Once I got the Times To Failure (ttf) of the different pieces, I implemented the PLE algorithm and then the Weibull distribution, in order to achieve the reliability expression ( R(x) ).
Now I must calculate the otimal time to replace the mechanical parts by using the "Age-based replacement policy" (type I).
My main problem is that within my formula I have an integral I can't solve (you can find it attached and highlighted) .
May you help me in solving it?
Thank you in advance
You may see this paper for your question where a procedure is given.
Conference Paper Preventive Maintenance Scheduling using Weibull Distribution
Dear Marcello,
your integral ? is, up to a constant, an incomplete gamma function. The attached calculation shows how you can reach it.
Regards,
Tibor Pogany
Thank you very match because this was very helpful. I’m studying the gamma function because I had never heard before… And I don’t understand the last sentence. Is the mining ϒ(s,a) = Gamma[a, 0, z] in a Mathematica program? But in this case.. what is “z”?
Dear Marcello,
I have permuted the parameters, sorry. So, in TEX speaking:
\[ \gamma(s, a) = \int_0^a e^{-u} u^{s-1} du \]
is the lower incomplete gamma function, see e.g.
http://en.wikipedia.org/wiki/Incomplete_gamma_function
The Mathematica code for $\gamma(s, a)$ is Gamma[s,0,a], that is
\[ \gamma(s, a) = Gamma[s,0,a] \];
compare
http://mathworld.wolfram.com/IncompleteGammaFunction.html.
Regards,
TP
Dear Marcello,
You may see the below links for more detail regarding the optimal time for Preventive maintenance. Hope it will solve ur problem.
Regards
HG
http://link.springer.com/article/10.1007%2Fs13160-012-0099-4
Article Preventive maintenance scheduling of the pulping unit in a paper mill
The simplest calculus of an integral is to approximate it by an infinite sum of of integrals over [t_i, t_i+1] where the function is aproximated by its value at t_i as the length of the interval is small enough.
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