Measurement Theory for EngineersThe material in this book was first presented as a one-semester graduate course in Measurement Theory for M.Sc. students of the Industrial Engineering De partment of Ben Gurion University in the 2000/2001 academic year. The book is devoted to various aspects of the statistical analysis of data arising in the process of measurement. We would like to stress that the book is devoted to general problems arising in processing measurement data and does not deal with various aspects of special measurement techniques. For example, we do not go into the details of how special physical parameters, say ohmic resistance or temperature, should be measured. We also omit the accuracy analysis of particular measurement devices. The Introduction (Chapter 1) gives a general and brief description of the measurement process, defines the measurand and describes different kinds of the measurement error. Chapter 2 is devoted to the point and interval estimation of the popula tion mean and standard deviation (variance). It also discusses the normal and uniform distributions, the two most widely used distributions in measurement. We give an overview of the basic rules for operating with means and variances of sums of random variables. This information is particularly important for combining measurement results obtained from different sources. There is a brief description of graphical tools for analyzing sampIe data. This chapter also presents the round-off rules for data presentation. |
Contents
Introduction Measured and Measurement Errors | 3 |
Measuring Population Mean and Standard Deviation | 11 |
Comparing Means and Variances | 45 |
Sources of Uncertainty Process and Measurement | 61 |
Measurement Uncertainty Error Propagation Formula | 89 |
Calibration of Measurement Instruments | 97 |
Collaborative Studies | 115 |
Measurements in Special Circumstances | 125 |
Answers and Solutions to Exercises | 135 |
Normal Distribution | 139 |
Quant lies of the ChiSquare Distribution | 141 |
Critical Values of the Fdistribution | 143 |
Common terms and phrases
analysis ANOVA assumed assumption average batch bias box and whisker calibration curve cell Chapter chi-square distribution compute confidence interval consider control limits corresponding critical value data in Table defined degrees of freedom denoted diameter equal example experiment factor grams independent random variables laboratories likelihood function maximum likelihood mean value measurand measurement data measurement error measurement instrument measurement process measurement results n₁ normal distribution null hypothesis observed values obtain operator outlier parameters point estimates probability procedure produced pull strength quantiles random effects random errors random measurement rank regression rejected repeated measurements Round-off Errors sample mean sample variances Sect significance level Sinstr so-called specific weight specimens SSAB standard deviation statistical process control Statistix sum of squares Suppose surement systematic error t-test temperature uncertainty Var[X Var[Y variables with variance variations whisker plot wire Xijk zero zero-mean random variables