#### Expected Value (EV) with Monte Carlo Simulation (MCS) method

The ValidRisk tool quantifies project-specific risks using the expected value (EV) with Monte Carlo simulation (MCS) method. The EV method is perhaps the most time-honored QRA method. It is based on multiplying the probability of occurrence by the impact of each critical risk (P x I). This is done for each risk and the results are summed. The sum is the mean or expected value impact. By entering the time and cost impacts as 3-point estimates, and running a monte-carlo simulation, the result is a probabilistic distribution. MCS also requires that one quantify any correlation between the critical risk occurrence; e.g., if one risk is a 100-year rain event, and another is a site flood, these would be positively correlated.

The principle of EV is that out of the 2 or 3 up to about 15 or so identified possible critical risk, one would expect only a few to occur (if any). We do not know which ones. However, by using the sum of P x I, the result is a value that should provide enough funds and time to more or less cover a few of them, at least within the range of the distribution. This serendipity should highlight that risk quantification is highly stochastic. Given only a few critical risks will occur (if any), be humble and seek to avoid the “illusion of control”; i.e., do not use the risk register to guide contingency drawdown as if the register is a control tool. It is better to repeatedly re-assess risks during the project. ValidRisk’s simplicity makes regular QRA analysis easy.

The ValidRisk EV method uses 3-point time impact (critical path delay to completion date), an estimate of time-driven costs (delay times burn rate), and a 3-point non-time driven cost impact. These estimates are based on defined critical risk scopes. That scope is the contingency plan or risk response (a response is not a treatment) that one will follow IF the risk occurs. This risk response depends on the business cost/schedule strategy is; is the project cost or schedule-driven? For example, if business states the project business case depends on being completed on schedule, then every risk response will be the fastest, regardless of its cost. This is called cost/schedule trading.

A project-specific risk workshop is therefore largely focused on discussion of the risk response(s), from which impact estimates can be defined. It is important to have scheduling and estimating expertise involved in the discussion and estimates. Because EV does not use the CPM schedule directly (indeed, there may not be a quality CPM schedule which is a systemic risk), it is important that schedule and critical path knowledge be brought to bear on the delay analysis.

As a final note, ValidRisk integrates the parametric + expected value models using MCS. This is done simply by using the parametric cost growth and schedule slip output distributions as inputs to the expected value model; i.e., systemic risks are risk #1 in the EV tool for which, as uncertainty, probability of occurrence is 100%.