you have.
In your case, we have the value of MTBF. Assume you have Weibull distribution with shape parameter = 1.5. Calculate the value of the scale parameter.
MTBF = h.G(1+1/b)………………..(I)
h = Scale parameter
G(x) = Gamma function of x (Ask your MBB or Stats/Reliability expert to obtain this)
b = Shape parameter = 1.5 (assumed)
From (I),
h = MTBF / G (1+1/b)
Let me give the cumulative binomial equation, which for Weibull distribution appears as,
1 CL = iS f (n!/(i!(n-i)!)) .(1 e-(t/h)b)i . ( e-(t/h)b)(n-i))
…(II)
Now, knowing the values of n (no. of units), CL (Confidence level), f (no. of failures allowed),h (scale parameter), and b (shape parameter), all that remains is to solve the above equation (II) for test hours (‘t’).
Hope this helps. Alternatively, you may discover that instead of finding test hours, you require to find the no. of units required since you have at your disposal only specified test time given by the customer or dictated by the market. In this case, you can get the no. of units required to test for specified amount of time for a given % reliability (or MTBF). I think software tools are available in the market to do these calculations. If you haven’t got any of them, then you need to solve the equations manually.
Good luck !
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