The risk analysis model below examines the familiar production forecasting model for oil and gas
wells, the exponential decline curve. The standard equation, q = qie-at
(3.3), can be used with random variables for both qi (the
initial production rate, sometimes called IP) and a (the constant decline rate).
Here the model has an additional parameter, t (time), which makes the output
(Rate, STB/YR) more complicated than the volumetric reserves output.
No longer do we just want a distribution of numbers for output. Instead we
want a distribution of forecasts or graphs. The worksheet has two input cells,
IP and Decline, and a column of outputs for the Rate of production in STB/YR
over 15 years.
After simulation you can generate a summary graph like that shown in the
model. This graph shows uncertainty over the 15 year period. The shaded region
represents one standard deviation on each side of the mean. The dotted curves
represent the 5th and 95th percentiles. Thus, between these dotted curves is a
90% confidence interval. We can think of the band as being made up of numerous
decline curves, each of which resulted from choices of qi and a.
» @RISK Example model: Band.xls
This example was taken from Decisions
Involving Uncertainty: An @RISK Tutorial for the Petroleum Industry
by James Murtha, published by Palisade Corporation, where a
detailed, step-by-step explanation can be found.
When building a Monte Carlo simulation model in @RISK for project risk analysis, we can incorporate a risk register through risk factors. Risk factors are more concrete abstractions of risk and define situations that can be individually assessed with a limited amount of information.
Risk factors affect a project through the occurrence of events that disrupt the development of an activity or a group of activities causing variations from the expected duration and cost estimates. This means that risk factors do not affect project activities directly, but do so through conditional consequences given that a risk event has occurred as shown in the figure below.
The concept of risk factors is similar to one of common causes that is widely used in fault tree analysis in other engineering applications. The fact that a group of activities is affected by a common risk factor will indirectly induce correlation when consequences of that risk materialize. Risk factors are an alternative to deal with correlation between project activities. When a project is affected by several risk factors they are grouped in a risk register.
Risk Factor Model
The main advantage of using risk factors is that we can make use of causal relationships to relate the occurrence of a certain risk event with its consequences on project activities. One example of the application of a risk factor for a construction project is the risk of inclement weather; if inclement weather occurs, it delays not only the execution of open-sky activities that are scheduled at that time but also could affect the productivity of labor and machinery incurring in increased costs.
One of the main problems with risk factor models used in project risk analysis is that risks affecting project performance are considered mutually independent; moreover it examines risk impact of each risk factor separately. In reality, risk factors are very often interdependent and their impact varies simultaneously with a compounding effect. This interdependency can be modeled using event trees.
Dr. Javier Ordóñez
Palisade Training Team
On Thursday of last week, I attended a free webinar, Minitab Methods to Deal with “Bad” Data, which was given by Master Black Belt Rick Haynes of Smarter Solutions. This is a topic that typically isn’t addressed in most Six Sigma Black Belt courses, but is extremely important for most six sigma practitioners to know and understand. Rick did an excellent job introducing and conveying the Minitab tools to deal with “bad” or missing data. As defined by Rick, “bad” data are values that are not accurate due to rounding or to data collection errors. Censored data analysis is a method developed to solve reliability issues, which he discussed using in new ways. To complete the presentation, he followed up by sending the technical paper to the attendees, which will make a good future reference.
This brings me to a point. There are many tools that a practicing Six Sigma Black belt needs to be aware of which are not covered in most Black belt courses because of time and complexity reasons. Technical webinars serve an excellent resource in the Six Sigma Community to expose Six Sigma Practitioners to tools or methods that they may not have otherwise be exposed to, such as different analysis techniques, discrete event and Monte Carlo Simulation to name a few.