Quality Progress - January 2014 - 53

STATISTICS ROUNDTABLE BY LYNNE B. HARE Assessing Analytical Equipment Accuracy Avoiding the pitfalls of automated systems MUCH INK AND TRAINING time have Most impactful quality education of its "knowns" (K) at three levels. It been devoted to measurement systems programs cover the precision portion of provides assessments (A) for each of the analysis (MSA)-the adopted child of MSA by teaching gauge repeatability and three. Table 1 shows an example. Next, it Six Sigma-and other statistical training reproducibility, and several statistical calculates a regression equation relating programs that continue to add great value software packages contain special point- the assessments to the knowns. through improvements in quality and and-click features for combined tabular productivity. and graphical analyses of data stemming intercept estimates of the least squares MSA embraces sample-to-sample (or from these studies. Carried out properly, fit together with a correlation coefficient. incident-to-incident variation) together they provide great value by isolating and The slope is 0.9040, the intercept is 0.0211 with accuracy and precision. Precision, in quantifying major sources of process and the correlation coefficient is 0.9997. turn, is often thought to consist of repeat- variation. The equation relating assessment to With these data come the slope and known is: ability and reproducibility. Repeatability The portion of MSA that seems to get is the variation from repeated measures less attention is accuracy. This could be of the same sample by the same operator, because it's easy to assume that an instru- while reproducibility is variation brought ment is accurate, or you think it is best to known observation, the difference be- about by operator-to-operator differences take the equipment vendor at his word, tween the predicted and the observed, and and the failure of differences among or it is difficult and time consuming to that difference expressed as a percentage samples to be the same from operator to assess accuracy, or for a variety of other of the corresponding known. As a bonus, operator. See Figure 1. reasons. there is a printer plot showing each of the A = 0.0211 + 0.9040K (equation one). In addition, we get predictions at each three plotted observations. Example MSA hierarchy of variation / FIGURE 1 Transformations are available, appar- A new reason, offered to me during a conthat the equipment Accuracy Precision mations are available to the user. Also, you are told that this is a linear regression data box routine, meaning reduction, so maybe there are other model one with a computer forms available. You would have to read algorithm that is the manual to find out. Does anyone read unknown to the user Measurement system variation the suggestion that some other transfor- contained a black Sample to sample presumably linear in both K and A, with sulting session, was Total variation ently, but the default is "linear/linear," the manual anymore? used for self-calibra- You can check, too, but I found that I tion. "What could possibly go wrong?" MSA = measurement systems analysis Operator by sample a linear model. See Table 2. Incidentally, I was delighted to see the plot of the data. It agrees with my advice: Always, always, exercises, the equip- always-without exception-plot the ment's computer Operator cept, slope and correlation, all assuming As part of its morning Reproducibility I thought, so I asked to take a closer look. Repeatability agreed closely with the estimates of inter- data, and look at the plot. requests submission The question is how best to use the January 2014 * QP 53 http://www.qualityprogress.com

Table of Contents for the Digital Edition of Quality Progress - January 2014

Up Front
LogOn
Expert Answers
Keeping Current
Mr. Pareto Head
Breaking Down Barriers
Follow the Fundamentals
Fresh Perspective
Back in Service
Quality in the First Person
Career Corner
Innovation Imperative
Statistics Roundtable
Standards Outook
QP Toolbox
QP Reviews
One Good Idea

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