When we often use statistical analysis tools and techniques, the underlying assumption is that process/ sub-process displays a “normal” behavior. Even if the limited data that we have shows non-normal behavior, we assume that the reason is the lack of data, and we approximate the distribution to normal.
This assumption and subsequent analysis, conclusions and decisions are therefore inaccurate, especially if we are combining “assumed” normal behavior across multiple processes, viz Process Performance Modeling.
“Normal” behavior is very rare in real life. For example, you travel from your home to office, let us say usually in 1 hour. The least time you have ever done the trip is in 30 mins. If the distribution was normal, the worst time should have been 1 hour 30 mins (symmetrical on both sides). You will find that on some days that you were delayed, the time could have been 2 or even 3 hours!
Another way of saying that real life does not behave in a “normal” way, is “there is a limit on how well you can do, but no limit on how badly you can screw up!”
There is more on this in the books “Fooled by Randomness” and “Black Swan” by Nassim Taleb — must-reads for anyone involved in high maturity CMMI® implementation.