DFSS-based Design Optimization using Design of Experiments and Monte Carlo Simulation

One of the main uses of Monte Carlo simulation in Six Sigma is with DFSS at the planning stage of a new product. Testing different processes on physical manufacturing or service models or prototypes can be cost prohibitive. Monte Carlo simulation allows engineers to simulate thousands of different outcomes on models without the cost and time associated with physical simulation. Benefits include the ability to experiment with different designs in Design of Experiment models.

The fundamental steps in the Design and Optimize phases of a Design for Six Sigma product development effort involve modeling a physical system using a designed experiment, and using the model to achieve the required system performance using Monte Carlo simulation to estimate system sensitivity and capability. You can see a recorded webcast on this topic given by Bausch & Lomb Worldwide Director of Six Sigma Jeff Slutsky.

Project risk analysis using Probabilistic Calendars, Part II

As you may have noticed in my previous posting on this subject, @RISK for Project‘s Probabilistic Calendars are a great way of modelling multiple occurrences of the same risk event over a defined period and as a result avoid having to set up lots of risk tasks. Furthermore, you can use them for modelling any type of calendar-related risk and affect just the tasks taking place in the period concerned.

The main disadvantage is that they are less visible in the plan, compared to a separate RISK/IF statements or discrete task, and the impact is not so variable. In addition, they have no effect on cost (if you have costed your plan), as the assumption is that non-working resources will be deployed elsewhere, which is not always the case.

Perhaps my favourite Probabilistic Calendar example is modelling hurricane seasons. Here we have a long project (4 years) where there is a 20% chance that 1 month will be lost each year due to the annual hurricane season.

(click to view larger image)

As no uncertainty has been put in the tasks (in order to see only the effect of the hurricanes each October) the pre-risk finish date is 19th February 2010. However, after taking the hurricane season into account, the finish date has the following distribution:

Probabilistic Calendars are therefore very appropriate for this type of long timescale forecast.

Out of interest, the model is also very similar to tossing a biased coin 4 times, as in the binomial distribution below, where the chance of more than 2 years with hurricanes is only 5% but there is a 40% chance of at least 1 hurricane in the 4 year period.

Ian Wallace, ACMA

Project risk analysis using Probabilistic Calendars

Often seen as a little too sophisticated for many project planners new to Monte Carlo simulation, a Probabilistic Calendar is an elegant way of modelling the uncertainty in resource availability and resource allocation in a project plan. Any project plan—whether in construction, oil & gas exploration and production, manufacturing, environmental remediation, operations management, etc.—is subject to uncertainty. This uncertainty may be due to, for example:

• Weather conditions or other uncontrollable but seasonal/calendar related events (e.g. rain or annual leave),
• Possible bottlenecks caused by sickness or the availability of key resources due to the demands of other projects,
• Initial learning curves of new resources recruited to the project.

Using Probabilistic Calendars, @RISK for Project (Pro version only, a Monte Carlo software add-in to Microsoft Project) will ‘take-out’ working days from either the standard working week or from an individual resource’s working calendar, according to the probabilities specified by the user, and therefore lengthen the tasks affected.

For example, let’s assume that the finish date distribution for a Construction project looks like this, excluding any lost time for Probabilistic Calendars:

Under this decision evaluation, you might decide to tell the client (or your bosses) that you are 95% sure you will finish by 25th October.

Now let’s model the same Construction schedule but with a 20% chance of non-working on each day between 17 Oct and 31st Dec (i.e. ‘Autumn’).  The Probabilistic Calendar dialogue would look like this with a (binomial) sample being taken each day in the date range:

(click to view larger image)

The resulting Finish date distribution will then look like this:

The P95, mean and range of uncertainty have all increased due to the possibility of lost working days in the Probabilistic Calendar.  In fact, the probability of meeting the 25th October is now lower than 5% – so beware!

This new risk assessment allows your client the most informed decision making under uncertainty.

Ian Wallace, ACMA

Monte Carlo Simulation in Process and Efficiency Improvement

Consulting with Impact, Ltd. is a Rochester, NY-area firm specializing in process and efficiency improvement, using tools such as Lean, Six Sigma, and ISO. The firm has found many uses for Monte Carlo simulation in the Lean Six Sigma process. Here, Ed Biernat, President of Consulting with Impact, discusses how Consulting with Impact uses @RISK to help businesses in many different industries minimize variability.

Watch a webinar presented by Ed Biernat: “Integrating @RISK into the DMAIC Process.”

Forming partnerships with experts in Six Sigma, LSS, and DFSS

As many Six Sigma black belts know, Monte Carlo simulation is an important
technique for Lean Six Sigma and Design for Six Sigma because it allows practitioners
to simulate and optimize process variables before implementation. This reduces
the time and cost of any Design of Experiment process.

Palisade actively forms partnerships with experts in Six Sigma, LSS, and DFSS to promote the use of Monte Carlo simulation in their fields.

Our latest partnership is with the management consulting firm Rath & Strong of Lexington, Massachusetts. Rath & Strong is an acknowledged leader in the field of change management
and counts many Fortune 500 companies among its clients. The firm’s current
consulting and training emphasizes Lean Six Sigma.

Does missing my plane mean that I got my risk assessment wrong?

A while ago I planned to take the last aeroplane of the evening to fly out for a client meeting the next day. Unfortunately the plane was cancelled and I had to miss the meeting. On speaking to the client, he said dryly: “But you are supposed to be a risk manager!”

I smiled but did not respond. However, as he was saying this (and indeed well before in anticipation), the following thoughts went through my head: First, the reason that I planned to take the last plane was that the client was particularly unwilling to pay my normal charge out rate, and after protracted negotiations we had just about come to a satisfactory solution. As a result to make the whole situation worthwhile, I had to do a full day’s chargeable work on the day before visiting the client. Second, in any case the only way of guaranteeing with close to 100% certainty that I would have been at the meeting would have been to take a flight two days earlier, and lose even more productive work time. Third, the client and I had prepared well for the meeting in advance, and he was well able to represent our joint project to his colleagues without my presence.

In other words, risk management is not really about risk elimination at all costs, but rather about balancing the costs of risk mitigation (e.g. high cost associated with travelling to a meeting two days early) with the consequences if risks materialise (costs associated with my not being at the meeting). Effective risk management is about finding the optimal balance between these. Even if all risks could be eliminated, generally doing so would be too costly.

In many everyday situations, we already optimise our actions to reflect this balance. When crossing the road, we look both ways, perhaps several times (an action which costs little but reduces the probability of an accident), but we do not build a bridge (an action that could eliminate the risk, but only at great cost). We intuitively find the optimum point and accept residual risk.  More formally one can approach optimisation problems by building quantitative risk models (e.g. using Monte Carlo simulation or decision tree analysis). Often such analysis is most easily implemented by the use of risk software such as @RISK, PrecisionTree or RISKOptimizer (which uses a genetic algorithm to optimise within the context of a Monte Carlo simulation).

The topic of residual risk (and optimisation) is an interesting one, as it does pose challenges from a communication perspective. Management may wish rather to hear that all risks have been eliminated (rather than their being a residual which is too costly to eliminate). In addition, the notion of an optimum does open the discussion of which criteria are used to assess that (e.g. maximising the total average profit after including the cost of risk mitigation measures, or minimising the losses in the worst 10% of cases etc.). In more complex cases (such as in some agricultural, veterinary, or environmental risk analysis situations), the costs of risk mitigation and the benefits associated with this are borne by different parties. Such externalities can make an appropriate assessment even more complex; perhaps there will be more on this in a later blog.

Dr. Michael Rees
Director of Training and Consulting

Steve Hunt, LSSBB

Whether in DMAIC, Design for Six Sigma (DFSS), Lean projects, or Design of
Experiments (DOE), uncertainty and variability lie at the core
of any Six Sigma analysis. I’m interested in how Monte Carlo simulation can be used to identify,
measure, and root out the causes of variability in production and service
processes and designs.

Actuaries Tune Risk Analysis to Improve Decision Making under Uncertainty

Actuaries are more risk-averse than you and I because they advise insurers and pension funds that have a lot at risk.  So they need to be better at decision making under uncertainty.   When they calculate requirements for pension fund investment, life insurance, or long-term care they try to account not only for the uncertainties–say, growth rates for bonds– but the factors that influence variation in the uncertainties, key economic indices.

A recent research study by noted authorities in actuarial practice Kevin Ahlgrim, Illinois State University, and  Steven D’Arcy and Richard Gorvett of the University of Illinois, Champaign-Urbana, provides a risk analysis model for projecting economic indices such as interest rates, equity price levels, inflation rates, unemployment rates, and real estate price levels.  The researchers undertook the project for the Society of Actuaries and the Casualty Actuary Society.  Their goal was not simply to create a model, but to help bring practicing actuaries up to date on current thinking and techniques for economic modeling and to lay the foundation for future advances. Their model was developed using @RISK, the popular Monte Carlo software for Excel, and if you want to take a look at it, it is available on the website for the Casualty Actuary Society (the model is a link to Appendix D).