Part Count Models

[Pooja]

How to associate level of confidence in part count model. (i.e. to give results like reliability 90% with 95% level of confidence)

[Rui Assis]

If p´ is the point estimator of p (the true proportion of units that pass a test) and if you run the test a sufficient number of times n which conforms to n.p > 5, then the normal approximation to the binomial is acceptable. Now, if you define E as being the error in estimating p by p´ (E = |p – p´|), then you can be 100(1 – alfa)% confident that this error is less than {Z*sqrt[p(1 – p)/n]}. If you set E equal to the previous expression and solve for n, the appropriate sample size will be:

n = [Z/E]^2*p(1 – p)

An estimate of p is required to use this equation. For this purpose, you estimate p´ from a previous or preliminary sample and it can then be substituted for p in the equation.

Suppose you use 0,9 as an initial estimate of p (reliability) and you want to be 95% confident that your estimate p´ of the true proportion of successes is less than 0,05. How large should the sample be?

n = (1.96/0.05)^2(0.9)(1-0.9) = 139

This result is to be recalculated as the test proceeds and the value of p´ is updated. Each time this is done, the number of units failed to that point, must be discounted from the result of the equation.

Hope this helps.

[Pooja]

Thanks Rui, for the nice explaination. But I am using MIL STD Method, i.e. I have number of components and their failure rates (Base failure rate), I want to associate level of confidence in this case.

[Nath]

There is no statistical confidence level associated with the MIL-hdbk-217 prediction. The prediction simply provides a design tool for comparing design options, identifying over-stressed parts and providing input for analysis.

[Rui Assis]

This subject has already been discussed in this forum. Please see the thread:

"Confidence level and reliability level relationship"

I wonder whether Pooja will find an answer to his problem in it.