No doubt these are all very interesting.  But what is the 20 percent of this material that will solve 80 percent of people’s problems?   Some of the topics above are very specialized, rarely used, and can only be understood when people have a practical working knowledge of the other material after actually using it.  

Many trainers also fall into the trap of thinking that hypothesis testing and ANOVA should be taught as separate topics.  A well-respected statistical colleague says it so well [my emphasis]:

A basic knowledge of full and fractional factorial designs, screening designs, and their analysis / diagnostics is a good place to start.  This knowledge, though necessary and useful when one is at a low state of knowledge about one’s process, is not sufficient.  It usually needs to be supplemented by some basic, extremely useful designs from response surface methodology (RSM).

[There is no finer reference for a process-oriented approach to DOE than Moen, Nolan, and Provost‘s  Quality Improvement through Planned Experimentation.  RSM is not covered.]

In my industrial career, many of my clients found much more ultimate value in obtaining a process road map – called a contour plot – which is accomplished through RSM. In its basic form it is hardly an advanced technique;  but, it does go a bit beyond factorial designs.  Many times RSM can even build on factorial designs in a nice efficient sequential strategy as one evolves to a higher state of knowledge, which leads to much more effective optimization and process control.   

A typical contour plot is below (scenario explained shortly).  It shows how the predictive model from the design analysis can be turned into a road map of the process studied.  Temperature (x-axis) and an ingredient’s concentration (y-axis) were varied over the ranges on their respective axes.  For any combination of those two variables, one can read the predicted value of the response being studied (objective in this case is to minimize it).

The contour plot above maps a real production process where the desired product immediately decomposes into a pesky, tarry byproduct that is difficult and expensive to remove.  The process is currently averaging approximately 15 percent tar, and each achievable percent reduction equates to $1 million (1970 dollars) in annual savings.

Process history has determined three variables to be crucial for process control:  temperature, copper sulfate concentration, and excess nitrite. Any combination of these three variables within the ranges of  temperature, 55-65° C;  copper sulfate concentration, 26-31 percent;  and excess nitrite, 0-12 percent would represent a safe and economical operating condition. The current operating condition is the midpoint of these ranges.

For purposes of experimentation only, the equipment is capable of operating in the following ranges if necessary:   temperature, 50-70° C;  copper sulfate concentration, 20-35 percent; and excess nitrate, 0-20 percent.

Suppose you had a budget of 25 (expensive) experiments that need to answer these questions:

This is the scenario I use to introduce my experimental design seminars. I form groups of three to four people and give them a process simulator where they can enter any condition and get the resulting percent tar. 

It almost never fails:  I get as many different answers for optimum settings, resulting tar, and variation as there are groups in the room – and just as many strategies (and number of experiments run) for reaching their conclusions.   Human variation!

I have each group present its results to me, and I act like the many mercilessly tough managers to whom I have made similar presentations.

General observations:

 
What usually happens as a result:  

My simulator generates the true number from the actual process map above along with a random, normally distributed variation that has a standard deviation of four (the actual process had a standard deviation of eight!).  In looking at the contour plot, tar is minimized at 65° C and approximately 28.8 percent CuSO4, resulting in six to eight percent tar +  ~8-10 for any production run.

In 1983, I heard the wonderfully practical C.D. Hendrix say:  People tend to invest too many experiments in the wrong place!

As it turns out, by the end of the class, human variation is minimized when every group independently agrees on the same 15 experiment strategy (a few choose an alternative, equally effective 20 experiment strategy).  When they see quite different numerical results from each individual design, they are initially leery, but then pleasantly surprised when they all get pretty close to the real answer. 

Reduced human variation = higher quality, more consistent results in only 15-20 experiments!  They are now in "the right place" and have 5-10 more experiments to refine their optimum.

More next time...

Kind regards,

Davis