Change is constant. Or so the saying goes. However, even change is ever-varying. So perhaps we should say: Change is constantly changing. As occupants of planet earth, we intuitively know this and yet strive to keep everything the same, at least those things that do well by us. Uncertainty derails the best of our plans, even uncertainties that we recognize up front.
So how do we cope with "un-constant" change? What mechanisms in our not-so-orderly lives do we use to account for uncertainty while striving for our goals? For most of us, contingency planning (if we do it at all) is our frontline defense. We hedge our future risk with cash or other alternatives chosen up front, to smooth out the bumps of uncertainty. How much we should hedge is another question. We can deal with that question by performing Monte Carlo Analysis (MCA). (See the Introduction to Monte Carlo Analysis post for more background.)
The first necessary item to perform MCA is a mathematical and/or logical model which relates inputs to outputs (see Transfer Function post for more detail). The second is defined uncertainty around input variables with probability distributions (learn more about PDFs here). Of course, as with any other analytical approach, garbage-in produces garbage-out. The analyst must therefore take great care in defining both the mathematical model and distributions applied to that model. Thus there are two places that the analyst can mess up. Putting aside the question (and uncertainty) around mathematical models, here is a recommended sequential approach in defining uncertainty around input variables:
- Use Historical Data
- Query the Subject Matter Experts
- Make Your Best Guess
First question: Do you have Data? If yes, Second question: Do you trust the Data? (Laying to rest the second question can be filled with obstacles. For the product or manufacturing engineer, these questions are answered through Gage R&R. For other applications, answers arrive through data examination and practical experience with the variables.) Hopefully both answers are yes; otherwise, do not pass "GO," do not collect $200. Consider a data collection plan. If data will take too much time or cost to collect, skip ahead to querying the subject-matter experts (SME).
But if we did have data and we believe the data and we believe it is representative of future uncertainty, we could use it to define the risk in future uncertainty. The dangerous ground we tread is sometimes-blind belief that historical data represents the future. (Or, as those disclaimers state: "Past performance is not necessarily indicative of future results.") It can be dangerous indeed, when combined with rickety mathematical constructs. Let us undertake such efforts to capture uncertainty with the understanding that mishaps lie in wait at every turn. Being ever vigilant does not mean we will anticipate the black swans (such is the nature of a black swan). It does mean that we can adjust model or input probabilities as our knowledge and experience with the system-at-hand grows. Let us use the model first, assess its effectiveness over time and adjust with guiding hands.
What follows will be posts illustrating the uses of Monte Carlo Analysis in risk mitigation. We will examine risk scenarios, modeled in the spreadsheet universe. Since I am an engineer, many of these will revolve around product engineering design applications and manufacturing process applications. But they are not limited to these uses, by any means. Examples from the program management world, the business transaction world, and even the team sports world will be used. Through repeated application of MCA principles, we can gain insight with and, ultimately, more comfort with the MCA approach. We can deal with uncertainty in our daily lives, not just in our business decisions. Our journey begins with a look at discrete probability distribution fitting, in both Crystal Ball and ModelRisk.