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Chapter 9 of Integrated Cost-Schedule Risk Analysis (978-0-5660-9166-7) by David Hulett

Integrated Cost and Schedule Risk Analysis : Method and Case Study Basic Results


In Chapter 8 we illustrated the fundamental principles and results of integrated cost and schedule risk analysis. These principles used a very simple home construction project with few resources and few risks.

In this chapter we will show how to implement integrated cost and schedule on a somewhat more complicated schedule. In this chapter we continue to focus on the fundamental risks to drive the Monte Carlo simulation by using the Risk Driver method first introduced in Chapter 6 applied to cost risk but applied now to schedule and cost risk using the schedule as the model, as shown briefly in Chapter 8. This chapter shows what happens when risks are assigned to more than one activity and when some activities have several risks assigned to them. We have some uncertainties with 100 percent probability and some risk events with less than 100 percent probability in the list of risks.

The result of doing the risk analysis this way is that we are able to:

  • estimate the risk to the overall project schedule

  • estimate the cost risk of the project, taking into account the impact of schedule risk on cost risk directly and clearly

  • prioritize the risks, which is essential for efficient risk mitigation.


Prioritizing the risks using the Monte Carlo simulation model enables us to identify the important risks. For instance, many of the risks to cost are actually risks to schedule, operating on activities with resources that have costs that depend on the activities’ durations.

Conducting risk mitigation is important because we do not want to give the project a report card but rather a tool to improve performance.

  • If the project manager believes that the risk analysis is like grading his homework he will be unenthusiastic about the exercise and will not be willing or cooperative when his team leads are bothered by workshops, meetings and interviews. In fact some of these project managers will argue with the results or discard them instead of deriving benefits for the project.

  • However, if the project manager sees the exercise as providing information and a tool enabling management to be proactive in mitigating project risk he may become enthusiastic and even be a champion of the process.

  • Sometimes, of course, project managers need to be told to do risk analysis before they can learn to embrace it. If the customer or owner wants the risk analysis done, or has a corporate policy that risk analysis is to be done, say before major decision points, then the project manager may be forced to cooperate. This sometimes works since some of these managers become believers after experiencing risk analysis.

The chapter develops the integrated cost and schedule risk analysis in a logical progression:

  • Review and improve the schedule logic.

  • Incorporate the project budget through assigning costed resources to activities in the schedule.

  • Use the Risk Register as the basis of in-depth quantitative risk data interviews.

  • Model the application of risks to the schedule durations and cost elements for a Monte Carlo simulation.

  • Derive results such as the contingency reserves of time and cost as well as the prioritization of risks to time and cost.

  • Lead the project team in workshops to develop a risk mitigation strategy for better project results. Analyze the mitigation strategies to determine their net impact on project time and cost risk.

  • Compute the risk-adjusted cash flow and compare it to the budget for the project to determine the feasibility of the project if the budget is specified in advance.


Integrated Cost-Schedule Risk Analysis Case Study

The Summary Schedule

The project that is the subject of this case study is still a simple project, but in this chapter we focus on overall schedule and cost risk. The project is another construction project, shown in Figure 9.1.

It may seem illogical to start with a schedule when the objective is to derive a cost risk assessment, but it is the best way to reflect the effect of schedule risks on cost risk and to identify separately schedule risk and cost risk impacts on cost risk for risk mitigation. Finally, if we want to know which risks are most important to determining the need for a cost contingency reserve we need to account for the schedule risks because their impact on cost risk is sometimes greater than the risks that are usually thought of as cost risks.1 [69]

Figure 9.1 Simplified schedule of a 27-month construction project


Time-Dependent and Time-Independent Resources

Since the project schedule is the basis of the cost risk analysis we need to incorporate the entire contingency-free budget into the schedule. This is done using resources, which also give us the opportunity to distinguish between time-dependent and time-independent resources.

  • Time dependent resources include labor, rented equipment and any resource that charges by the amount of time it is employed, such as tower cranes, drill rigs or heavy lift barges. Their costs will be affected by risks to schedule that cause them to work more days and to be paid more. The durations of the activities are key ingredients of the Basis of Estimate (BOE) that reflects the fact that the cost and schedule are, at least initially in the approved baseline, consistent with each other. When schedule risk occurs, the assumptions of the BOE are changed and the current cost estimate (not the baseline cost estimate) needs to reflect the new durations for time-dependent resources. It is common that the cost estimate does not reflect the project schedule after the project starts because the cost estimators and schedulers may not communicate with each other. They may even not be in the same department. Schedule events are often not transmitted to the cost estimators to incorporate into their current estimate.

  • Time-independent resources are often procured items such as equipment and bulk materials. If the procurement process is longer than expected, the project schedule and delivery dates may change but the equipment and materials may not cost more because of the longer process. However, the cost to the project of equipment and bulk materials is usually uncertain, but just not because of the time it takes to fabricate and deliver the items after the procurement has been approved. Analysts and management are tempted to put subcontracts in this time-independent category if the subcontract is fixed price. Sometimes fixed price means fixed price and sometimes it is just the basis for claims that will be settled later, usually increasing the price paid to the subcontractor. In general we need to be skeptical and not rely on the certainty of fixed prices when we analyze cost risk.

The resources need not be detailed to be used in an integrated cost and schedule risk analysis. Indeed, identifying the resources at a summary level may be preferable for the risk analysis. It becomes more difficult to price detailed resources and place them on the activities. Experience shows that you can analyze multi-billion dollar projects with 8 to 12 summary resources. These summary resources cannot be used for resource planning or resource leveling because they are too general for that. But keeping the resources at the summary level makes the loading of the project budget feasible and accurate both in the overall total cost sense and the time phasing of the budget to individual activities. These are both crucial to the success of the integrated cost and schedule risk analysis. The example case study uses the resources shown below in Figure 9.2.

Figure 9.2 Summary resources used to place the project budget in the schedule2 [70]


Notice that the procurement resource is designated as “Materials” whereas all the others are “Labor.” This means that the Monte Carlo simulation using the Primavera Risk Analysis Risk Factors Module will treat the effect of risks on procurement differently depending on its type. Any risk that is assigned to an activity with procurement resources will vary the activity as follows:

  • Schedule risk on procurement activities may delay the fabrication and delivery of procured equipment, and hence any installation or commissioning successor activities, but will not change the cost.

  • A cost risk assigned to that activity will affect the cost of the procured equipment even if the schedule is not risky, that is, independent of its schedule risk.


The other resources are designated as “Labor” resources. The cost of those resources can be affected using the Risk Driver approach (implemented in Pertmaster’s Risk Factors Module)3 [71] in two ways:

  • Any schedule risk that is assigned to an activity with labor resources will affect the activity’s cost proportionately to the impact on the activity’s duration, since the average burn rate per day will be extended (or reduced in the case of opportunities) by the number of days the risk adds (or subtracts). The proportionality assumption can be interpreted as reflecting agnosticism concerning when during the activity the risk occurs. The risk may stretch out the peak labor period, or may stretch out the mobilization or demobilization periods, but we are not sure. Hence, the default option of proportionality is appropriate. This consideration is particularly important for summary schedules in which the activities are often longer than for the detailed schedules.

  • Any cost risk applied to labor resources will affect the burn rate per day. This applies to the burn rate on the scheduled duration as well as on the added (or subtracted) duration caused by schedule risks. Variation in the burn rate can reflect changes from baseline in the number of labor resources actually working on the activity or their average pay per day or both. Optimally these changes would be communicated to the cost estimators, and the risks may actually arise from discussions with the cost estimators. Varying the burn rate using a cost-type risk on time-dependent resources will cause uncertainty in those costs even when the schedule is fixed.


Notice that each resource is given a value of $1. That means that the units of the resources applied to any activity will be the total value of that resource for that activity.

Assigning the Resources to the Activities

Adding these resources to the project schedule in this chapter’s case study yields a total project cost of $624,220 thousand. The cost by activity is shown in Figure 9.3 below. Notice that the milestones that represent moments in time do not take resources or cost.

Figure 9.3 Activities with resources added to a total of $624,220 thousands


To see how these estimates are built up from resources, Figure 9.4 shows the two resources, CONS and PMT, that are assigned to the construction of the facility activity and add up to $335,800 thousand.

Figure 9.4 Resources assigned to the construction activity


Notice that the entire budget is remaining cost for this project that has no progress recorded yet because the project is still in the planning phase. Notice too that when the $322,000 thousand construction budget is assigned to construction the program automatically spreads this amount to the 460 working days of the construction activity and calculates a daily rate of $700 thousand.

The resource assignments by activity are shown in Table 9.1 below. Notice that the project management team (PMT) is spread over all activities whereas the other resources are generally assigned to one activity. If this were a real schedule of hundreds (but, hopefully, not thousands) of activities, each of these areas such as construction of the facility would be comprised of several, perhaps tens of activities. In that case the resource shown here would be spread as the estimator feels it should be over all of the construction activities, and the sum of the assigned resources would equal the budget for that particular resource.

Table 9.1 Resources applied to the schedule activities










Activity total


Approval process










Construction permits




















Procurement of equipment










Install equipment










Construction of the facility




















Resource total









In Figure 9.5 we see the resource loading in the schedule.

Figure 9.5 Schedule showing resource loading


Detailed vs. Summary Schedules and Resources

Some schedulers and cost estimators who do not have experience with loading resources are concerned that resource loading will prove to be an insurmountable task. They are thinking of identifying and loading 50 to 100 resources in some detail. Of course loading many detailed resources, particularly on detailed schedules with thousands of activities, would be a daunting task. We have seen resources listed down to the named individual level for multi-hundred million dollar programs, so even this is possible.9 [72] Other programs have loaded detailed resources but not costed them. In this case the resources should be good for planning purposes but, without associated costs, are one step short of helping us with the cost implication of the schedule.

The main way to look at resource loading of the budget as feasible is to consider summary resources to be sufficient and to construct a summary schedule. The natural reaction of schedulers when resource loading is discussed evokes the detailed approach using both detailed schedules and detailed resources. This approach would work to do integrated cost and schedule risk analysis but it is difficult and not necessary to the generation of valuable risk analysis results. Summary schedules that include all of the work and summary resources that can place the entire project budget on the schedule is the least-aggravating way to go and should be chosen whenever possible. Executing a risk analysis with the summary schedule and cost approach is better than complaining how hard it would be to identify and load detailed schedules with detailed resources and then not doing it.

Identifying the Risks

Notice that the title of this subsection is identifying the risks, not specifying the risk. This distinction is deliberate since we are using the Risk Driver approach wherein we specify the probability of occurring, impact range in multiplicative terms and the activities that they affect for individual risks, whether they are uncertainties or risk events.

We also distinguish and specify separately the schedule impacts and the cost impacts, where:

  • The schedule impacts affect the duration of the activity and will affect the cost of any time-dependent resources assigned to the activity.

  • The cost impacts affect the burn rate of the time-dependent resources and the total cost of the time-independent resources. Hence the effect of the cost impact depends on whether any resource assigned to the activity is time dependent or time independent.


The emphasis on using the Risk Driver approach in this chapter and indeed in much of this book (see Chapter 6) is not to imply that the traditional 3-point estimate approach has no place in integrated cost and schedule risk analysis. There are at least three main ways to specify the risk, and each has its role in a risk analysis. These are:

  • Risk Drivers allow risks to affect the duration of the activities that are included in the schedule.

  • The existence risks, also represented by the Risk Register method in Primavera Risk Analysis, allows the analyst to specify discontinuous activities, such as recovery after a failed test, that are not generally included in the schedule.

  • Three-point estimates can be used to represent uncertainty, usually the error in estimating activity durations or project element costs. In specifying this uncertainty it is important to abstract the estimating uncertainty ranges from the additional effect of risk events, since the risk events are included in the Risk Drivers or as existence risks.


The benefits of focusing on the risks that are usually found in the Risk Register rather than on the impact of the risks on activity durations (the traditional 3-point estimate of durations) should become clear, especially in the risk mitigation section. Unfortunately the use of Risk Drivers limits the Monte Carlo software choices today, but this is not necessarily a permanent condition.

The initial list of risks is found in the Risk Register that should be available from the qualitative risk analysis. The Risk Register includes a prioritized list of risks, perhaps risks grouped as “high,” “moderate,” and “low” in their importance for the project. Optimally the Risk Register specifies the risks that are important for different objectives, and the ones we need to look at are those important for time and for cost. Risks to scope, quality or other objectives may have time or cost implications, and if those are important the Risk Register should indicate their cost and schedule implications.

The list of risks from the Risk Register will probably not be complete and the risk interviews tend to uncover additional risks that are added to the expanding risk list. Participating in the risk interviews or risk workshop can and will cause some to think of risks that were never on the list. This creative activity of identifying new risks is encouraged by the risk interviewer.

Specifying the Parameters of the Risks

A project risk is an uncertain event or condition that, if it occurs, has a positive or negative on at least one project objective (PMI 2008). This definition of project risk usually refers to risk events that may or may not happen with some probability. In this analysis of integrated cost and schedule risk we need to include uncertainties that are not uncertain in their probability of occurring but have uncertain impacts. The definition also refers to “risks that matter” (Hillson and Simon 2007), which are those with probabilities and impacts on cost or schedule that are sufficiently large to be material. The definition highlights the need to interview (or gather in a workshop) to collect data on both probability of occurring and impact.

We typically interview the project teams and subject matter experts (SMEs), perhaps interviewing as many as 30 to 40 different people or small groups of people with the same area of expertise. Suppose we have done this and the reports from different interviewees/workshop participants differ on the relevant probabilities and impacts for at least some of the risks. Since the participants have different personal experiences with projects they have different impressions about probability and impact. What is the risk analyst to do with these different inputs on the same risks?

We typically gather the inputs from different interview sources together for each risk and examine them. The risk interviewer and perhaps others from the project management office (PMO) have been in all of the workshops and interviews and know which interviewees were most knowledgeable about which risk. The inputs from the most knowledgeable would be given more weight, but the inputs from others should not be entirely discounted. It would be difficult to construct a set of rules to give various weights (importance) to different respondents. Ultimately the risk lead must conclude which quantitative probability and impact range parameters are going to be used for each risk.

Suppose we have finished the interviews or workshops and have concluded that the risks with their parameters are those shown in Table 9.2 below.

Table 9.2 Risk Drivers’ probability and impact ranges quantified

Risk Driver

Sched. Opt.

Sched. ML

Sched. Max

Cost Opt.

Cost ML

Cost Max


Design complexity may challenge engineers








Site conditions/site access may slow logistics





Equipment suppliers may be busy








Capable management may not be assigned





Permitting agency may be slow





Activity duration estimates are inaccurate





Cost estimate is inaccurate





Key engineering personnel may be unavailable








An examination of the Risk Drivers and their parameters indicates that several risks are deemed to impact schedules, and hence may impact costs of time-dependent resources, but not to have impacts in addition to these on the resources’ burn rate (for time dependent resources) or total cost (for time-independent resources). These risks have blank cells under the three cost range column headings. There is one entry that has cost uncertainty implications but does not affect the schedule.

Risk Events and Uncertainties

Notice that there are two uncertainties: activity duration estimates are inaccurate and cost estimate is inaccurate. (All of the other risks represent specific risk events and have the word “may” in them, indicating that they may occur or not and their probabilities are less than 100 percent.) But the uncertainties are not risk events. They are certain to occur and their probabilities (far right-hand column in Table 9.2) are listed at 100 percent.

The schedule uncertainty and cost uncertainty can be handled (in Primavera Project Risk) by using 3-point estimates on activity durations and resources. This indicates that the traditional 3-point estimate and the Risk Driver approach can coexist if they are used properly. Since the 3-point estimate only varies the impact on activities’ duration it is only appropriate to be used for uncertainties such as errors in estimating durations. There is a parallel operation to put 3-point estimates on resources which represents cost estimating error. In addition if the 3-point estimate were called upon to represent the impact on the activity’s cost or duration of more than one risk we get back into murky waters. That is, developing 3-point estimates of impact representing the combined impact of more than one risk is a tricky calculation to do off-line and it is best left to the modelling process. The interviewee needs to make a number of calculations and approximations in his head to create the compound 3-point estimates. If there are two or more uncertainties on costs or on schedule durations it is best to make them Risk Drivers. Using Risk Drivers the Monte Carlo simulation process will develop during the simulation the appropriate probability distribution of cost or of schedule durations from application of multiple risks to the activity and its resources. (See Chapter 6, which illustrates this process with two risks on a single cost element.)

Assigning the Risks to Activities

Suppose we have a project with the activities shown in Figure 9.1 above and resources/costs as shown in Figure 9.2 and distributed as in Table 9.1 above. Also, suppose we have interviewed for the probability and time/cost impacts as shown previously in Table 9.2 above. After the risks are listed and their parameters quantified they need to be assigned to the activities and their resources. For this case study the risks are assigned according to Table 9.3.

The risks, called “Risk Factors” in Primavera Risk Analysis, are indicated in the schedule for each activity in Figure 9.6.

Table 9.3 Assigning risks to activities



Approval process




Install equipment



Design complexity may challenge engineers



Site conditions/site access may slow logistics



Equipment suppliers may be busy



Capable management may not be assigned




Permitting agency may be slow


Activity duration estimates are inaccurate







Cost estimate is inaccurate







Key engineering personnel may be unavailable







Figure 9.6 Risk Drivers (called risk factors) appear in the schedule


Simulating the Resource-Loaded Schedule

The resource- and risk-loaded schedule is simulated. Each iteration will produce both schedule dates and costs that are consistent with each other. This simulation will provide the traditional schedule and cost histograms and cumulative distributions. In addition we will be able to look at time-cost scatter plots and probabilistic cash flows.

Occasionally someone will ask about the number of iterations that should be used. Without getting technical the following seems to work for simulating the resource-loaded schedule:

  • For draft results for which the analyst is gaining information, testing alternative modelling strategies and making comparisons that will not make it into the final report, 1,500 iterations seems to be sufficient.

  • For final report simulations more iterations are recommended, in the 3,000–5,000 iteration range. The results may not be much different from the draft runs, but the resulting distributions seem to be smoother and the customer of the analysis feels better with more iterations.


The balance of this chapter covers the results and their interpretation, as well as the use of the model to assist in the development of risk mitigation plans.

Schedule Risk Results

The schedule histogram for the case study is below in Figure 9.7. It shows that the deterministic date of 29 April 2012 is about 9 percent likely to be achieved following the current plan and without further risk mitigation actions. If we assume that the project stakeholders have agreed that their acceptable level of confidence is at the 80th percentile, it is 80 percent likely that the current project plan with all of its risks will finish on or before 22 October 2013.

Given these results, this project needs about a 5.8-month contingency reserve of time from its scheduled date to its P-80 date. At the P-80 point the project is expected to finish on that date or earlier with a probability of 80 percent, and finish later with a 20 percent probability. These results are shown in Figure 9.7 and in Table 9.4.

Figure 9.7 Histogram with cumulative distribution (S-curve) for the project completion date


Table 9.4 Summary schedule risk analysis results for the example construction project









29 Apr 13






Schedule dates at percentiles


8 Apr 13

6 Aug 13

22 Oct 13

10 Jan 14






Difference from deterministic







Cost Risk Results

The cost risk results, including the impact on cost of schedule risk, indicate the need for a contingency reserve of cost of about $124 million or 20 percent at the 80th percentile. At that level there is an 80 percent probability that the project will cost $748 million or less, given the risks and following the current plan. Remember that these results incorporate the impact of schedule risk on the cost of time-dependent resources. These results are shown below in Figure 9.8 and Table 9.5.

Figure 9.8 Histogram with cumulative distribution (S-curve) for the project cost


Table 9.5 Summary cost risk analysis results for the example construction project ($ millions)















Cost at pecentiles





Difference from deterministic cost $






Difference from deterministic cost %





Source of Cost Risk: Is it from Cost or Schedule Risks?

Above we have seen standard results. However, while the cost risk results appear to be conventional, we know that the cost results are affected by the schedule risk and uncertainty as well as the cost risks and uncertainty. This additional content of the source of cost risk in the integrated analysis results occurs automatically when the resources are put into the schedule with their costs as previously shown.

One thing we can do is to see to what extent the schedule risks have affected the cost risk results. What is the contribution of the hard work we expended putting the resources into the schedule with their contingency-free costs and then simulating the resource-loaded schedule? We can find out whether cost-type risks or schedule-type risks are more important in determining the cost contingency to the P-80 point. The source of the cost contingency can be discovered by eliminating all schedule risks to compute the marginal impact of cost risks, then repeating the process by eliminating the cost risks and computing the impact of schedule risks on contingency. The results are shown below in Table 9.6.

Table 9.6 Sources of cost contingency reserve by risk type



Marginal impact


($ millions)

Contingency-free cost estimate


All risks


Add only cost risks



Add only schedule risks



Total of two adds


Total contingency


Note: amounts do not add at P-80

Table 9.6 shows that if only cost-type risks (burn rate risks and equipment cost risks) were added the contingency could be $49 million, whereas if only schedule risks were added (duration risk) the contingency would be $89 million. These results depend on the case study assumptions, but in many examples of integrated cost and schedule risk conducted on projects the majority of the risk to cost arises from uncertainty in the schedule rather than from cost-type risks such as uncertain equipment costs.

Notice also that the sum of the two “Adds” is $138 million, which is more than the total cost contingency reserve of ($748 − $624 = $124) $124 million. This is a case of “curves do not sum except at their means.” When the mean values are considered, the sum of the two means is $75.6 million and the total contingency at the mean is $76.9 million, a very similar number.

Contribution of Cost and Schedule Risks to Overall Cost Risk

Comparing the contribution to the total contingency, Figure 9.9 shows the cumulative distributions for the curve with just the cost risks, the curve with just the schedule risks and the total risk curve with both cost and schedule risk are included. It indicates that any analysis of cost risk that does not take account of both cost-type and schedule-type influences on project risk is underestimating cost risk. This comparison shows the basis and the value of integrating cost and schedule risk.

Figure 9.9 The impact on the contingency reserve of schedule risks exceeds that of cost risks incorporating both sources of risk produces a full risk effect



The purpose of integrating cost and schedule risk analysis is to capture the impact on cost risk of risks that are initially seen as affecting activity durations or otherwise delaying the project.[73] [73] Historically most cost risk analyses were based on parametrics or on cost risks alone, with perhaps some nod toward the possible effects of uncertain schedules. In recent years we have seen that it is possible to integrate the two, schedule and cost risk analyses, to provide a more complete and consistent picture of project cost and schedule risk.

In the process of integrating cost and schedule risk we have captured the mechanism, direction and magnitude of influence of schedule uncertainty on cost uncertainty. The mechanism is through the impact of delays on the cost of time-dependent resources. The direction of influence is clearly from schedule to cost. The magnitude of the influence depends on both probability and impact of the schedule risk as well as the activity or activities that it affects. A few modern Monte Carlo simulation packages can model this relationship directly and accurately.

Including the impact of schedule risk on cost risk we achieve two main benefits:

  • We produce a better, more accurate and complete cost risk analysis result.

  • We can identify the main drivers of cost risk, many of which may be risks to schedule, which is described in Chapter 10.


In this chapter we applied the Risk Driver method to the integrated risk analysis of cost and schedule.

  • Because this book emphasized cost risk analysis in the previous chapters we needed to introduce the project schedule, which will be our platform for the integrated analysis.

  • We make the distinction between time-dependent and time-independent resources.

  • We illustrate the process of assigning resources to the schedule activities, inserting the entire project budget in the project schedule. The resource-loaded schedule becomes our platform for cost risk analysis, and as an intermediate product the schedule risk analysis.

  • A common question is whether to use detailed or summary schedules and resources. Summary schedules and resources are perfectly adequate and even preferred because:

    • − a risk analysis is a strategic analysis;

    • − we are interested in a best-practice schedule;

    • − we are not using these resources for leveling.


  • Identifying the important strategic risks is usually based on the risks prioritized using qualitative risk analysis methods and included in the Risk Register. Risk interviews often unearth additional risks, and some risks are dropped while others may be consolidated. Often even very large projects (for example, multi-billion dollar energy construction projects) can be risked with 20–40 risks.

  • We have distinguished risks from uncertainties. “Risk” usually refers to risk events with probabilities of less than 100 percent, while “uncertainties” are often 100 percent likely but with impact uncertainty. Uncertainties can be handled with Risk Drivers or traditional 3-point estimates.

  • Different methods of representing risk can be used together in the same risk analysis and Monte Carlo simulation:

    • − Three-point estimates can represent estimating error for durations or costs.

    • − Existence risks can represent a discontinuous event such as failing a qualifying test and the required recovery activities not usually in the schedule.

    • − Risk Drivers that represent the uncertainty in the durations of activities that are already in the plan and schedule.


  • Assigning risks to activities can lead to some risks impacting multiple activities and some activities being impacted by multiple risks, if they occur. This is how risks impact the project schedule and cost so we are modelling reality. The method has another benefit – a risk’s total impact on the schedule and cost of a project can be isolated and measured even if it affects multiple activities. This characteristic will be important in developing risk mitigation actions, discussed in the next chapter.

  • We have performed simulations of the schedule-based cost and schedule risk model and have achieved both schedule and cost results. Though the cost results appear to be like the other cost risk results in earlier chapters, these results have directly and clearly incorporated the influence of uncertain schedule on costs.

  • We have seen that schedule risk can contribute significantly to cost risk, making the point that cost and schedule risk need to be analyzed together in an integrated way in order to estimate the complete risk to project cost.

In the next chapter results more specifically linked to the integration of cost and schedule risk are presented.


[1] It is interesting that these same consumers of project planning and control information usually refuse to consider a contingency reserve of time for schedules while they insist on contingency on cost estimates. The estimation of realistic costs and of durations is similarly affected by project risk and should be treated similarly, with contingency reserve for project risk required by both.

[2] These observations are based on 20 years of project risk analysis experience. Since project risk analysis may be practiced on projects that are already in trouble, the sample may be biased. However, it does us no good to assume a perfect world of unbiased cost estimates and fair dealing when it comes to bidding a cost figure, when there is evidence that this is not always practiced.

[3] In this author’s experience the likelihood of success for the original schedule can be much less than 50 percent – even less than 1 percent – and that of cost success can be less as well, although with the addition of a contingency reserve of cost it is less likely that cost success is in such jeopardy.

[4] Later, in Chapter 6 we will show how to use quantitative risk analysis to prioritize individual risk events more accurately than possible with usual qualitative techniques.

[5] Project elements could include procured items, construction of specific project elements, installation and commissioning or testing, programming of a specific software element, fabrication of a component, engineering, and spread (level of effort) costs such as project management or quality control.

[6] Since adding contingency reserves to cost estimates is common, and is usually required, the risk analysis is re-analyzing the specific risks to develop a realistic contingency reserve that is appropriate to the specific project. In scheduling it is uncommon to find a contingency reserve of time included in the schedule, so a schedule risk analysis is analyzing the risks to the schedule often for the first time. For the cost contingency result of a risk analysis we have something in the standard cost estimate to compare, but in the schedule risk analysis there is usually no time contingency in the original schedule for comparison purposes.

[7] Some of the most important risks to project cost are risks to the project schedule, which cause resources to work longer and hence increase cost. We introduce integration of cost and schedule risk analysis in Chapters 8 to 10.

[8] The software used here is Crystal Ball, a Microsoft Excel add-in, developed by Decisioneering which has been acquired by Oracle.

[9] The MOM will not apply accurately, and is not recommended for, cost models that have multiplicative formulae such as “quantity multiplied by unit cost.” Monte Carlo simulation works in that case, however, and is more robust and therefore the best practice standard approach. Simulation is discussed in the next section.

[10] In Chapter 6 the Risk Driver approach to cost risk analysis shows that we can incorporate risk events that have a chance to occur or not and if they occur to have an impact on the project element’s cost, in our analysis. At this point there is nearly a 100 percent likelihood that the cost will differ from the estimated project element’s cost.

[11] This image was created in @RISK for Excel from Palisade Corporation.

[12] A table of the normal standard distribution is provided in Appendix A. A Table of the right half of the normal distribution in terms of any distribution’s mean and standard deviation is provided in Appendix A. Find the percent of a standard deviation that provides an 80 percent likelihood of success.

[13] There are more than two “moments” that describe probability distributions shapes, including skewness, and the like. In project risk analysis we need to deal only with the first two moments, the mean and the standard deviation of variance.

[14] This chart was created in @RISK 5.0 for Excel from Palisade corporation.

[15] The simulations in this chapter were conducted with 10,000 iterations and each simulation took less than 5 seconds. Of course the spreadsheet has been kept small to be used for illustrative purposes, but even larger spreadsheets simulate rapidly.

[16] Note that the sums of the optimistic and pessimistic values in Table 3.1 would have been $1,455 and $2,475 respectively, outside of the lowest and highest values out of 10,000 generated by the simulation. The simulation results differ because there is cancelling out in each iteration – where one cost element is high in its range another may be low, moderate or high in its own range. The elements’ costs are considered to be independent of one another and there is no correlation between costs in this example. This is why summing those columns in Table 3.1 is not professional and not advised.

[17] Of course, when the standard contingency calculation has been overridden by the application of political pressure, it becomes essentially unusable.

[18] Two popular simulation software packages that add in to Microsoft Excel are Crystal Ball from Oracle and @RISK from Palisade Corporation. Each of these is used in this book. There are other simulation tools as well, several of them simulating project schedules.

[19] This chapter is taken largely from Chapter 5 of Practical Schedule Risk Analysis, David Hulett, Gower Publishing, 2009, since the data quality issues in schedule and cost risk are much the same.

[20] Using the Risk Drivers approach, which is introduced in Chapter 6 the separate impacts of uncertainties and of risk events can be represented with their own probability and 3-point estimate of impact.

[21] Craig Peterson, then President of the Project Management Institute’s Risk Management Specific Interest Group has often said that the Risk Management chapter of the PMI’s PMBOK® Guide would be only one page with: “This Page Left Intentionally Blank” if it only reflected current practice at most companies.

[22] The earned value data had been projecting significant cost overruns for some time before cancellation of the A-12 project. The corporate culture of the contractors and the Navy overrode those forecasts for months.

[23] On one project the new estimate was about 25 percent over the early estimate and it took many briefings before the concept of a new estimate based on a risk analysis was accepted.

[24] See Flyvbjerg, B., Holm, M.S., and Buhl, Søren (2002) for some examples of optimistic estimating in public transportation projects.

[25] A classic article by pioneers in this discipline is Amos Tversky and Daniel Kahneman, (1974). This section is based on that article. A recent compendium of more recent articles is Gilovich, T., Griffin, D., and Kahneman, D., (2002), which is an edited compendium of articles in this discipline.

[26] Tversky and Kahneman, ibid., 1129.

[27] Some risk analysts prefer to collect risk data in workshops with many attendees. One serious problem with this approach is that strong personalities or high-ranking attendees may dominate the workshop and intimidate others who have information to contribute. There is no way for the facilitator to correct for this except to ask the dominating persons to leave the room, a hard thing to do.

[28] This section draws from Salim and Hulett, 2008.

[29] These figures were created by Crystal Ball, a program that simulates models created in Microsoft Excel. Crystal Ball, created by Decisioneering, is now owned by Oracle.

[30] We have assumed that these project elements’ costs are independent. An alternative assumption could be that they are correlated. The difference is between a correlation coefficient of 0.0 for independent and a coefficient close to 1.0 for perfect positive correlation. See Chapter 5, Correlation.

[31] The analyst can put different parameters into the software and generate different (wider) triangles. A common situation occurs when the interviewees state that their numbers are “the P-10 and P-90 values.” The analyst will use 10 percent and 90 percent for the parameters and the Trigen function will extend the triangle’s optimistic and pessimistic tails out so that there is 10 percent probability below the value called the “P-10” and 10 percent probability above the value called the “P-90” value by the interviewees.

[32] The same correction factor also works well with the BetaPERT distribution.

[34] There is also negative correlation in which high costs of one project element tend to coincide with low costs of another element. We do not see negative correlation much in project risk analysis.

[35] Causality going the opposite direction would be illogical –- subcontract management will not drive the cost of the subcontract.

[36] Each of these project elements will be varying within their own probability distribution so the fluctuation in cost of one project element is generally not the same as that for the other correlated element of the pair even if correlation is perfect (coefficient of 1.0).

[37] In the most recent PMBOK® Guide (Project Management Institute 2008) the mistake was made to add up the low and high extreme ranges of project cost estimates for all three project elements shown in Figure 11.13. In earlier editions the temptation was avoided, and we have also not summed those columns in Figure 3.1.

[38] In these examples the risk was assigned and a simulation of 10,000 iterations was run. The resulting 10,000 pairs of costs were saved to Microsoft Excel and its correlation function calculated the correlation coefficient between the two project element’s costs. In other words, we are creating correlation, not assuming correlation, with these experiments.

[39] In the next section we discuss how difficult choosing the coefficient may be.

[40] This finding differs from that in schedule risk analysis. The cost model we are using is a simple summation model where the mean is the same with or without correlation. In schedule risk analysis the schedule has a structure of paths, some of which are in parallel that merge at major milestones. This structure is the reason the Method of Moments does not work for schedules but does work for simple summation cost estimate risk analysis. See Appendix 1: The Problem with PERT in Hulett (2009).

[41] In statistical terms, this matrix is not positive semi-definite. See Risk Glossary Website (2010).

[42] Crystal Ball is made and sold by Decisioneering, a unit of Oracle.

[44] In discussions with John Neatrour in January 2010, I learned that it has been shown that the commonly used approach of Gaussian Elimination to correcting correlation matrices that are not positive semi-definite can cause false negative results in some circumstances. Although some analysts use Gauss Elimination to perform the test for positive semi-definiteness of Eigenvalues to weed out bad correlation matrices this practice is not well advised. Standard texts on numeric analysis such as Stoer and Bulirsch (1980) and Press, Vetterling, Teukolsky, and Flannery (2002) do not recommend Gauss Elimination for finding Eigenvalues of symmetric matrices. Instead Jacobi rotation and Cholesky decomposition are preferred because the pivoting problems that have to be dealt with to make Gauss Elimination stable do not appear.

[45] The Risk Driver approach introduced in Chapter 6 models the creation of correlation, eliminating the need to estimate correlation coefficients and the possibility of trying to impose an inconsistent correlation matrix on the simulation. This is just one of the benefits of the Risk Driver approach to project risk analysis.

[46] This chapter is derived from Hulett, Hornbacher and Whitehead (2008) and Hulett (2009b). This chapter is also similar to Chapter 8 in Hulett (2009a) which introduces the risk driver method applied to schedule risk analysis.

[47] These criticisms also apply to the standard schedule risk analysis approaches, which are based on the application of 3-point estimates to schedule activity durations.

[48] Chapters 710 introduce the integration of cost and schedule risk analysis that takes the full effect of schedule on cost into account.

[49] In this chapter we are using a cost and cost risk model developed in Microsoft Project and using @RISK from Palisade. The equivalent exercise can be successful using Crystal Ball from Oracle.

[50] The figures in this chapter were generated using @RISK for Excel from Palisade Corporation.

[51] The correlation coefficient of 45 percent is found by running the simulation of these two project elements 10,000 times, exporting the cost A – cost B pairs to Excel and running Excel’s correlation function on the data.

[52] The cost risk sensitivity tornado diagrams are based on correlation concepts that are themselves defined relative to the means of the input and output distributions. The risks that are important at the P-80 level may not be those that are important in describing differences from the distributions’ means.

[53] Appendix B describes the spreadsheet’s structure and logic to accomplish these steps

[54] Earlier in the project life cycle the cost and schedule and their risk analysis are conducted parametrically. This book does not cover parametric analysis of cost and schedule.

[55] Some risk analysts recommend conducting schedule risk with schedules as small as 25–30 activities, although it is difficult to count on such a small schedule being able to take all of the strategic risks of the project and the key logical dependencies.

[56] The PMI definition of a “schedule” as a set of completion dates is wrong. The schedule is the set of input data and rules that produce important dates and critical paths, along with other information, as outputs, not inputs. See PMI (2008), A Guide to the Project Management Body of Knowledge, Newtown Square, PA, Project Management Institute.

[57] It would be naïve to assume that all project participants (team leads, schedulers) are given the permission to make objective, realistic and most-likely duration estimates, or that the scheduler has all the knowledge to do so available to him.

[58] This figure and several others shown below are screen shots from Primavera Risk Analysis, formerly Pertmaster Risk Expert, now owned by Oracle.

[59] There are some software utilities that could cause a cost curve with a shape other than uniform, but these are really in beta test at this time.

[60] There are even some people, mostly in aerospace, who are trying to implement parametric methods on schedules. This may be because the parametric approach is all they know and they are unfamiliar with the profession of scheduling. This development calls for integrating the two staffs and forcing them to talk regularly.

[61] This topic is covered in more detail in Chapter 4.

[62] In this approach the risks from the Risk Register drive the simulation. In more traditional approaches the activity durations and component costs are given a 3-point estimate of potential impact. These 3-point estimates, introduced in Chapter 2, result from the workings of, potentially, several risks, the influences of which are difficult to disentangle. We are using the Risk Driver approach that is introduced in Chapter 6.

[63] According to NASA Policy Directive (NPD) 1000.5A, Policy for NASA Acquisition (Revalidated March 17, 2010), Programs are to be baselined or rebaselined and budgeted at a confidence level at which there is a 70 percent (or the level approved by the decision authority of the responsible Agency-level management council) chance of project cost and schedule success.

[64] The examples in this chapter and the next use the Risk Factors Module of Primavera Risk Analysis (previously Pertmaster). Primavera Risk Analysis will read projects from Primavera P3 and P6, Microsoft Project and Open Plan Professional. If the project is scheduled in Microsoft Project the @RISK for Project tool can be configured to derive most of these results.

[65] Basic cost impacts of project schedule risks can be calculated with risks specified as 3-point estimates on durations in Risk+ from Deltek, which is a Microsoft Project add-in.

[66] This figure and other figures in this chapter are derived using Primavera Risk Analysis. The author has no financial interest in this software product or Oracle that owns it.

[67] Time and cost may not be proportional depending on when the risk occurs, whether the activity is a highly mobilized state or not. However, since we do not know when during the construction period this risk will occur it is acceptable to assume proportionality.

[68] “Programs are to be baselined or rebaselined and budgeted at a confidence level of 70 percent or the level approved by the decision authority of the responsible Agency-level management council. For a 70 percent confidence level, this is the point on the joint cost and schedule probability distribution where there is a 70 percent probability that the project will be completed at or lower than the estimated amount and at or before the projected schedule. The basis for a confidence level less than 70 percent is to be formally documented” (NASA, 2010).

[69] This logically leads to cost estimators and cost risk analysts needing to be familiar with project scheduling. Experience shows that schedules need to be checked, particularly for complete logic, before they can be certified as fit for Monte Carlo simulation, and the risk analyst may be the one to check the schedules. Hence the analysis of costs starts with the project schedule and the analyst needs to be comfortable with project schedules. Some analysts may need to be retrained, which will help to make their practice of risk analysis more inclusive and accurate.

[70] The images in this chapter come from Primavera Risk Analysis (formerly Pertmaster), an Oracle product.

[71] Some other simulation software can be configured to do the same processes. @RISK from Palisade can replicate some of these functions if configured correctly.

[72] The specific project mentioned was a program with a lot of time to do the planning and an expert scheduler-cost estimator combination in the project controls office that thought resource loading was the only way to do scheduling and cost estimating right.

[73] Most risks are threats that cannot help the schedule or cost, or are mostly threats with the pessimistic results outweighing the optimistic results. This is not to rule out opportunities that can improve the schedule or cost estimate. It just recognizes reality that it is easier to delay the project, given the types of schedules we see, than to accelerate it. Experience tells us this is true (Flyvbjerg et al. 2002).

[74] This calculation is made by taking the 3,000 pairs of cost and dates into Microsoft Excel and specifying a “Linest” function with a constraint. In other words, the slope does not represent the line’s starting at the origin but at a positive dollar figure that fits the data.

[75] The JCL policy is located in NPD 1000.5 under Section H3 with “Joint cost and schedule confidence levels are to be developed and maintained for the life cycle cost and schedule associated with the initial lifecycle baselines (for example, for space flight programs and projects baselines established at KDP-I or KDP-C).”

[76] “Risk critical” means that, with risks considered, that path will usually be longer than parallel paths and it will generally determine the schedule’s finish date.

[78] The Risk Driver concept is discussed in Hulett, D. Practical Schedule Risk Analysis (2009 Gower) in Chapter 6.

Integration of Cost and Schedule Risk Analysis

[79] Even if the contract specifies a “fixed price” contract, there will be circumstances leading to schedule delays that may be “compensable” so the contractor will get more than originally budgeted.

[80] The Risk Driver method available today exists in the Risk Factors module of Primavera Risk Analysis, formerly Pertmaster, from Oracle.

[81] Pertmaster created the Risk Factors module in 2007 for a client. The author and an associate, Waylon Whitehead, specified the objectives of the module and de-bugged the initial versions. Since that time the module has shipped with Pertmaster / Primavera Risk Analysis.



Flyvbjerg, B. , Holm, M.S. , and Buhl, Søren (2002). “Underestimating Costs in Public Works Projects, Error or Lie?” Journal of the American Planning Association, vol. 68, (No. 3).


Hillson, D. and Simon, P. (2007). Practical Project Risk Management: The ATOM Methodology. Vienna, VA, Management Concepts.


Hulett, D. (2009). Practical Schedule Risk Analysis. Farnham, England, Gower Publishing.


NASA PA&E (2009). Joint Confidence Level (JCL) FAQ.


PMI (2008). A Guide to the Project Management Body of Knowledge. Newtown Square, PA, Project Management Institute.

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