Risk Assessment and Allocation for Highway Construction Management

4. Risk Analysis

4.1. Objectives of Risk Analysis

Typically, a project's qualitative risk assessment will recognize some risks whose occurrence is so likely or whose consequences are so serious that further quantitative analysis is warranted. A key purpose of quantitative risk analysis is to combine the effects of the various identified and assessed risk events into an overall project risk estimate. This overall assessment of risks can be used by the transportation agency to make go/no-go decisions about a project. It can help agencies view projects from the contractor's perspective through a better understanding of the contractor's risks. More commonly, the overall risk assessment is used to determine cost and schedule contingency values and to quantify individual impacts of high-risk events. The ultimate purpose of quantitative analysis, however, is not only to compute numerical risk values but also to provide a basis for evaluating the effectiveness of risk management or risk allocation strategies.

Many methods and tools are available for quantitatively combining and assessing risks. The selected method will involve a tradeoff between sophistication of the analysis and its ease of use. There are at least five criteria to help select a suitable quantitative risk technique:

1. The methodology should be able to include the explicit knowledge of the project team members about the site, design, political conditions, and project approach.
2. The methodology should allow quick response to changing market factors, price levels, and contractual risk allocation.
3. The methodology should help determine project cost and schedule contingency.
4. The methodology should help foster clear communication among the project team members and between the team and higher management about project uncertainties and their impacts.
5. The methodology should be easy to use and understand.

Figure 13: Cost risk assessment top-level diagram

4.2. Characterizing Risk

Three basic risk analyses can be conducted during a project risk analysis: technical performance analysis (will the project work?), schedule risk analysis (when will the project be completed?), and cost risk analysis (what will the project cost?). Technical performance risk analysis can provide important insights into technology-driven cost and schedule growth for projects that incorporate new and unproven technology. Reliability analysis, failure modes and effects analysis (FMEA), and fault tree analysis are just a few of the technical performance analysis methods commonly used. However, this discussion of quantitative risk analysis will concentrate on cost and schedule risk analysis only. The following section will discuss the various alternative methods that can be used for quantitative risk analysis.

At a computational level there are two considerations about quantitative risk analysis methods. First, for a given method, what input data are required to perform the risk analysis? Second, what kinds of data, outputs, and insights does the method provide to the user? Figure 13, adapted from DOE's Project Management Practices: Risk Management, illustrates the relationship between the computational method (the model) and its required inputs and available outputs.

4.3. Input Risk Parameters

The most stringent methods are those that require as inputs probability distributions for the various performance, schedule, and costs risks. Risk variables are differentiated based on whether they can take on any value in a range (continuous variables) or whether they can assume only certain distinct values (discrete variables). Whether a risk variable is discrete or continuous, two other considerations are important in defining an input probability: its central tendency and its range or dispersion. An input variable's mean and mode are alternative measures of central tendency; the mode is the most likely value across the variable's range. The mean is the value when the variable has a 50 percent chance of taking on a value that is greater and a 50 percent chance of taking a value that is lower. The mode and the mean of two examples of continuous distributions are illustrated in figure 14.

Figure 14: Mean and mode in normal and lognormal distributions

The other key consideration when defining an input variable is its range or dispersion. The common measure of dispersion is the standard deviation, which is a measure of the breadth of values possible for the variable. Normally, the larger the standard deviation, the greater the relative risk. Probability distributions with different mean values and different standard deviation values are illustrated in figure 15.

Finally, its shape or the type of distribution may distinguish a probability variable. Distribution shapes that are commonly continuous distributions used in project risk analysis are the normal distribution, the lognormal distribution, and the triangular distribution. These three distributions and a typical discrete distribution are shown in figure 16.

All four distributions have a single high point (the mode) and a mean value that may or may not equal the mode. Some of the distributions are symmetrical about the mean while others are not. Selecting an appropriate probability distribution is a matter of which distribution is most like the distribution of actual data. For transportation projects this is a difficult choice because historical data on unit prices, activity durations, and quantity variations are often difficult to obtain. In cases where insufficient data is available to completely define a probability distribution, one must rely on a subjective assessment of the needed input variables.

Figure 15: Probability distributions for high, medium, and low dispersions

Figure 16: Distributions for risk analysis.

4.4. Outputs of Risk Analyses

The type of outputs a technique produces is an important consideration when selecting a risk analysis method. Generally speaking, techniques that require greater rigor, demand stricter assumptions, or need more input data generally produce results that contain more information and are more helpful. Results from risk analyses may be divided into three groups according to their primary output:

1. Single parameter output measures
2. Multiple parameter output measures
3. Complete distribution output measures

The type of output required for an analysis is a function of the objectives of the analysis. If, for example, an agency needs approximate measures of risk to help in project selection studies, simple mean values (a single parameter) or a mean and a variance (multiple parameters) may be sufficient. On the other hand, if an agency wishes to use the output of the analysis to aid in assigning contingency to a project, knowledge about the precise shape of the tails of the output distribution or the cumulative distribution is needed (complete distribution measures). Finally, when identification and subsequent management of the key risk drivers are the goals of the analysis, a technique that helps with such sensitivity analyses is an important selection criterion.

Sensitivity analysis is a primary modeling tool that can be used to assist in valuing individual risks, which is extremely valuable in risk management and risk allocation support. A "tornado diagram" is a useful graphical tool for depicting risk sensitivity or influence on the overall variability of the risk model. Tornado diagrams graphically show the correlation between variations in model inputs and the distribution of the outcomes; in other words, they highlight the greatest contributors to the overall risk. Figure 17 is a tornado diagram for a portion of the Panama Canal Third-Lane Locks expansion project. The length of the bars on the tornado diagram corresponds to the influence of the items on the overall risk. Figure 17 depicts only a portion of the tornado diagram from one analysis of technical risks on the project.

Figure 17: Example of sensitivity analysis with tornado diagram

4.5. Risk Analysis Methods

The selection of a risk analysis method requires an analysis of what input risk measures are available and what types of risk output measures are desired. The following paragraphs describe some of the most frequently used quantitative risk analysis methods and an explanation of the input requirement and output capabilities. These methods range from simple, empirical methods to computationally complex, statistically based methods.

4.5.1. Traditional Methods

Traditional methods for risk analysis are empirically developed procedures that concentrate primarily on developing cost contingencies for projects. The method assigns a risk factor to various project elements based on historical knowledge of relative risk of various project elements. For example, pavement material cost may exhibit a low degree of cost risk, whereas acquisition of rights-of-way may display a high degree of cost risk. Project contingency is determined by multiplying the estimated cost of each element by its respective risk factors. This method profits from its simplicity and does produce an estimate of cost contingency. However, the project team's knowledge of risk is only implicitly incorporated in the various risk factors. Because of the historical or empirical nature of the risk assessments, traditional methods do not promote communication of the risk consequences of the specific project risks. Likewise, this technique does not support the identification of specific project risk drivers. These methods are not well adapted to evaluating project schedule risk.

4.5.2. Analytical Methods

Analytical methods, sometimes called second-moment methods, rely on the calculus of probability to determine the mean and standard deviation of the output (i.e., project cost). These methods use formulas that relate the mean value of individual input variables to the mean value of the variables' output. Likewise, there are formulas that relate the variance (standard deviation squared) to the variance of the variables' output. These methods are most appropriate when the output is a simple sum or product of the various input values. The formulas below show how to calculate the mean and variance of a simple sum.

For sums of risky variables, Y = x1 + x2 ; The mean value is E(Y) = [E(x1) + E(x2)] and the variance is sigma sub Y squared = sigma sub x1 squared + sigma sub x2 squared

For products of risky variables, Y = x1 * x2 ; The mean value is E(Y) = [E(x1) * E(x2)] and the variance is sigma sub Y squared = ( E(x1) squared * sigma sub x2 squared ) + ( E(x2) squared * sigma sub x1 squared ) + ( sigma sub x1 squared * sigma sub x2 squared )

Analytical methods are relatively simple to understand. They require only an estimate of the individual variable's mean and standard deviation. They do not require precise knowledge of the shape of a variable's distribution. They allow specific knowledge of risk to be incorporated into the standard deviation values. They provide for a practical estimate of cost contingency. Analytical methods are not particularly useful for communicating risks; they are difficult to apply and are rarely appropriate for scheduled risk analysis.

4.5.3. Simulation Models

Simulation models, also called Monte Carlo methods, are computerized probabilistic calculations that use random number generators to draw samples from probability distributions. The objective of the simulation is to find the effect of multiple uncertainties on a value quantity of interest (such as the total project cost or project duration). Monte Carlo methods have many advantages. They can determine risk effects for cost and schedule models that are too complex for common analytical methods. They can explicitly incorporate the risk knowledge of the project team for both cost and schedule risk events. They have the ability to reveal, through sensitivity analysis, the impact of specific risk events on the project cost and schedule.

However, Monte Carlo methods require knowledge and training for their successful implementation. Input to Monte Carlo methods also requires the user to know and specify exact probability distribution information, mean, standard deviation, and distribution shape. Nonetheless, Monte Carlo methods are the most common for project risk analysis because they provide detailed, illustrative information about risk impacts on the project cost and schedule.

Figure 18 shows typical probability outputs from a Monte Carlo analysis. The histogram information is useful for understanding the mean and standard deviation of analysis results. The cumulative chart is useful for determining project budgets and contingency values at specific levels of certainty or confidence. In addition to graphically conveying information, Monte Carlo methods produce numerical values for common statistical parameters, such as the mean, standard deviation, distribution range, and skewness.

Figure 18: Typical Monte Carlo output for total costs

4.5.4. Probability or Decision Trees and Influence Diagrams

Probability trees are simple diagrams showing the effect of a sequence of multiple events. Probability trees can also be used to evaluate specific courses of action (i.e., decisions), in which case they are known as decision trees. Probability trees are especially useful for modeling the interrelationships between related variables by explicitly modeling conditional probability conditions among project variables. Historically, probability trees have been used in reliability studies and technical performance risk assessments. However, they can be adapted to cost and schedule risk analysis quite easily. Probability trees have rigorous requirements for input data. They are powerful methods that allow the examination of both data (aleatory) and model (epistemic) risks. Their implementation requires a significant amount of expertise; therefore, they are used only on the most difficult and complex projects. Figure 19 presents a typical probability tree analysis.

Figure 19: Example of decision tree or event tree

4.6. Conclusions

The risk analysis process can be complex because of the complexity of the modeling required and the often subjective nature of the data available to conduct the analysis. However, the complexity of the process is not overwhelming and the benefits of the outcome can be extremely valuable. Many methods and tools are available for quantitatively combining and assessing risks. The selected method will involve a tradeoff between sophistication of the analysis and its ease of use. Adherence to sound risk analysis techniques will lead to more informed decisionmaking and a more transparent allocation of project risk.

4.7. Illustration: Risk Analysis and Range Cost Estimate

The following describes how the risks assessed in the Chapter 3 illustration were quantitatively assessed for inclusion in a risk-based cost estimate for the US 555-SH 111 interchange project. It also provides a range output for the project cost.

US 555-SH 111 Interchange Project Risk Analysis

QDOT management has determined that it will conduct a rigorous risk analysis for the project. It will use this information to develop a comprehensive risk management plan and generate a range cost estimate to communicate the uncertainty in the project to the internal and external stakeholders. The team determined that the most appropriate method to generate a range estimate is a Monte Carlo simulation. The team also wanted to use the sensitivity analysis and other output from the simulation model to support the risk management plan.

The consultant continued the elicitation process to gather more detailed information from the team members on quantitative measurements for cost and schedule risks. Two examples are shown here. This information was integrated with the project estimate to generate a range estimate.

Figure 20: Range estimate for project costs