There are no rules and what you propose sounds fine to me :)

Hi Lachlan,

Nice question. It seems to me that the Monte Carlo (MC) analysis is useful in your context. I would make sure that whatever distribution functions I use has a theoretical basis in the main physical principles of gas chromatography. I would not use a normal distribution because it has negative and positive values ( mass cannot be negative for these applications). I would also be careful about the uniform (e.g., rectangular) distribution. It implies lack of knowledge because all outcomes are equally probable, which should not be the case for the application you consider. I suspect that the log-normal distribution may be appropriate, You can also use a triangular distribution to identify the variability about a peak and keep thing simple.

You might run the MC for, say 10,000 times and generate an empirical distribution. You can then fit a smooth function to judge the output (from the MC). The MC algorithm will give you the sample mean, median, s.d,. and other information. Because you have the MC distribution, it seems that you have all you need.

I hope this makes some sense. If you do your own coding, then you will have to do some more work ... such as decide on the method to use for the simulation, stopping rule (10,000 is arbitrary) and so on.

Hope this helps a little bit.

Best,

Paolo

An advantage of Monte Carlo simulation is you are not limited by a Normal, or rectangular, or the "usual" triangular distribution. If you have sufficient data, you could use the actual empirical distribution. However, a Monte Carlo simulation is usually not used unless you have an interaction going on that is too difficult to calculate with a simple empirical or theoretical distribution. If you have data and are simply trying to predict future data from that data, Monte Carlo is gross overkill. A better tool may be Statistical Process Control to give an analysis of are your past results stable, and can indeed be used to make a prediction of future performance from.

Ok thank you very much for your responses I will keep this in mind when choosing the model and running the simulation

Dear Lachlan,

You are writing that you regularly analyze the QC samples and want to estimate the measurement uncertainty on the basis of these data. OK! It is not clear from your question whether the concentration of the QC sample (that you put on before and after the bath samples) is identical for all batches or not - this slightly changes the calculation scheme. In any case, you get the experimental standard deviation that is a first approximation to the standard uncertainty you seek for. If so, you do not need to apply a Monte Carlo simulation at all. There is no need to think about probability distributions of input quantities in the measurement model, the number of runs to perform, and many other things determining the quality of simulated results. In short, if you have a set of experimental data (that you gathered for a year!), a set of simulated data is quite unnecessary.

Of course, some additional contributions to the combined uncertainty should be taken into account, following the measurement model, that have not been properly covered during the experimental measurements. The full discussion of the methods for estimating measurement uncertainty in chemical analysis, including the use of Monte Carlo simulation, has been presented in the EURACHEM/CITAC Guide "QUAM" (https://www.eurachem.org/images/stories/Guides/pdf/QUAM2012_P1).

Regards,

Rouvim Kadis

Did you look at the historical trend of the data, are they stable. Then check for normality (anderson darling test) and if it follows normal distribution use the mean and standard deviation to perform monte carlo simulation.

Also try the other options of bootstrapping and resampling approaches.

All the best.

You may want to check this somewhat related RG discussion:

https://www.researchgate.net/post/Where_I_can_find_examples_of_Montecarlo_tests_to_demonstrate_effectiveness_of_parameter_identification_under_different_noise_levels