Monte Carlo simulation for Weibull

[Aleksandar]

Hi...

I have a question and I hope someone will be able to answer it. I have been doing some analysis of ffailures. I have the year of installation, number of miles of installed material in each year, number of miles of replaced material in each year, and number of failures. I have managed to get the best fit curve for the number of failures. Now, I am trying to get the coefficients from the column for the number of failures for the weibull distribution. I got those coefficients (a, and b), and now, how do I generate the number of failures for each year (say 1000 times) in order to simulate this case so that I can get confiedence levels...For example, if in my original system, number of failures in year 25 was 50, and I estimated with my best fit curve it to be 46, I need to simulate this 1,000 times to see where is the confidence level, so that I can say that my failures will be 40 - 55 in year 25, but with probability of 95%, it will be between 45-49...Or something similar...Any help appreciated...

[tarik]

If your goal is to simply estimate your result with a confidence bound, I suggest that you use one of the confidence bounds estimation methods (Fisher Matrix, Likelihood Ratio,..) to estimate the metric you are calculating and obtain the appropriate bounds based on a desired confidence level. More details can be found at: http://www.weibull.com/LifeDataWeb/confidence_bounds.htm

Simulation based bounds can be obtained via the use of repeated Monte Carlo simulations and repeated estimation of the parameters, or the function result of interest. In your example, you can generate a number of failure times (and suspensions) based on the defined parameters and recalculate the parameters based on the generated failures. This process can be repeated multiple times.

ReliaSoft has decided not to include simulation-based bounds in the standard version of Weibull++ 6 (mainly due to the fact that simulation based results tend to be slightly different every time you compute them).

However, if you are interested in experimenting with, or using simulation based methods ReliaSoft is making available a free tool that can be utilized for this. This tool is available free to all licensed users of Weibull++. The tool is called Simumatic and is availabable at http://www.weibull.com/freetools/index.htm#simumatic