# Uses of the Uniform Continuous Distribution

The continuous uniform distribution represents a situation where all outcomes in a range between a minimum and maximum value are equally likely.

From a theoretical perspective, this distribution is a key one in risk analysis; many Monte Carlo software algorithms use a sample from this distribution (between zero and one) to generate random samples from other distributions (by inversion of the cumulative form of the respective distribution).

On the other hand, there are only a few real-life processes that have this form of uncertainty. These could include for example: the position of a particular air molecule in a room, the point on a car tyre where the next puncture will occur, the number of seconds past the minute that the current time is, or the length of time that one may have to wait for a train. In oil exploration, the position of the oil-water contact in a potential prospect is also often considered to be uniformly continuously distributed.

For the distribution to apply to each situation, implied assumptions need to hold, and it is the validity of these assumptions that can be questioned. In the example concerning the waiting time for a train, one would need to assume that trains arrive in regular intervals but that we have no knowledge of the current time, not of other indicators (sound, wind) that a train is in the process of arriving. For this reason, the distribution is sometimes called the “no knowledge” distribution. One of the reasons that such a distribution is not of frequent occurrence in the natural world is that in many cases it is readily possible to establish more knowledge of a situation, and that in particular there is usually is a base case or most likely value that can be estimated.

Dr. Michael Rees
Director of Training and Consulting

# Six Sigma Baking?

In the midst of the holiday season, I want to bring up the subject of applying Six Sigma to food preparation, mainly baking.  I am not implying that you try to apply Six Sigma variation reducing techniques to anyone’s holiday baking as it could cause negative unintended consequences, like boxed macaroni and cheese dinners for the New Year.

As a child, I recall sitting around the dinner table after consuming a huge holiday meal, listening to the discussions about my grandmother’s homemade cheesecake and lemon meringue pie.  Statements such as “the cheesecake was the best ever”, “this year’s lemon meringue pie wasn’t a tart as last year’s”, “the crust came out perfect” etc . . . To be honest as a 10 year old, I was not able to discriminate such subtleties. Now that I am an adult, I question whether they really could either, particularly after such an eating event, not mention comparing samples 12 months apart. With that said, the deserts were always phenomenal.

Now, onto present day . . .  why not apply Lean Six Sigma to baking? Well, some do! A few years ago a regional supermarket chain in the mid Atlantic region hired a Lean Six Sigma consultant to optimize their chocolate cake for ultimate customer satisfaction, taste, pricing and of course profitability.  Using taste tests,  QFD,  Kano models and a little DOE, they were able to identify the characteristics that were most important, then worked on reproducing those characteristics every time with little variation.

The project was a success for both the customers and company producing ultimate chocolate cake experience. Going back to my statement of unintended negative consequences, the Black Belt may have gained a few extra pounds during that assignment.

What’s next? If we can apply Lean Six Sigma to baking cakes to maximize profits and customer satisfaction, doesn’t it make sense to apply it to all food industries?