# SPERT-Beta Confidence Interval v. Monte Carlo Simulation

Today I created ten, 3-point estimates with various skews and Most Likely Confidence levels in a SPERT-Beta Excel workbook.  The values I chose might be something like what a project manager might choose when estimating ten tasks on a project.  Tasks were often skewed to the right, meaning that there was a greater likelihood that an outcome would be greater than the most likely outcome than less.  I included one triangular distribution where the minimum point-estimate was the same as the most likely estimate (50, 50, 100).

Now, according to the Central Limit Theorem, you obtain a bell-shaped distribution for the sum of underlying distributions, irrespective of what kind of an underlying distribution you choose.  The CLT also stipulates that the variables should be independent, too, and they should all have the same kind of distribution.  Clearly, my ten tasks didn’t neatly fit into the stipulations for relying on the CLT to create confidence intervals for the entire ten estimates.

And yet….sometimes it’s good enough to be close enough so you obtain useful results.  While I used a variety of distributions among my ten, 3-point estimates, they did trend to being a little skewed to the right (but not always).

When I compared the resulting 90% confidence interval using SPERT-Beta with a 90% confidence interval obtained through Monte Carlo simulation (using @Risk’s RiskBetaGeneral function), I found amazingly close results, even though I wasn’t following the CLT stipulations perfectly.

• SPERT-Beta, the 90% confidence interval was 793 – 938
• Monte Carlo simulation, the 90% confidence interval was 796 – 940

Shockingly close!

Have a look at the results (all results were copied from the Excel file I was working in to do the compare).  If you have access to Monte Carlo simulation software, try comparing your own SPERT-Beta confidence intervals with results from a simulation model.  Try breaking the rules for using the CLT by using different, underlying distributions (that is, skewed to the left, skewed to the right, triangular, and with different Most Likely Confidence levels for each 3-point estimate) and see what effect that has on SPERT-Beta confidence intervals compared to simulated results.

Comparison of SPERT-Beta with Monte Carlo Simulation using RiskBetaGeneral