## PMI-RMP®

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# PMI-RMP Perform Quantitative Risk Analysis Tutorial

## 8.1 Perform Quantitative Risk Analysis

Hello and welcome to the Project Management Institute’s Risk Management Professional Certification Preparatory Course offered by Simplilearn. This is the eighth lesson of this course. In this lesson, we will discuss the fourth process of project risk management processes, which is “Perform Quantitative Risk Analysis”. Let us begin with the objectives of this lesson in the next screen.

## 8.2 Objectives

After completing this lesson, you will be able to: Explain the purposes and objectives List the tools and techniques Describe EMV analysis List the uses of Monte Carlo analysis Describe probability distribution In the next screen, we will discuss the purposes and objectives of the perform quantitative risk analysis process.

## 8.3 Purposes and Objectives

Performing quantitative risk analysis provides a numerical estimate of the overall effect of risk on the objectives of the project. It is used to evaluate the likelihood of success in achieving the project objectives, and to estimate contingency reserve which is usually applicable for time and cost. Quantitative risk analysis is not mandatory especially for smaller projects. However, it helps in calculating estimates of the overall project risk which is the main focus of this process. In the next screen, we will discuss what is required for the effective implementation of overall risk analysis.

## 8.4 Implementation of Overall Risk Analysis

The implementation of overall risk analysis requires complete and accurate representation of the project objectives built from individual project elements. For example, project schedule (Read as: ske-jule) or cost estimate. The next requirement is to identify risks on individual project elements such as schedule activities or line-item costs, at a level of detail that lends itself to specific assessment of individual risks. Also, inclusion of generic risks, that have a broader effect than individual project elements helps in overall risk analysis. The final requirement is to apply a quantitative method using Monte Carlo simulation that incorporates multiple risks simultaneously. This helps in determining the impact on the overall project objective. Monte Carlo is a modeling and simulation tool which is used to predict the overall impact of the decisions you make for a project. We will discuss this simulation tool in detail in the later part of this lesson. In the next screen, we will find out what happens to the risk after the implementation of overall risk analysis.

## 8.5 Overall Risk Analysis—Post Implementation

In this screen, we will understand what can be predicted after implementing the overall risk analysis. It answers the following: First, implementation of risk analysis will help us realize the probability of meeting the project objectives. Next, it will give us an idea of how much contingency reserve is needed. Note that, here contingency refers to budget and timeline. Once the risk analysis process is implemented, you will come to know which are the line-item costs or schedule activities that contribute more risks when all risks are considered simultaneously. Then, the implementation of overall risk analysis will help us figure out which individual risk contribute the most to overall project risk. Additionally, estimating the overall project risk using quantitative methods help us in identifying the projects where quantified risks threaten objectives beyond the tolerance of the stakeholders. Lastly, it helps us find out which project objectives have risks that are well within acceptable tolerances. Overall risk management becomes simpler once the factors given on the screen can be predicted. Let us discuss some of the high-level comparisons between qualitative and quantitative risk analysis, in the next screen.

## 8.5 Overall Risk Analysis—Post Implementation

In this screen, we will understand what can be predicted after implementing the overall risk analysis. It answers the following: First, implementation of risk analysis will help us realize the probability of meeting the project objectives. Next, it will give us an idea of how much contingency reserve is needed. Note that, here contingency refers to budget and timeline. Once the risk analysis process is implemented, you will come to know which are the line-item costs or schedule activities that contribute more risks when all risks are considered simultaneously. Then, the implementation of overall risk analysis will help us figure out which individual risk contribute the most to overall project risk. Additionally, estimating the overall project risk using quantitative methods help us in identifying the projects where quantified risks threaten objectives beyond the tolerance of the stakeholders. Lastly, it helps us find out which project objectives have risks that are well within acceptable tolerances. Overall risk management becomes simpler once the factors given on the screen can be predicted. Let us discuss some of the high-level comparisons between qualitative and quantitative risk analysis, in the next screen.

## 8.6 Qualitative and Quantitative Risk Analysis—High Level Comparison

Qualitative risk analysis addresses individual risks descriptively; and it assesses the discrete probability of occurrence and impact on project objectives if risk occurs. This type of analysis also helps to prioritize individual risks for subsequent treatment it adds to the risk register; and finally, it leads to quantitative risk analysis. On the other hand, quantitative risk analysis predicts the likely project outcomes based on combined effects of risks; and it uses probability distribution to characterize the risk related to cost and schedule values. It involves the usage of a quantitative method and requires specialized tools, like Monte Carlo simulation. Quantitative risk analysis estimates the likelihood of achieving targets and contingency needed to achieve the desired level of comfort. It also identifies risks which can have the greatest effect on the overall project.

## 8.6 Qualitative and Quantitative Risk Analysis—High Level Comparison

Qualitative risk analysis addresses individual risks descriptively; and it assesses the discrete probability of occurrence and impact on project objectives if risk occurs. This type of analysis also helps to prioritize individual risks for subsequent treatment it adds to the risk register; and finally, it leads to quantitative risk analysis. On the other hand, quantitative risk analysis predicts the likely project outcomes based on combined effects of risks; and it uses probability distribution to characterize the risk related to cost and schedule values. It involves the usage of a quantitative method and requires specialized tools, like Monte Carlo simulation. Quantitative risk analysis estimates the likelihood of achieving targets and contingency needed to achieve the desired level of comfort. It also identifies risks which can have the greatest effect on the overall project.

## 8.7 Critical Success Factors

As discussed earlier in this lesson, while managing the overall risk management process, particularly for large projects, you have to make the quantitative risk analysis process a success as it provides a clear picture in the form of numerical value. Some of the critical success factors to perform quantitative risk analysis process are as follows: prior risk identification and qualitative risk analysis, appropriate project model, commitment to collecting high-quality risk data, unbiased data, overall project risk derived from individual risks, and interrelationships between risks in quantitative risk analysis. Click each tab to learn more. Prior risk identification and qualitative risk analysis: Before performing quantitative risk analysis, you need to identify all the important risks associated with the project. In other words, all the important risks must be taken into account before analyzing them quantitatively. Appropriate project model: An appropriate project model should be used as the basis of quantitative risk analysis. Some of the models are project schedule for time, line-item cost estimate for cost, decision tree for risk, etc. The outcome of perform quantitative risk analysis process depends on the selected project model. Commitment to Collecting High-Quality Risk Data: You can collect high-quality risk data with the help of interviews, workshops, and expert judgment. This calls for time, resources, and management support. Unbiased Data: There are two common sources of bias called motivational and cognitive bias. Motivational bias is where someone tries to bias the result in one direction or another and cognitive bias is where bias occur as people are using their best judgment and applying heuristics. It is important to dispose the biased data and use the unbiased data. Overall Project Risk Derived from Individual Risks: The perform quantitative risk analysis process is based on a methodology that correctly derives the overall project risk from individual risks. For cost estimation and time scheduling, Monte Carlo simulation is the best. A decision tree is used when the future events are uncertain. Risks are specified at the level of detailed tasks or line-item costs, and incorporated into the model of the project to calculate the effects on project objectives like cost, time, etc. Interrelationships between risks in quantitative risk analysis: You need to analyze and find out if individual risks in the project model are related. For example, several risks may have a common root cause and they might occur together. For the successful execution of the quantitative risk analysis process, you need to correlate and link risks that have a common root cause. In the next screen, we will discuss the perform quantitative risk analysis process and its ITTOs that is, inputs, tools and techniques, and output.

## 8.8 Inputs, Tools and Techniques, and Output

The inputs of perform quantitative risk analysis process are: risk register, risk management plan, cost and schedule management plans, enterprise environmental factors, and organizational process assets. These are basically the lessons learned from previous similar projects. The tools and techniques of perform quantitative risk analysis process are data gathering and representation techniques, quantitative risk analysis and modeling techniques, and expert judgment. The output of perform quantitative risk analysis process is the project documents updates, which include the overall impact on the project objective. In the next screen, we will discuss the inputs required to perform quantitative risk analysis process in detail.

## 8.9 Inputs

The first input is risk register as it identifies and categorizes risks, potential risk responses, and triggers warning signs. The second input is risk management plan and it includes roles and responsibilities, budget and schedule for risk management activities, risk breakdown structure (RBS), risk categories, probability and impact matrix, and risk tolerances. The third input, which is cost management plan establishes the criteria for making plans, structuring, preparing an estimate, budgeting, and establishing control over project costs. The fourth input is schedule management plan. This describes the scheduling methodology, the scheduling tool or tools to be used, and the format and established criteria for developing and controlling the project schedule (Read as: ske-jule). Enterprise environmental factors are the fifth input. These factors provide context and insight to risk assessment, like industry studies of similar projects conducted by risk specialists, and risk databases available from proprietary sources or the industry. Organizational process assets are the last input. These include existing processes that may impact a project's success. These may include policies, guidelines, historical information, or knowledge gained from previous projects. In the following screen, we will look into the tools and techniques that are used to perform quantitative risk analysis process.

## 8.10 Tools and Techniques

As mentioned earlier, there are 3 main techniques to perform quantitative risk analysis process called data gathering and representation techniques, quantitative risk analysis and modeling techniques, and expert judgment. Click each tab to learn more. Interviewing and probability distribution are the main techniques within this first tool. Interviewing techniques draw on experience and historical data, to quantify the probability and impact of risks on project objectives. Probability distribution is used extensively in modeling and simulation, representing the uncertainty in values such as duration of scheduled activities and costs of project components. There are four tools within quantitative risk analysis and modeling techniques. The first tool is sensitivity analysis, which describes the sensitivity of risk in terms of its impact on the entire project. It does not take into account the combination of risks, but considers single risks in isolation. Sensitivity analysis places a value on the impact of altering a single variable in a project by analyzing that impact on the project plan. The second tool is expected monetary value analysis, which assesses the average outcome of both known and unknown scenarios. This technique is popularly used in decision tree analysis. The third tool is decision tree analysis. It factors both probability and impact for each variable, indicating the decision providing the greatest expected value, when all uncertain implications and subsequent decisions are quantified. The last tool for quantitative risk analysis is modeling and simulation. This technique uses models that calculate the potential impact of events on the project, based on random input values. A popular tool used for modeling and simulation is the Monte Carlo simulation. Besides using the quantitative tools and techniques, the project manager needs to involve subject matter experts to analyze potential costs, identify schedule impacts, and validate risks. Additionally, the project manager must have the expertise to interpret data and identify strengths and weaknesses of the tools used. Expert judgment is required to identify potential cost and schedule impacts, to evaluate probability, and to define inputs such as probability distributions into the tools. Let us discuss a real life example in the next screen.

## 8.11 Sensitivity Analysis—Example

Jimmy is a construction project manager for a bridge project in New Jersey. He is just beginning quantitative analysis for his project and is notified from his boss that there might be a union strike in the near future. This would mean that some human resources, which are members of the union, might not show up for work, which is supposed to begin in three weeks. Jimmy immediately has the team begin reviewing near-term work packages to determine how many people might be needed to complete them, as well as other areas of the project where various types of work are required. After receiving the results later in the day, he conducts sensitivity analysis to see which areas of his project will be most impacted by the potential strike. Let us continue discussing the example in the next screen

## 8.11 Sensitivity Analysis—Example

Jimmy is a construction project manager for a bridge project in New Jersey. He is just beginning quantitative analysis for his project and is notified from his boss that there might be a union strike in the near future. This would mean that some human resources, which are members of the union, might not show up for work, which is supposed to begin in three weeks. Jimmy immediately has the team begin reviewing near-term work packages to determine how many people might be needed to complete them, as well as other areas of the project where various types of work are required. After receiving the results later in the day, he conducts sensitivity analysis to see which areas of his project will be most impacted by the potential strike. Let us continue discussing the example in the next screen

## 8.12 Sensitivity Analysis—Example (contd.)

Jimmy determines that the foundation work packages are the most impacted as many union employees will be mixing and pouring concrete. He also discovers that the transport areas of the project are also at risk because the concrete must be moved around the job location by construction vehicles. The least sensitive area appears to be designed as none of the engineers are members of the union. Jimmy forwards his results to his boss who uses it to negotiate with the union to avoid the strike. To further protect the project from the risk, Jimmy enters into a contract with another labor construction company to fill these positions in case the union decides to go on a strike later in the project. The proper use of sensitivity analysis enabled Jimmy to see which areas of his project were most impacted by the potential strike, and then to plan accordingly. Let us look into the characteristics of Tools and Techniques for the Perform Quantitative Risk Analysis Process in the next screen.

## 8.12 Sensitivity Analysis—Example (contd.)

Jimmy determines that the foundation work packages are the most impacted as many union employees will be mixing and pouring concrete. He also discovers that the transport areas of the project are also at risk because the concrete must be moved around the job location by construction vehicles. The least sensitive area appears to be designed as none of the engineers are members of the union. Jimmy forwards his results to his boss who uses it to negotiate with the union to avoid the strike. To further protect the project from the risk, Jimmy enters into a contract with another labor construction company to fill these positions in case the union decides to go on a strike later in the project. The proper use of sensitivity analysis enabled Jimmy to see which areas of his project were most impacted by the potential strike, and then to plan accordingly. Let us look into the characteristics of Tools and Techniques for the Perform Quantitative Risk Analysis Process in the next screen.

## 8.13 Tools and Techniques-Characteristics

Following are the characteristics of tools and techniques: The characteristics of tools and techniques are comprehensive risk representation, risk impact calculation, quantitative method appropriate to analyze uncertainty, and data gathering tools. Comprehensive Risk Representation: In case of comprehensive risk representation, risk models provide the risk representations that affect the project objective simultaneously. For example: quality and timeline. They also permit representation of both opportunities and threats.

## 8.14 Tools and Techniques-Characteristics (contd.)

A few other characteristics of tools and techniques are: effective presentation of quantitative analysis results, the elements and structure of quantitative risk analysis, iterative quantitative risk analysis, and information for response planning. Effective Presentation of Quantitative Analysis Results: In case of effective presentation of quantitative analysis results, the results from quantitative analysis are generally not available in standard methods or formats. For example, choosing the probability distribution, gives the following results: Whether the project can be completed within the time or budget, Contingency reserve requirement in terms of cost, time, or resource, and Identity or location of most important risks. Example of this is, sensitivity analysis in case of cost risk analysis or criticality analysis in case of schedule risk analysis. Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs. In case of Elements and Structure of Quantitative Risk Analysis, firstly, you need to prioritize risks, in other words, you need to perform qualitative risk analysis; after which you need to examine the interrelationships between the risks; and then you need to collect the high-quality risk data using project models like schedule (read as: ske-jule), cost estimate etc. Using the outputs of this method, you will be able to perform quantitative analysis. Here, you can use modeling techniques like Monte Carlo simulation, decision tree analysis etc., which provides answers to questions like: How likely is the project’s success after implementation of risk analysis? How much contingency is required to meet the targets? And, which are the risks that are of high priority? As discussed earlier, it is impossible to know all the risks in advance. So, iterative method is considered as the best to analyze risks as the project progresses. Information for Response Planning: For response planning, the overall contingency reserve in time and cost should be reflected in the project’s schedule (Read as: ske-jule) and budget. If adjustment is required in scope, then the changes are agreed upon between the stakeholders and documented. A new quantitative risk analysis is carried out to reflect the new aspects of the project. So far, we discussed the characteristics of tools and techniques for perform quantitative analysis process. We know that risks are analyzed based on the probability. Let us look into the basic principles of probability in the next screen.

## 8.15 Basic Principles of Probability

Quantitative risk analysis is strongly based on probability and statistics. The table on this screen provides details of basic principles of probability and its description. Here, we will discuss each principle and its description in detail. The first principle is sum of probabilities. The sum of the probabilities of all events that may occur should be equivalent to 1 or 100% The second principle is probability of single event. The probability of any single event must be greater than or equal to 0 (zero) and less than or equal to 1. The third principle is dependent joint events. Suppose, A and B are 2 dependent joint events. The probability of occurrence of events A and B will be denoted as P (A) and P (B) respectively. Then the probability of a dependent joint event will be calculated as product of P (A) and P (B/A) where P (B/A)denotes probability of occurrence of event B, provided event A has already occurred. The fourth principle is independent joint events. Suppose, A and B are 2 independent joint events. Then, the probability of an independent joint event will be calculated as product of P (A) and P (B) When the probability of joint events is the product of the probabilities of each, the events are considered to be independent. We will continue discussing the basics principles of probability in the next screen.

## 8.16 Basic Principles of Probability (contd.)

In this screen, let us look into other basic principles of probability such as mean, median, average, and standard deviation. Mean is defined as the sum of the events divided by the number of occurrences. Whereas, median is the number that separates the higher half of a probability distribution from the lower half. Average is the number which represents the data in a set. It is calculated by adding the values of a group of numbers and dividing the sum by the number of objects considered. Standard deviation is a measure of the spread of data, or the statistical dispersion of the values in your data set. In the next screen, we will focus on historical documentation.

## 8.17 Historical Documentation

One invaluable source of information for a project, is any available data on previous projects that were similar to the current one. There are many risks that will reoccur from one project to the next. To capitalize on lessons learned, you will need access and it must be well structured. It is also beneficial to talk to previous project stakeholders who can fill in any gaps in the information. Speaking to the previous project manager would be ideal. Do not be surprised if you find incomplete details as poor strategies are rarely documented. Examples of historical documentation includes previous risk plans, risk registers, contracts, project post-mortem documentation, change requests, cost and time estimates, etc. In the next screen, we will focus on Fault Tree Analysis.

## 8.18 Fault Tree Analysis

Fault Tree Analysis is also known as Failure Modes and Effects Analysis (FMEA). This type of model is structured to identify the points of failure that are risks by themselves, or in combinations with one another. In the example on the screen, you can understand what might happen as you progress into detailed levels of risks that could lead to a power outage. Let us discuss the system dynamics in the next screen.

## 8.19 System Dynamics

System Dynamics model represents the flow of information and interactions among stakeholders or teams on a project. It is useful for revealing feedback loops or feed-forward loops that can lead to risks. The feedback loop represents moving information back to a source waiting for a response while the feed-forward loop highlights an entity waiting for information that is necessary to perform an activity or function. In the example on the screen, there is a dissatisfied customer. If the dissatisfaction came after the sale then the Sales team will need the customer feedback. If the problem is related to functionality the Maintenance team will need information. Customer care may get involved if a rebate or warranty is involved and marketing will need to know if advertising mislead the customer before the purchase. You can see how the loops might become complex. In the next screen, we will understand the Expected Monetary Value or EMV analysis.

## 8.20 EMV Analysis

Expected Monetary Value analysis also called as EMV analysis is a method of calculating the average outcome when the future is uncertain. It is the product of the expected monetary value of an outcome and the probability that it will occur. It is used in decision tree analysis. It is calculated to find the best outcome, which is the lowest combination of cost and EMV. For example, if there is a probability of 50% of a machine breakdown and the impact of buying a new machine is \$80,000 then EMV = 50% times - 80,000 which is - 40,000. Here, let us consider the cost of buying a new machine as negative, as it is an add-on to the project which may become applicable if the risk of machine breakdown occurs. Let us discuss the Decision Tree Analysis with an example in the following screen.

## 8.21 Decision Tree Analysis

Let us see how the decision tree is used. EMV is popularly used in decision tree analysis. For example, let us think of a scenario where a primary contractor signs a contract with a customer and agrees to complete the work in 6 months, with a penalty clause of \$1,000 (Read as: one thousand dollars) for every one day of delay. The primary contractor wants to outsource a part of his work to a vendor and hence he has screened two vendors. Vendor A’s bid value is \$110,000 (Read as: one hundred ten thousand dollars) and Vendor B’s bid value is \$140,000 (Read as: one hundred forty thousand dollars). With vendor A, there is a 50% (Read as: fifty percent) probability of delay in completing his part of work by three months, and this will have an impact of \$90,000. On the other hand, with vendor B, there is a 10% (Read as: ten percent) probability of delay in completing his part of work by one month, and this will have an impact of \$30,000. Therefore, the expected monetary value with vendor A is 50% times \$90,000 which is \$45,000 and the expected monetary value with vendor B is 10% times \$30,000 which is \$3,000. Therefore, the cost of outsourcing the work to vendor A is \$110,000 + \$45,000 = \$155,000 (Read as: one hundred thousand dollars plus forty five thousand dollars equals one hundred fifty five thousand dollars) whereas the cost of outsourcing it to vendor B is \$140,000 + \$3,000 = \$143,000. In the next screen, let us move on to discuss the Monte Carlo analysis in detail.

## 8.22 Monte Carlo Analysis

Monte Carlo analysis is used for the estimation of time, cost, and the predictability of risk occurrence, in terms of probability. An example of Monte Carlo analysis is the three-point estimate (optimistic, most likely, and pessimistic). This tool uses the optimistic, most likely, and pessimistic estimates, and simulates various outcomes to predict a range of possible results. It is used to predict the likely outcome for schedules and costs. It uses sophisticated software applications and is very effective with large number of inputs. This tool is particularly effective while predicting the business risks. Let us discuss a real life example in the next screen.

## 8.23 Monte Carlo Software for Risk Modeling—Example

After deciding which risks require further analysis, Bob, a project manager with an IT company, decides to assess the overall project risk by quantifying the impact of several risks. During analysis he discovers that the impacts of several risks are beyond the company’s predetermined thresholds. Bob is concerned that this new development could mean that the project may have had unrealistic expectations set against it. He employs the use of Monte Carlo software for risk modeling. He carefully inputs all available data and discovers that there is a low probability of meeting the management determined finish date utilizing the available budget allotted for this project. Let us continue discussing the example in the next screen.

## 8.23 Monte Carlo Software for Risk Modeling—Example

After deciding which risks require further analysis, Bob, a project manager with an IT company, decides to assess the overall project risk by quantifying the impact of several risks. During analysis he discovers that the impacts of several risks are beyond the company’s predetermined thresholds. Bob is concerned that this new development could mean that the project may have had unrealistic expectations set against it. He employs the use of Monte Carlo software for risk modeling. He carefully inputs all available data and discovers that there is a low probability of meeting the management determined finish date utilizing the available budget allotted for this project. Let us continue discussing the example in the next screen.

## 8.24 Monte Carlo Software for Risk Modeling—Example (contd.)

Bob takes the supporting information to upper management and explains the precarious situation. Bob’s boss determines that the project is underfunded and also has an unrealistic finish date. Because Bob supported his conclusions with software, management decides to provide additional funding and postpones the projected finish date by sixty days. Bob then inputs the new budget and schedule data into the Monte Carlo program, which reflects a much higher probability of project completion. In the following screen, we will understand the probability distribution.

## 8.24 Monte Carlo Software for Risk Modeling—Example (contd.)

Bob takes the supporting information to upper management and explains the precarious situation. Bob’s boss determines that the project is underfunded and also has an unrealistic finish date. Because Bob supported his conclusions with software, management decides to provide additional funding and postpones the projected finish date by sixty days. Bob then inputs the new budget and schedule data into the Monte Carlo program, which reflects a much higher probability of project completion. In the following screen, we will understand the probability distribution.

## 8.25 Probability Distribution

This screen presents a representative picture of normal distribution. The normal or Gaussian distribution is a continuous probability distribution, defined on the entire real line, that has a bell-shaped probability density function, known as the Gaussian function or informally known as the bell curve. The normal distribution is said to be the most important probability distribution in statistics. When you plot a bell curve, you need to check whether the values plotted are falling outside or inside the bell curve. If a point falls inside the bell curve, the probability that the corresponding event will occur is positive. So, you can conclude that the bell curve is a visual depiction of the likelihood of events occurring. The events are plotted as values, and this representation in mathematical language is termed as probability density function (PDF). In the next screen, we will understand project risk ranking with an example.

## 8.26 Project Risk Ranking

Quantitative risk analysis helps in prioritizing the risks further on the project. For example, the table on this screen depicts the exposure of the top four risks on the project. You can manage about 73.6% (Read as: seventy three point six percent) of total project risk exposure if you have a strategy to deal with the first four risks. The project risk ranking table, as depicted in the screen, helps in the estimation of overall risk ranking for the final deliverable. The risks which can hinder the final deliverable of the project can be assigned with individual risk rankings, which in total can give a more accurate estimate of the overall risk ranking for the final deliverable. Using the risk ranking table, you can also compare projects and project risks by the risk ranking assigned. Based on that, the project sponsor can decide if a particular project is viable. In the next screen, we will understand how to perform quantitative risk analysis and what are the components updated during the quantitative risk analysis process.

## 8.27 Steps to Perform Quantitative Risk Analysis

To carry out quantitative risk analysis, you need to review the risk, cost, and schedule (Read as: ske-jule) management plans. Always begin with the original estimate of time or cost. Then calculate and assess the impact of changing the range of results on the overall project estimate. If this does not provide the required estimate, then you must refer to historical information. The other techniques of analyzing risks can be using the appropriate interviewing technique and obtaining probability distributions from stakeholders and subject matter experts, depicting the distributions in a PDF, performing a sensitivity analysis, and conducting a project simulation. Once you perform quantitative risk analysis process, you must update the risk register, project management plan, and other project documents. This analysis cannot be done alone. So, it is essential to involve the stakeholders as well. In the following screen, we will discuss the output of Perform Quantitative Risk Analysis process.

## 8.28 Perform Quantitative Risk Analysis Output

The output of perform quantitative risk analysis process is the project documents updates. This includes a probabilistic analysis of the project, the probability of fulfilling cost and time objectives, a prioritized list of quantified risks, and trends in the results of quantitative risk analysis. In the next screen, we will discuss the various components of quantitative risk analysis updates.

## 8.29 Components of Quantitative Risk Analysis Update

A point of interest here is that risks are further prioritized according to the threat or opportunity they pose on the project. Now, let us see some of the components which will be updated. The first component is probabilistic analysis of the project. Here, once risks are qualitatively and quantitatively analyzed, the project team should be able to forecast the possible completion dates and costs, and provide a level of confidence for each decision. The next component is probability of fulfilling the cost and time objectives. Using quantitative risk analysis, the project team can estimate the likelihood of fulfilling the project objectives with the current plan and knowledge of the project risks. The third component is prioritized list of quantified risks. Here, identified risks are prioritized according to the threat they pose or the opportunity they present to the project. This prioritized list includes a measure of the impact of each identified risk. The last component is trends in quantitative risk analysis results. Repeating the quantitative risk analysis process helps the project's risk management team to analyze the trends and make adjustments as necessary. Information on the project schedule, cost, quality, etc., and performance gained through the quantitative risk analysis process will help the team to prepare a quantitative risk analysis report. In the next screen, we will understand how to document the results of perform quantitative risk analysis process.

## 8.30 Documenting the Results

Let us look into a few points which are documented upon completing this process. The contingency reserve calculated in the quantitative project cost and schedule (Read as: ske-jule) risk analysis to be incorporated into the cost estimate and schedule, is documented. Contingency reserve established to capture the opportunities that are judged to be priorities of the project. If the contingency reserve exceeds the time or resource available which changes the scope and plan, then these have to be documented. And finally, the results of quantitative risk analysis must be recorded and passed on to the project management team for further actions to be taken. Let us move on to the quiz questions to check your understanding of the concepts covered in this lesson.

## 8.32 Summary

Here is a quick recap of what was covered in this lesson: ? Performing quantitative risk analysis provides a numerical estimate of the overall effect of risk on the project objectives. ? The three techniques to perform quantitative risk analysis process are Data gathering and representation techniques, Quantitative risk analysis and modeling techniques and, Expert judgment. ? EMV analysis is a method of calculating the average outcome when the future is uncertain. ? Monte Carlo analysis is used to predict likely outcome for schedules and costs. ? The Normal or Gaussian distribution is a continuous probability distribution, defined on the entire real line that has a bell-shaped probability density function, known as the Gaussian function or informally known as the bell curve.

## 8.33 Conclusion

This concludes, Perform Quantitative Risk Analysis. The next lesson covers, Plan Risk Responses.

## 8.1 Perform Quantitative Risk Analysis

Hello and welcome to the Project Management Institute’s Risk Management Professional Certification Preparatory Course offered by Simplilearn. This is the eighth lesson of this course. In this lesson, we will discuss the fourth process of project risk management processes, which is “Perform Quantitative Risk Analysis”. Let us begin with the objectives of this lesson in the next screen.

## 8.2 Objectives

After completing this lesson, you will be able to: Explain the purposes and objectives List the tools and techniques Describe EMV analysis List the uses of Monte Carlo analysis Describe probability distribution In the next screen, we will discuss the purposes and objectives of the perform quantitative risk analysis process.

## 8.3 Purposes and Objectives

Performing quantitative risk analysis provides a numerical estimate of the overall effect of risk on the objectives of the project. It is used to evaluate the likelihood of success in achieving the project objectives, and to estimate contingency reserve which is usually applicable for time and cost. Quantitative risk analysis is not mandatory especially for smaller projects. However, it helps in calculating estimates of the overall project risk which is the main focus of this process. In the next screen, we will discuss what is required for the effective implementation of overall risk analysis.

## 8.4 Implementation of Overall Risk Analysis

The implementation of overall risk analysis requires complete and accurate representation of the project objectives built from individual project elements. For example, project schedule (Read as: ske-jule) or cost estimate. The next requirement is to identify risks on individual project elements such as schedule activities or line-item costs, at a level of detail that lends itself to specific assessment of individual risks. Also, inclusion of generic risks, that have a broader effect than individual project elements helps in overall risk analysis. The final requirement is to apply a quantitative method using Monte Carlo simulation that incorporates multiple risks simultaneously. This helps in determining the impact on the overall project objective. Monte Carlo is a modeling and simulation tool which is used to predict the overall impact of the decisions you make for a project. We will discuss this simulation tool in detail in the later part of this lesson. In the next screen, we will find out what happens to the risk after the implementation of overall risk analysis.

## 8.5 Overall Risk Analysis—Post Implementation

In this screen, we will understand what can be predicted after implementing the overall risk analysis. It answers the following: First, implementation of risk analysis will help us realize the probability of meeting the project objectives. Next, it will give us an idea of how much contingency reserve is needed. Note that, here contingency refers to budget and timeline. Once the risk analysis process is implemented, you will come to know which are the line-item costs or schedule activities that contribute more risks when all risks are considered simultaneously. Then, the implementation of overall risk analysis will help us figure out which individual risk contribute the most to overall project risk. Additionally, estimating the overall project risk using quantitative methods help us in identifying the projects where quantified risks threaten objectives beyond the tolerance of the stakeholders. Lastly, it helps us find out which project objectives have risks that are well within acceptable tolerances. Overall risk management becomes simpler once the factors given on the screen can be predicted. Let us discuss some of the high-level comparisons between qualitative and quantitative risk analysis, in the next screen.

## 8.6 Qualitative and Quantitative Risk Analysis—High Level Comparison

Qualitative risk analysis addresses individual risks descriptively; and it assesses the discrete probability of occurrence and impact on project objectives if risk occurs. This type of analysis also helps to prioritize individual risks for subsequent treatment it adds to the risk register; and finally, it leads to quantitative risk analysis. On the other hand, quantitative risk analysis predicts the likely project outcomes based on combined effects of risks; and it uses probability distribution to characterize the risk related to cost and schedule values. It involves the usage of a quantitative method and requires specialized tools, like Monte Carlo simulation. Quantitative risk analysis estimates the likelihood of achieving targets and contingency needed to achieve the desired level of comfort. It also identifies risks which can have the greatest effect on the overall project.

## 8.7 Critical Success Factors

As discussed earlier in this lesson, while managing the overall risk management process, particularly for large projects, you have to make the quantitative risk analysis process a success as it provides a clear picture in the form of numerical value. Some of the critical success factors to perform quantitative risk analysis process are as follows: prior risk identification and qualitative risk analysis, appropriate project model, commitment to collecting high-quality risk data, unbiased data, overall project risk derived from individual risks, and interrelationships between risks in quantitative risk analysis. Click each tab to learn more. Prior risk identification and qualitative risk analysis: Before performing quantitative risk analysis, you need to identify all the important risks associated with the project. In other words, all the important risks must be taken into account before analyzing them quantitatively. Appropriate project model: An appropriate project model should be used as the basis of quantitative risk analysis. Some of the models are project schedule for time, line-item cost estimate for cost, decision tree for risk, etc. The outcome of perform quantitative risk analysis process depends on the selected project model. Commitment to Collecting High-Quality Risk Data: You can collect high-quality risk data with the help of interviews, workshops, and expert judgment. This calls for time, resources, and management support. Unbiased Data: There are two common sources of bias called motivational and cognitive bias. Motivational bias is where someone tries to bias the result in one direction or another and cognitive bias is where bias occur as people are using their best judgment and applying heuristics. It is important to dispose the biased data and use the unbiased data. Overall Project Risk Derived from Individual Risks: The perform quantitative risk analysis process is based on a methodology that correctly derives the overall project risk from individual risks. For cost estimation and time scheduling, Monte Carlo simulation is the best. A decision tree is used when the future events are uncertain. Risks are specified at the level of detailed tasks or line-item costs, and incorporated into the model of the project to calculate the effects on project objectives like cost, time, etc. Interrelationships between risks in quantitative risk analysis: You need to analyze and find out if individual risks in the project model are related. For example, several risks may have a common root cause and they might occur together. For the successful execution of the quantitative risk analysis process, you need to correlate and link risks that have a common root cause. In the next screen, we will discuss the perform quantitative risk analysis process and its ITTOs that is, inputs, tools and techniques, and output.

## 8.8 Inputs, Tools and Techniques, and Output

The inputs of perform quantitative risk analysis process are: risk register, risk management plan, cost and schedule management plans, enterprise environmental factors, and organizational process assets. These are basically the lessons learned from previous similar projects. The tools and techniques of perform quantitative risk analysis process are data gathering and representation techniques, quantitative risk analysis and modeling techniques, and expert judgment. The output of perform quantitative risk analysis process is the project documents updates, which include the overall impact on the project objective. In the next screen, we will discuss the inputs required to perform quantitative risk analysis process in detail.

## 8.9 Inputs

The first input is risk register as it identifies and categorizes risks, potential risk responses, and triggers warning signs. The second input is risk management plan and it includes roles and responsibilities, budget and schedule for risk management activities, risk breakdown structure (RBS), risk categories, probability and impact matrix, and risk tolerances. The third input, which is cost management plan establishes the criteria for making plans, structuring, preparing an estimate, budgeting, and establishing control over project costs. The fourth input is schedule management plan. This describes the scheduling methodology, the scheduling tool or tools to be used, and the format and established criteria for developing and controlling the project schedule (Read as: ske-jule). Enterprise environmental factors are the fifth input. These factors provide context and insight to risk assessment, like industry studies of similar projects conducted by risk specialists, and risk databases available from proprietary sources or the industry. Organizational process assets are the last input. These include existing processes that may impact a project's success. These may include policies, guidelines, historical information, or knowledge gained from previous projects. In the following screen, we will look into the tools and techniques that are used to perform quantitative risk analysis process.

## 8.10 Tools and Techniques

As mentioned earlier, there are 3 main techniques to perform quantitative risk analysis process called data gathering and representation techniques, quantitative risk analysis and modeling techniques, and expert judgment. Click each tab to learn more. Interviewing and probability distribution are the main techniques within this first tool. Interviewing techniques draw on experience and historical data, to quantify the probability and impact of risks on project objectives. Probability distribution is used extensively in modeling and simulation, representing the uncertainty in values such as duration of scheduled activities and costs of project components. There are four tools within quantitative risk analysis and modeling techniques. The first tool is sensitivity analysis, which describes the sensitivity of risk in terms of its impact on the entire project. It does not take into account the combination of risks, but considers single risks in isolation. Sensitivity analysis places a value on the impact of altering a single variable in a project by analyzing that impact on the project plan. The second tool is expected monetary value analysis, which assesses the average outcome of both known and unknown scenarios. This technique is popularly used in decision tree analysis. The third tool is decision tree analysis. It factors both probability and impact for each variable, indicating the decision providing the greatest expected value, when all uncertain implications and subsequent decisions are quantified. The last tool for quantitative risk analysis is modeling and simulation. This technique uses models that calculate the potential impact of events on the project, based on random input values. A popular tool used for modeling and simulation is the Monte Carlo simulation. Besides using the quantitative tools and techniques, the project manager needs to involve subject matter experts to analyze potential costs, identify schedule impacts, and validate risks. Additionally, the project manager must have the expertise to interpret data and identify strengths and weaknesses of the tools used. Expert judgment is required to identify potential cost and schedule impacts, to evaluate probability, and to define inputs such as probability distributions into the tools. Let us discuss a real life example in the next screen.

## 8.11 Sensitivity Analysis—Example

Jimmy is a construction project manager for a bridge project in New Jersey. He is just beginning quantitative analysis for his project and is notified from his boss that there might be a union strike in the near future. This would mean that some human resources, which are members of the union, might not show up for work, which is supposed to begin in three weeks. Jimmy immediately has the team begin reviewing near-term work packages to determine how many people might be needed to complete them, as well as other areas of the project where various types of work are required. After receiving the results later in the day, he conducts sensitivity analysis to see which areas of his project will be most impacted by the potential strike. Let us continue discussing the example in the next screen

## 8.12 Sensitivity Analysis—Example (contd.)

Jimmy determines that the foundation work packages are the most impacted as many union employees will be mixing and pouring concrete. He also discovers that the transport areas of the project are also at risk because the concrete must be moved around the job location by construction vehicles. The least sensitive area appears to be designed as none of the engineers are members of the union. Jimmy forwards his results to his boss who uses it to negotiate with the union to avoid the strike. To further protect the project from the risk, Jimmy enters into a contract with another labor construction company to fill these positions in case the union decides to go on a strike later in the project. The proper use of sensitivity analysis enabled Jimmy to see which areas of his project were most impacted by the potential strike, and then to plan accordingly. Let us look into the characteristics of Tools and Techniques for the Perform Quantitative Risk Analysis Process in the next screen.

## 8.13 Tools and Techniques-Characteristics

Following are the characteristics of tools and techniques: The characteristics of tools and techniques are comprehensive risk representation, risk impact calculation, quantitative method appropriate to analyze uncertainty, and data gathering tools. Comprehensive Risk Representation: In case of comprehensive risk representation, risk models provide the risk representations that affect the project objective simultaneously. For example: quality and timeline. They also permit representation of both opportunities and threats.

## 8.14 Tools and Techniques-Characteristics (contd.)

A few other characteristics of tools and techniques are: effective presentation of quantitative analysis results, the elements and structure of quantitative risk analysis, iterative quantitative risk analysis, and information for response planning. Effective Presentation of Quantitative Analysis Results: In case of effective presentation of quantitative analysis results, the results from quantitative analysis are generally not available in standard methods or formats. For example, choosing the probability distribution, gives the following results: Whether the project can be completed within the time or budget, Contingency reserve requirement in terms of cost, time, or resource, and Identity or location of most important risks. Example of this is, sensitivity analysis in case of cost risk analysis or criticality analysis in case of schedule risk analysis. Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs. In case of Elements and Structure of Quantitative Risk Analysis, firstly, you need to prioritize risks, in other words, you need to perform qualitative risk analysis; after which you need to examine the interrelationships between the risks; and then you need to collect the high-quality risk data using project models like schedule (read as: ske-jule), cost estimate etc. Using the outputs of this method, you will be able to perform quantitative analysis. Here, you can use modeling techniques like Monte Carlo simulation, decision tree analysis etc., which provides answers to questions like: How likely is the project’s success after implementation of risk analysis? How much contingency is required to meet the targets? And, which are the risks that are of high priority? As discussed earlier, it is impossible to know all the risks in advance. So, iterative method is considered as the best to analyze risks as the project progresses. Information for Response Planning: For response planning, the overall contingency reserve in time and cost should be reflected in the project’s schedule (Read as: ske-jule) and budget. If adjustment is required in scope, then the changes are agreed upon between the stakeholders and documented. A new quantitative risk analysis is carried out to reflect the new aspects of the project. So far, we discussed the characteristics of tools and techniques for perform quantitative analysis process. We know that risks are analyzed based on the probability. Let us look into the basic principles of probability in the next screen.

## 8.15 Basic Principles of Probability

Quantitative risk analysis is strongly based on probability and statistics. The table on this screen provides details of basic principles of probability and its description. Here, we will discuss each principle and its description in detail. The first principle is sum of probabilities. The sum of the probabilities of all events that may occur should be equivalent to 1 or 100% The second principle is probability of single event. The probability of any single event must be greater than or equal to 0 (zero) and less than or equal to 1. The third principle is dependent joint events. Suppose, A and B are 2 dependent joint events. The probability of occurrence of events A and B will be denoted as P (A) and P (B) respectively. Then the probability of a dependent joint event will be calculated as product of P (A) and P (B/A) where P (B/A)denotes probability of occurrence of event B, provided event A has already occurred. The fourth principle is independent joint events. Suppose, A and B are 2 independent joint events. Then, the probability of an independent joint event will be calculated as product of P (A) and P (B) When the probability of joint events is the product of the probabilities of each, the events are considered to be independent. We will continue discussing the basics principles of probability in the next screen.

## 8.16 Basic Principles of Probability (contd.)

In this screen, let us look into other basic principles of probability such as mean, median, average, and standard deviation. Mean is defined as the sum of the events divided by the number of occurrences. Whereas, median is the number that separates the higher half of a probability distribution from the lower half. Average is the number which represents the data in a set. It is calculated by adding the values of a group of numbers and dividing the sum by the number of objects considered. Standard deviation is a measure of the spread of data, or the statistical dispersion of the values in your data set. In the next screen, we will focus on historical documentation.

## 8.17 Historical Documentation

One invaluable source of information for a project, is any available data on previous projects that were similar to the current one. There are many risks that will reoccur from one project to the next. To capitalize on lessons learned, you will need access and it must be well structured. It is also beneficial to talk to previous project stakeholders who can fill in any gaps in the information. Speaking to the previous project manager would be ideal. Do not be surprised if you find incomplete details as poor strategies are rarely documented. Examples of historical documentation includes previous risk plans, risk registers, contracts, project post-mortem documentation, change requests, cost and time estimates, etc. In the next screen, we will focus on Fault Tree Analysis.

## 8.18 Fault Tree Analysis

Fault Tree Analysis is also known as Failure Modes and Effects Analysis (FMEA). This type of model is structured to identify the points of failure that are risks by themselves, or in combinations with one another. In the example on the screen, you can understand what might happen as you progress into detailed levels of risks that could lead to a power outage. Let us discuss the system dynamics in the next screen.

## 8.19 System Dynamics

System Dynamics model represents the flow of information and interactions among stakeholders or teams on a project. It is useful for revealing feedback loops or feed-forward loops that can lead to risks. The feedback loop represents moving information back to a source waiting for a response while the feed-forward loop highlights an entity waiting for information that is necessary to perform an activity or function. In the example on the screen, there is a dissatisfied customer. If the dissatisfaction came after the sale then the Sales team will need the customer feedback. If the problem is related to functionality the Maintenance team will need information. Customer care may get involved if a rebate or warranty is involved and marketing will need to know if advertising mislead the customer before the purchase. You can see how the loops might become complex. In the next screen, we will understand the Expected Monetary Value or EMV analysis.

## 8.20 EMV Analysis

Expected Monetary Value analysis also called as EMV analysis is a method of calculating the average outcome when the future is uncertain. It is the product of the expected monetary value of an outcome and the probability that it will occur. It is used in decision tree analysis. It is calculated to find the best outcome, which is the lowest combination of cost and EMV. For example, if there is a probability of 50% of a machine breakdown and the impact of buying a new machine is \$80,000 then EMV = 50% times - 80,000 which is - 40,000. Here, let us consider the cost of buying a new machine as negative, as it is an add-on to the project which may become applicable if the risk of machine breakdown occurs. Let us discuss the Decision Tree Analysis with an example in the following screen.

## 8.21 Decision Tree Analysis

Let us see how the decision tree is used. EMV is popularly used in decision tree analysis. For example, let us think of a scenario where a primary contractor signs a contract with a customer and agrees to complete the work in 6 months, with a penalty clause of \$1,000 (Read as: one thousand dollars) for every one day of delay. The primary contractor wants to outsource a part of his work to a vendor and hence he has screened two vendors. Vendor A’s bid value is \$110,000 (Read as: one hundred ten thousand dollars) and Vendor B’s bid value is \$140,000 (Read as: one hundred forty thousand dollars). With vendor A, there is a 50% (Read as: fifty percent) probability of delay in completing his part of work by three months, and this will have an impact of \$90,000. On the other hand, with vendor B, there is a 10% (Read as: ten percent) probability of delay in completing his part of work by one month, and this will have an impact of \$30,000. Therefore, the expected monetary value with vendor A is 50% times \$90,000 which is \$45,000 and the expected monetary value with vendor B is 10% times \$30,000 which is \$3,000. Therefore, the cost of outsourcing the work to vendor A is \$110,000 + \$45,000 = \$155,000 (Read as: one hundred thousand dollars plus forty five thousand dollars equals one hundred fifty five thousand dollars) whereas the cost of outsourcing it to vendor B is \$140,000 + \$3,000 = \$143,000. In the next screen, let us move on to discuss the Monte Carlo analysis in detail.

## 8.22 Monte Carlo Analysis

Monte Carlo analysis is used for the estimation of time, cost, and the predictability of risk occurrence, in terms of probability. An example of Monte Carlo analysis is the three-point estimate (optimistic, most likely, and pessimistic). This tool uses the optimistic, most likely, and pessimistic estimates, and simulates various outcomes to predict a range of possible results. It is used to predict the likely outcome for schedules and costs. It uses sophisticated software applications and is very effective with large number of inputs. This tool is particularly effective while predicting the business risks. Let us discuss a real life example in the next screen.

## 8.23 Monte Carlo Software for Risk Modeling—Example

After deciding which risks require further analysis, Bob, a project manager with an IT company, decides to assess the overall project risk by quantifying the impact of several risks. During analysis he discovers that the impacts of several risks are beyond the company’s predetermined thresholds. Bob is concerned that this new development could mean that the project may have had unrealistic expectations set against it. He employs the use of Monte Carlo software for risk modeling. He carefully inputs all available data and discovers that there is a low probability of meeting the management determined finish date utilizing the available budget allotted for this project. Let us continue discussing the example in the next screen.

## 8.24 Monte Carlo Software for Risk Modeling—Example (contd.)

Bob takes the supporting information to upper management and explains the precarious situation. Bob’s boss determines that the project is underfunded and also has an unrealistic finish date. Because Bob supported his conclusions with software, management decides to provide additional funding and postpones the projected finish date by sixty days. Bob then inputs the new budget and schedule data into the Monte Carlo program, which reflects a much higher probability of project completion. In the following screen, we will understand the probability distribution.

## 8.25 Probability Distribution

This screen presents a representative picture of normal distribution. The normal or Gaussian distribution is a continuous probability distribution, defined on the entire real line, that has a bell-shaped probability density function, known as the Gaussian function or informally known as the bell curve. The normal distribution is said to be the most important probability distribution in statistics. When you plot a bell curve, you need to check whether the values plotted are falling outside or inside the bell curve. If a point falls inside the bell curve, the probability that the corresponding event will occur is positive. So, you can conclude that the bell curve is a visual depiction of the likelihood of events occurring. The events are plotted as values, and this representation in mathematical language is termed as probability density function (PDF). In the next screen, we will understand project risk ranking with an example.

## 8.26 Project Risk Ranking

Quantitative risk analysis helps in prioritizing the risks further on the project. For example, the table on this screen depicts the exposure of the top four risks on the project. You can manage about 73.6% (Read as: seventy three point six percent) of total project risk exposure if you have a strategy to deal with the first four risks. The project risk ranking table, as depicted in the screen, helps in the estimation of overall risk ranking for the final deliverable. The risks which can hinder the final deliverable of the project can be assigned with individual risk rankings, which in total can give a more accurate estimate of the overall risk ranking for the final deliverable. Using the risk ranking table, you can also compare projects and project risks by the risk ranking assigned. Based on that, the project sponsor can decide if a particular project is viable. In the next screen, we will understand how to perform quantitative risk analysis and what are the components updated during the quantitative risk analysis process.

## 8.27 Steps to Perform Quantitative Risk Analysis

To carry out quantitative risk analysis, you need to review the risk, cost, and schedule (Read as: ske-jule) management plans. Always begin with the original estimate of time or cost. Then calculate and assess the impact of changing the range of results on the overall project estimate. If this does not provide the required estimate, then you must refer to historical information. The other techniques of analyzing risks can be using the appropriate interviewing technique and obtaining probability distributions from stakeholders and subject matter experts, depicting the distributions in a PDF, performing a sensitivity analysis, and conducting a project simulation. Once you perform quantitative risk analysis process, you must update the risk register, project management plan, and other project documents. This analysis cannot be done alone. So, it is essential to involve the stakeholders as well. In the following screen, we will discuss the output of Perform Quantitative Risk Analysis process.

## 8.28 Perform Quantitative Risk Analysis Output

The output of perform quantitative risk analysis process is the project documents updates. This includes a probabilistic analysis of the project, the probability of fulfilling cost and time objectives, a prioritized list of quantified risks, and trends in the results of quantitative risk analysis. In the next screen, we will discuss the various components of quantitative risk analysis updates.

## 8.29 Components of Quantitative Risk Analysis Update

A point of interest here is that risks are further prioritized according to the threat or opportunity they pose on the project. Now, let us see some of the components which will be updated. The first component is probabilistic analysis of the project. Here, once risks are qualitatively and quantitatively analyzed, the project team should be able to forecast the possible completion dates and costs, and provide a level of confidence for each decision. The next component is probability of fulfilling the cost and time objectives. Using quantitative risk analysis, the project team can estimate the likelihood of fulfilling the project objectives with the current plan and knowledge of the project risks. The third component is prioritized list of quantified risks. Here, identified risks are prioritized according to the threat they pose or the opportunity they present to the project. This prioritized list includes a measure of the impact of each identified risk. The last component is trends in quantitative risk analysis results. Repeating the quantitative risk analysis process helps the project's risk management team to analyze the trends and make adjustments as necessary. Information on the project schedule, cost, quality, etc., and performance gained through the quantitative risk analysis process will help the team to prepare a quantitative risk analysis report. In the next screen, we will understand how to document the results of perform quantitative risk analysis process.

## 8.30 Documenting the Results

Let us look into a few points which are documented upon completing this process. The contingency reserve calculated in the quantitative project cost and schedule (Read as: ske-jule) risk analysis to be incorporated into the cost estimate and schedule, is documented. Contingency reserve established to capture the opportunities that are judged to be priorities of the project. If the contingency reserve exceeds the time or resource available which changes the scope and plan, then these have to be documented. And finally, the results of quantitative risk analysis must be recorded and passed on to the project management team for further actions to be taken. Let us move on to the quiz questions to check your understanding of the concepts covered in this lesson.

## 8.32 Summary

Here is a quick recap of what was covered in this lesson: ? Performing quantitative risk analysis provides a numerical estimate of the overall effect of risk on the project objectives. ? The three techniques to perform quantitative risk analysis process are Data gathering and representation techniques, Quantitative risk analysis and modeling techniques and, Expert judgment. ? EMV analysis is a method of calculating the average outcome when the future is uncertain. ? Monte Carlo analysis is used to predict likely outcome for schedules and costs. ? The Normal or Gaussian distribution is a continuous probability distribution, defined on the entire real line that has a bell-shaped probability density function, known as the Gaussian function or informally known as the bell curve.

## 8.33 Conclusion

This concludes, Perform Quantitative Risk Analysis. The next lesson covers, Plan Risk Responses.

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