by John Schuyler, PMP
WHEN EVENTS START to go wrong in a project, they often begin going very wrong together. A delay in one early activity delays a chain of subsequent activities. Encountering unexpected complexity or bad weather increases most activity completion times. When modeling projects, a common beginner's mistake is assuming that chance events are independent. Often, an uncertainty event is related to one or more other uncertainties. Decision variables can influence chance events also. These are examples where we have associations, or correlations, between variables in the project model. Characterizing the association between events is a second dimension of assessing uncertainty. I'll describe some of the causes of correlation and ways to represent this in project models.
“Correlation” and “association” are synonyms, referring to a relationship between two variables. For example, cost is associated with time to complete an activity.
If we have data for two variables, an X-Y graph shows a pattern when there is correlation. Exhibit 1 shows data where a clear pattern exists.
If an increase in one variable is generally—though not always—associated with an increase in another, then they are said to have a positive correlation.
A statistic, called a correlation coefficient, measures the degree of linear association between paired data values. Microsoft Excel's CORREL function is a convenient way to obtain the correlation coefficient statistic, ρ. Perfect positive correlation has ρ= +1, and perfect anti- or negative correlation has ρ= -1. In these extreme cases, one variable is simply a deterministic function of the other variable. Unrelated variables have ρ≅ 0. The two strongly related variables shown in Exhibit 1 have ρ= 0.85.
Sources of Correlation. Here are situations causing correlation:
■ Direct cause-and-effect relationship. Often one variable is partially dependent upon one or more other variables. For example, vehicle cost is determined, in part, by distance driven, weight of the vehicle, and average load.
■ Common drivers. Two variables may be related by a common influence. The number of people on a project team obviously affects salary expenses. Having more people also means more communication channels, which leads to higher costs in coordination efforts. Thus, salary and coordination costs are correlated.
■ System constraints. Bottlenecks, exclusive use, and other resource constraints can cause correlations. For example, higher demand for shared resources and common materials usually results in longer lead times.
Most often, correlation adds to uncertainty in a project. If variations in time and materials increase together, for example, the effect on the project is greater than the sum of the variances in time and materials alone. That is, total project uncertainty is worse than if time and materials were independent.
Ways to Represent Correlation. An influence diagram is an excellent way to map relationships between elements in a system. Decision, chance, calculation, and payoff variables are connected with “influence” arcs showing the direction of cause-and-effect relationships and calculation-precedence relationships.
There are several ways to represent correlation between variables in the project calculation model. The amount of effort in modeling correlation should be appropriate to the variables’ importance to the decision at hand.
Most project models will use Monte Carlo simulation as the stochastic calculation process. The following correlationmodeling methods are presented roughly in sequence of increasing model quality:
■ Sample actual data. When a sizable group of representative data is available, we sometimes randomly sample from those data sets in our Monte Carlo simulation. The advantage is simplicity. No analysis is required, though this is perhaps dangerous.
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Exhibit 1. A pattern seen in this type of graph, sometimes called a cross-plot, shows a correlation between the variables. Direct labor hours explains most of the cost. Workforce composition, materials, and other variables affect total cost also.
■ Curve-fitting. Often we know the cause-and-effect relationship. Regression analysis can fit a function relating the partially dependent variable to one or more independent variables. Adding a “noise” function characterizes the residuals not explained by curve-fitting.
■Probability table. A joint probability table works well to relate discrete events. Each dimension of the table shows possible outcomes of a variable and their probabilities. Two, even three, variables can be represented easily in this way. This is especially useful with decision-tree analysis.
■Correlation coefficients. This method has become very popular in recent years. The advantages are simplicity and ability to correlate many variables together with a correlation matrix. However, we are only approximating reality. Not all variables are linearly related, which is when this method works best.
■ Detailed modeling. The superior approach, if the situation warrants, is to model the system's relationships as best understood. Breaking down correlation by representing common drivers, for example, provides a more accurate and complete representation of the system. Ask yourself, “How are these variables related?” If you can explain why or describe how the project works, then we can express that knowledge in a model.
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Exhibit 2. Who does the work often is as important as how the work gets done. Factor the people into the project plan and forecasts.
Analysis is always easier with good data. Fully objective probabilities are possible when we completely understand the system, such as with most games of chance. Unfortunately, biases creep into our judgments about uncertainty. Further, human behavior affects the outcome of a process in progress. Here are two examples where chance events are affected by human behavior.
Competence. Often, cost or time to complete is judged without sufficient consideration as to who will be doing the work. With programmers, for example, individual productivities can range by a factor of 10 or more. Similarly, a project manager can have a dramatic influence on the project team's productivity.
Response to Progress. As I read Eliyahu Goldratt's book, Critical Chain [North River Press, 1997], I was struck by the importance of human factors in project performance. The book vividly explains why judgments about uncertainty so often are biased.
In project planning, we may detail the work to be done and then apply metrics and various methods in estimating time and cost. This is straightforward planning and cost estimation.
What spoils the plan is people. You will probably recognize these behaviors:
■ Multitasking. Our original intent may be to work systematically on tasks in a logical sequence. Urgencies and waiting delays often necessitate overlapping different tasks and different projects. The resulting inefficiency worsens matters, creating need for further multitasking.
■ Wasting slack times. This is partly procrastination, what Goldratt called the “student syndrome” in Critical Chain. Early finishes are not reported, while late finishes push back successor activities.
■ Embellishment. If you are ahead of schedule and cost budget, why not add more features? Gold-plating is especially true in software development. Less-driven workers may be inclined to coast a bit.
■ Catch-up. If behind schedule and budget, most conscientious people are inclined to work harder. Beyond a point, however, some will give up.
Project progress reporting bolsters a feeling of control. Some companies have found that this is an illusion and that reporting provides little impact on project success. The procrastination and embellishment behaviors suggest why. Some organizations do not share the progress reports with people actually doing the work.
People like to work toward objectives. Just knowing a time-to-complete target provides an achievement incentive. This is why “stretch” budgets are so popular.
Garbage in produces garbage out. Decomposition is a key method project managers use for better forecasts. Breaking down tasks into the details reduces biases in estimation and the undesired behavior effects. Detailed WBS construction leads to more realistic work assessment. For example, contingencies can be segregated from the normal portion of an activity's work.
A COLLEAGUE APPROACHED ME ONCE, saying, “I could use the decision analysis methods if only I had good data.” When do we ever have “good” inputs to planning evaluations models? Rarely! My response is always to point out that the decision is going to be made anyway. A decision analysis approach lets us do the best we can given what we know, even when some of those inputs are very subjective.
Detailed planning reduces biases in estimation and the undesired behavior effects. For example, contingencies can be segregated from the normal portion of an activity's work.
People newly working with decision analysis often voice concern, “What type distribution should I use?” The next article in this series provides a brief overview of common distribution types and some guidelines for their applications. ■
John Schuyler, PMP, of Decision Precision in Aurora, Colo., provides training and assistance in economic decision analysis and in project risk management. Questions about this article should be directed to email@example.com. Comments on this series should be directed to firstname.lastname@example.org.
May 2000 PM Network