SPC Guide
GREGORY P. FERGUSON

The world is a complicated place, but statistics can help you understand it. One type of statistical tool, called a designed experiment, is simply an organized way to sort through complicated and confusing data. I once utilized an easy-to-use designed experiment called a 2³ factorial to help me solve a complex problem.

The 2³ factorial contains three variables, and each variable is set at two different levels. Table 1 shows the standard layout for the experiment. It contains eight (2³) cells in which the experimental data can be recorded.

 In this case, the three variables are: the lot of paste used, the time the parts spent at the soak temperature and the value of the soak temperature.

In this experiment, we attached pieces of metal to pieces of ceramic, a harder task to do than you might think. It was important to make a very strong bond between the metal and the ceramic. I conducted a series of designed experiments to identify which variables affected the bond. Table 1 illustrates one of my early attempts. The ceramic cylinders were coated with an exotic metallic paste (or paint). Then they were fired in a nitrogen and hydrogen atmosphere. The parts were then nickel-plated, and a Kovar metal strip was brazed to the surface.

We tested the adhesion by peeling the Kovar strips off the cylinder and measuring (with a pressure transducer) the force required to separate them. These pressures (in pounds) are the numbers recorded in the appropriate cells in Table 1.

These three parts saw the same conditions, yet one had the lowest value and the others are high. This means that some other variable changed, something far more important to the process. In other words, the variables in this experiment aren't especially important to the output--we've been looking at the wrong variables.

Sometimes knowing that something isn't true can be valuable: It tells you where not to look. The exercise of checking all of the variables in a production process can be worthwhile, even if most (or all) of the variables turn out to have little effect on the output values.

Several more experiments were run, with results similar to those in Table 1. Although this outcome was discouraging, it did provide useful information: these variables didn't matter.

As far as adhesion between the metal and ceramic, there were only so many variables to test. Although it took months, we tested every variable in the process. Eventually, we identified the most important variable (see Table 2): the type of grinding wheel (metal or resin) used to machine the parts. The cell in the lower left corner of Table 2 contains 37, 26 and 32. These numbers are reasonably consistent. In fact, all the cells in Table 2 contain consistent values. This indicates that the variables being changed are important to the process output.

The type of grinding wheel used to machine the ceramic cylinder before it was metallized turned out to be the most important variable in this process by far. In this example, it's possible to simply look at Table 2 and see that the type of wheel used is important. Sometimes the result isn't so apparent, in which case the data should be examined using the analysis of variance (ANOVA) tool. The ANOVA for the data in Table 2 is shown in Table 3.

I like the 2³ design because it yields a lot of information about a process in a relatively short time, but it isn't so complicated that it can't be administered effectively.

This was one of the more difficult problems I've worked on. I almost thought it was too complicated to solve. But by using designed experiments and hundreds of hours of work, I was able to sort through the data and understand the process. Once the proper wheels were used, the bonds became very strong and our customer was able to get back in business.

About the author

Gregory P. Ferguson is quality manager of Parker Hannifin's Tucson, Arizona, facility. He has published technical articles and assisted in the publication of two books. Comments can be e-mailed to him at gferguson@qualitydigest.com .