Welcome to “Statistics in the Laboratory.” This column will appear four times a year and will build on the popular “Statistics in Analytical Chemistry” series by David Coleman and Lynn Vanatta published in American Laboratory from September 2002 through April 2013.
So who is this new columnist, and what are his qualifications? I’m a professor emeritus (read: “old guy”) in the Department of Chemistry at the University of Houston. My training is in the field of analytical chemistry. I received my B.A. in chemistry (1966) from Carleton College and my M.S. (1970) and Ph.D. (1971) from Purdue University working under the guidance of Professor Harry L. Pardue, and under the influence of Professor Sam P. Perone. I was a graduate student when computers were just beginning to come into the laboratory. While working on my dissertation—the project involved automating the development of analytical chemical methods—Grant Wernimont, who was an adjunct professor at Purdue, introduced me to the efficiency and effectiveness that statistical design could bring to experiments.
I taught four years (1970–1974) in the Department of Chemistry at Emory University before moving to the University of Houston. During my academic career I had the pleasure of being the major research advisor for 16 Ph.D. and 19 M.S. students. In 1975, along with one of my first graduate students, Stephen L. Morgan, now a professor at the University of South Carolina, I started to teach short courses on the topics of sequential simplex optimization, the statistical analysis of laboratory data, and the fundamentals of experimental design. Since then we have team-taught over 650 short courses, many of them in open sessions through the American Chemical Society, and even more as in-house offerings at various companies, organizations and government agencies. We soon realized that these short courses were a “window on the world” and showed us what real life was like (exciting!) outside the university.
I retired from academia on January 1, 2001, to have more freedom to teach short courses and consult. For those of you who knew him, or know of him, I am distantly related to the famous statistician William Edwards Deming; he and I are seventh cousins once removed.
Let’s start talking about “statistics in the laboratory” with a bit of a warmup about the fundamental importance of the measurement process.
Figure 1 – An out-of-specification event in industry.Figure 1 shows a typical situation: Starting materials go into an industrial process and a product comes out. The quality Q of the product is important to our customers, so if we want to make money, Q is important to us as well. We measure Q and graph it as a function of time or batch number in the small chart in the upper right of Figure 1. The horizontal lines in the small chart are specifications—the value of quality has to stay between these two horizontal lines.
It’s clear from the last plotted point that the quality measure Q has gone out of specification. This can lead to a lot of wasteful fingerpointing. The engineers say, “You analysts! You’ve messed up again. Remeasure this sample and give us a good number.” And the analysts say, “You engineers! You’ve messed up again. Recenter your process and get it back in specification.” The engineers know they’re right. The analysts know they’re right.
Figure 2 – An out-of-specification event in industry, and it’s not the analyst’s fault.Figure 1 is misleading; Figure 2 shows the real story. The value of Q doesn’t come out of the industrial process. Instead, a sample of production output becomes the input of the measurement process, and the measurement process produces the value of Q. In fact, the data are ambiguous. It’s possible that the out-of-specification data point is the fault of the industrial process, and it’s equally possible that the fault lies with the measurement process. If the analysts capitulate, this leads to what quality control statisticians call “rework”— in this case, subsequent (and perhaps unnecessary) measurements of the sample by the analytical chemists.
To disentangle the ambiguity, the measurement process must be observed separately. A reference material is sent through the measurement process every so often, and the value Q’ is plotted in a separate small control chart (at the lower right). In the example in Figure 2, it’s clear that the measurement process is working just fine, and the out-of-specification problem is that of the engineers. Of course, sometimes the problem is the measurement process, and the chart will show that as well.
Reference material doesn’t have to come from NIST—it just needs to be similar to the industrial product (in fact, it can be part of a previous batch), but it does need to be stored in a such a way that it remains stable over time.
Some managers offer the objection that making such charts is expensive because it takes resources away from running routine samples. Au contraire. In my experience it’s money well spent—when engineers (or auditors) have concerns about the measurement process, it’s handy to pull this chart out and show them that, in fact, the measurement process is quite well behaved.
So what are these control charts and how do they work? That will be the topic of the second column in this series.
Dr. Stanley N. Deming is an analytical chemist who can be found, as he says, masquerading as a statistician, at Statistical Designs, 8423 Garden Parks Dr., Houston, Texas 77075, U.S.A.; e-mail: [email protected]; www.statisticaldesigns.com