I am using the DataFit function to fit a list of data to a suitable distribution in order to use this for the "Duration" field of a process' failure data (not using MTTR and availability --> the box is unchecked). The list of data I am using is in minutes (decimal places, i.e. 0,3 minutes etc.) and is within the green column of the attached Excel file of this post.
My problem is that Plant Simulation chooses the LogNorm distribution as "best fit", which is fine, however the parameters "my" and "sigma" generated by Plant Simulation seem very strange. Doing the same calculations for "my" and "sigma" manually in Excel using the same column of data, I receive much more reasonable parameter data (this is also in the attached Excel file).
How should the parameter values in DataFit be interpreted when using the input data I am using?
I have attached both the Excel-document containing the data I am using (green column) and the Plant Simulation model with the DataFit component with the data already inside.
Edit: I am also wondering why my model has the exact same output with failures enabled according to distributions. The failures work, but shouldn't they be different from simulation run to simulation run? I make sure to reset the simulation every time I am to run a new one. It seems pointless to model failures with a time distribution if the failures occur at the exact same times in each simulation run, resulting in the exact same output every time. I have made sure that my failures are active, and as I said before I can see that the processes are failing. They are just not failing "randomly" according to the distributions I have set between simulation runs. Something seems wrong when the simulation is functioning in this way.
Thank you very much for your help.
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there are two different ways to estimate the distribution parameter using a sample of observations.
Plant Simulation uses the Maximum Likelihood Estimators for the Lognorm distribution, which is described in
A.M. Law; W.D. Kelton: Simulation Modeling & Analysis. McGraw-Hill, 1991, page 337.
In your EXCEL table the Method of Moments is used. The advantage of the Method of Moments is that the mean value and variance of the parameterized distribution match the corresponding values of the sample. Both methods determine the parameter mu0 and sigma0 of the underlying normal distribution (mu0 and sigma0 are explained in the Plant Simulation manual, your formulas can be obtained by solving the two equations for mu and sigma with respect to mu0 and sigma0).
The Method of Moments is for all distributions available, but not for the Maximum Likelihood Estimator. Your remark is very good. If both methods are available we will use both methods for the parameter estimation and compare the results by the goodness-of-fit test. Then DataFit will offer the better results. That would be a good enhancement.
About your second question: you are right, the result of simulations runs are reproducible. That is a reasonable feature for considerations and debugging of a discrete event simulation. If you want to change the random behavior, you can change the setting Random Numbers Variant in the menu Tools of the Eventcontroller. If you use an older version of Plant Simulation 11 you will change the Random Number seed values seed values in the Tools menu of Plant Simulation.
Was just writing something similar but not as technical as Peters but thought I would just add one minor thing.
If you want to see the Method of Moments parameters using the Data Fit object, then if you click Messages (on Evaluation Tab) there is a message in Lognormal row telling you what the parameters are.
Thank you for the explanation, Peter. I wonder what the advantages are for the Maximum Likelihood Estimator compared to the Method of Moments? Does it depend on sample size?
Macfaro: Thank you, however the values still seem to be a little disparate from each other despite using the same method to calculate m0 and sigma0. I guess this is down to accuracy of both my formulae and excel versus Plant Simulation's calculations