Monday, February 9, 2015

Introduction to Monte Carlo Simulations for Exposure Assessment

Exposure assessment modeling has its Stars.   Last week I discussed some of the work of Dr. Zhishi Guo, this week it is Thomas W. Armstrong PhD, CIH and AIHA Fellow.   I am happy and grateful to count Tom as a friend and colleague.  He is a steady and tireless worker in Industrial Hygiene education and in the development of tools for the profession of exposure assessment.  He gives freely of his time in these endeavors and his overall approach and judgment in the realm of exposure and risk assessment is first-rate   It has been his most recent contribution that is being highlighted here today; namely, an article in this month’s AIHA Synergist on Monte Carlo Simulation (MCS) and its role in making decisions.   

Like all good educational pieces, it is clearly written making it easy for the beginner to understand.  Anyone can see it online at:

I just wanted to highlight some of the lower level details of the process along with some of my basic experience with the commercial software mentioned in the article.   For me the really neat aspect of most MSC software is that it sits on top of Microsoft Excel as an add-on. Many, if not most, of us know and love Excel as a remarkably capable program that can do some very complex calculations.   Indeed, given all the functionality that it has, Excel should be a basic tool of any technologist.  What it cannot do easily by itself is treat any cell as a DISTRIBUTION rather than a single value or a single value resulting from a calculation within the spreadsheet.   Let us assume that we have, say, cell B3 in a normal spreadsheet with the value 7.  What MCS add-on software can do is to easily and simply allow you to describe that cell (B3) as a DISTRIBUTION.  Let us say we want it to be a normal (Gaussian) distribution with a mean of 7 and a standard deviation of 2.    The MCS add-on will allow you to do this.  You could have just as easily chosen a uniform distribution with a minimum of 2 and a maximum of 12.   In the case of the normal distribution mean = 7 sd = 2 the MCS software samples the cell and gets a value constrained by the distribution; that is, it literally samples the distribution.  Say, for example, this single sample returns the value: 5.2.   That value could be used elsewhere in the spreadsheet with other values that were either constant or also samples from a defined distribution.   After all this, the spreadsheet has done exactly ONE set without any iteration.   Set the MCS software to 10,000 iterations and the PC goes through the sampling and calcuations again and again automatically and never gets tired.  It will keep a record of the output distributions of the cells that you choose.   Anything that can be represented as a single deterministic outcome calculation in Excel can now be presented as a DISTRIBUTION of outcomes. It is, IMHO technological magic!

My first IBM compatible PC had an early generation 8086 CPU which was well before 286, 386 or Pentium CPUs which are now considered ancient in our world of multi-core monster processors. The commercial MCS software in those early days cost a few hundred bucks and came on a single 3.5” floppy.  I would set up a spreadsheet to do 10,000 MCS iterations and leave to have dinner!   It was usually complete when I returned an hour or two later.   Today, a typical CPU will do 10,000 iterations in seconds!

Today the MCS commercial software is also considerably more expensive and typically requires an annual fee for commercial (not educational) customers to keep it up to date through the various evolving versions of Excel.  If you have the need for all its “bells and whistles” (and there are a lot) and a company or client to purchase it then I think the commercial software makes sense.  If not, then you may want to look into the freeware versions that Tom mentions in his piece.

If any of the readers of this blog have considerable experience with these freeware versions, either Simular or Simulacion, I would love to hear the details of your experience which I would be happy to pass on here.


  1. Interesting comment Mike. I'm glad Tom is still active in the exposure community.


  2. HI Tip,

    Tom is not only still active - I believe he is hitting his stride. Best Regards, Mike

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