Approximate expression of renewal function for weibull distr

[pbambina]

If each system failure is fit by a perfect maintenance action (so that the failure distribution restart) the expected number or failures, in a fixed period T,is given by the "renewal function" H(t)=sumFi(T) (for i=1..infinite), where Fi(T) is the probability of having AT LEAST i failure all over T.
Does anybody know if approximate expressions of H(t) or Fi(T) for a weibull distribution does exist? Thank you.

[RS Support]

I am little bit confused, but I assume what you are asking for is the expected number of failures assuming a Weibull distribution and instant replacement over a period of time.
A quick estimate for this can be obtained by integrating the failure rate function (e.g. Weibull failure rate function) over the desired period of time. (See Reference 7 at http://www.reliasoft.com/Books/index.html per page 193)

[kcarr]

The interesting aspect of this is that for a Weibull, the integral of the Failure Rate function is a simple power law function with Beta as the exponent. This is a good approximation of the expected number of failures with 50% confidence. The use of total failures over time plotted on a log-log graph is easily fitted for this function. We have found that the Beta and Eta are in good agreement with the Weibull fit from tools like Weibull++ when repair times are short compaired to typical intervals between failures.