If you read my previous post, you will remember that design of experiments (DOE) is a systematic method used to find cause and effect. That systematic method includes a lot of (frightening music here!) statistics.

[I’ll be honest here. I was a biology major in college. I was forced to take a statistics course or two. I didn’t really understand why I had to take it. I also didn’t understand what was being taught. I know a lot of others who didn’t understand it as well. But it’s now starting to come into focus.]

Before getting into the concepts of DOE, we must get into the basic concepts of statistics (as they relate to DOE).

Basic Statistical Concepts:

**Variability**

In an experiment or process, you have inputs you control, the output you measure, and uncontrollable factors that influence the process (things like humidity). These uncontrollable factors (along with other things like sampling differences and measurement error) are what lead to variation in your results.

**Mean/Average**

We all pretty much know what this is right? Add up all your scores, divide by the number of scores, and you have the average score.

**Normal distribution**

Also known as a bell curve due to its shape. The peak of the curve is the average, and then it tails off to the left and right.

**Variance**

Variance is a measure of the variability in a system (see above). Let’s say you have a bunch of data points for an experiment. You can find the average of those points (above). For each data point subtract that average (so you see how far away each piece of data is away from the average). Then square that. Why? That way you get rid of the negative numbers; we only want positive numbers. Why? Because the next step is to add them all up, and you want a sum of all the differences without negative numbers getting in the way. Now divide that number by the number of data points you started with. You are essentially taking an average of the squares of the differences from the mean.

That is your variance. Summarized by the following equation:

\(s^2 = \frac{\Sigma(Y_i - \bar{Y})^2}{(n - 1)}\)

In this equation:

**Yi** is a data point**Ȳ** is the average of all the data points**n** is the number of data points

**Standard Deviation**

Take the square root of the variance. The variance is the average of the squares of the differences from the mean. Now you are taking the square root of that number to get back to the original units. One item I just found out: even though standard deviations are in the original units, you can’t add and subtract them. You have to keep it as variance (s2), do your math, then convert back.

“Multifactor testing via design of experiments (DOE) is the secret weapon for medical-device developers,” says Stat-Ease Principal Mark Anderson, lead author of the DOE and RSM *Simplified* series*. “They tend to keep their success to themselves to keep their competitive edge, but one story, that we can share, documents how a multinational manufacturer doubled their production rate while halving the variation of critical-to-quality performance. That’s powerful stuff!”

The case study that Mark is referring to can be found here: RSM for Med Devices.

Stat-Ease has guided many manufacturers in the medical device industry in the streamlining of their products and processes. Now, we have put that experience together into one place, the Designed Experiments for Medical Devices workshop.

In this one-of-a-kind workshop, learn how to optimize your medical device or process. Our DOE experts will show you how to use Design-Expert® software to help you save money or time while ensuring the quality of your product. We welcome scientists, engineers, and technical professionals working in this field, as well as organizations and institutions that devote most of their efforts to research, development, technology transfer, or commercialization of medical devices. Throughout this course you will get hands-on experience while using cases that come directly from this industry.

During a fast-paced two days, explore the use of fractional factorial designs for the screening and characterization of products or processes. Also see how to achieve top performance via response surface designs and multiple response optimization. Practice applying all these DOE tools while working through cases involving medical device design, pacemaker lead stress testing, and typical processes that may be used in the testing or production of these devices such as seal strength, soldering, dimensional analysis, and more.

For dates, location, cost, and more information about this workshop, visit: www.statease.com/training/workshops/class-demd-adin.html

*About Stat-Ease and DOE*

Based in Minneapolis, Stat-Ease has been a leading provider of design of experiments (DOE) software, training, and consulting since its founding in 1982. Using these powerful statistical tools, industrial experimenters can greatly accelerate the pace of process and product development, manufacturing troubleshooting and overall quality improvement. Via its multifactor testing methods, DOE quickly leads users to the elusive sweet spot where all requirements are met at minimal cost. The key to DOE is that by varying many factors, not just one, simultaneously, it enables breakthrough discoveries of previously unknown synergisms.

* *DOE Simplified* is a comprehensive introductory text on design of experiments*RSM Simplified* is a simple and straight forward approach to response surface methods