Modelling and Estimation of Measurement Errors

Interlaboratory comparisons of measurement data in physics and engineering are an intrinsically difficult task. However, there is a growing interest in these procedures, since interconnections between research institutes, universities and industrial laboratories nationwide, and even worldwide, become necessarily stronger. A first approach to solving the problems of handling measurement data is ISO standard 5725. ISO 5725 defines the terms trueness, precision, accuracy, systematic error (bias), random error and also proposes simple procedures for interlaboratory comparisons of measurement data. To deal with the imponderables of real life data, many simplifications had to be introduced. This might, in certain cases, cause erroneous conclusions to be drawn from the data under study. For a long time there has been a lack of a comprehensive summary of well established univariate descriptive statistical methods as well as inferential procedures for interlaboratory comparisons. The book Modelling and Estimation of Measurement Errors tries to close this gap. It is subdivided into five chapters, seven appendices, 17 tables and three charts. It contains a bibliography and an index. Chapters 1 and 2 are the introductory parts of the book. They deal with estimating the error of direct measurements - the variable looked for is directly measured - and the determination of the parameters of all important univariate probability distributions. Of course, statistical testing of the parameters is included. Exceptions are also discussed in detail. Already the first two chapters offer more information than an average university graduate course on handling of measurement data would provide on this special subject. Chapter 3 is entitled `Comparisons of Means' and gives a detailed overview on experimental designs: single factor experiments, factorial designs and nested designs. With the methods given, the estimation of the different components of measurement error is possible. Having dealt with the means of measurement results, it makes sense to look at the variability of the data - its variance. This is done in chapter 4. Here the uncertainty in the final result is examined. Consequently, the terms repeatability, accuracy, reproducibility, sensitivity and detection limit play an important role. Having studied the properties of measurement procedures in detail, the last step should always be the calibration of the instrument or measurement procedure. Only after this last step do interlaboratory comparisons and even the establishment of national or international standards make sense. All important univariate approaches are included: straight line regression, polynomial regression, nonlinear relationships and systems of curves. The remaining uncertainty after calibration is also dealt with. The book is written in a clear and concise style. The content is statistically sound and only well proven methods are given. The mathematical and statistical level is moderate and application oriented. Therefore, the book can serve as handbook, textbook for graduate courses at universities, or for self study. After having read some pages the reader notices that the authors have decades of hands-on experience in handling measurement data. Of course, there are also some caveats. The book deals only with univariate statistical methods. Therefore, it might not be suited for researchers in life sciences dealing with multivariate data. However, this is not a real disadvantage for physicists, chemists and engineers, since many measurement procedures in these areas are indeed univariate. Another point is the mathematical notation based on sums. Matrix notation is strictly avoided. Therefore, one can often find formulae like ... ∑i∑j∑k ijk... On the one hand, this might be sometimes confusing, on the other hand it can help to write code. And this is another point: the authors emphasize that all computations should be done with the help of a pocket calculator. And this could be, freely speaking, too old fashioned for younger readers, at least to a certain degree. Since the advent of general purpose mathematical packages, like Maple, Mathematica or Matlab, such books should be written to make use of the computational power of this software. These packages help to save time and are free from merely mechanical button pressing - it is simply convenient to make use of such helpful tools. However, these objections do not diminish the value of such an excellent book. Everybody dealing with comparisons of measurement data in daily practice should have a copy of this book readily available. Hendrik Rothe