Synopsis
The purpose of this book is to provide a guide to the estimation of uncertainty in calibration and in scientific measurements, and also to the estimation of uncertainty in quality control of manufacturing processes. Some attention is given to the matching of graded parts after manufacture and to the estimation of the percentage of faulty parts accepted because of uncertainties in the sizing machines used to measure the parts. Chapter 1 introduces the idea of uncertainty or error distributions, whilst chapter 2 deals with the normal or Gaussian distribution and with its properties. Chapter 3 is devoted mainly to the proof of a double integral theorem and to the derivation of some integral functions and in chapter 4 the integral functions are applied to the combination of rectangular distributions, both with themselves and with a Gaussian distribution. Chapter 5 is a new chapter dealing with applications to industry, such as the estimation of the percentage of faulty parts accepted and correct parts rejected because of uncertainty in the measuring equipment used.
Chapter 6 deals with distributions ancillary to the Gaussian distribution and chapter 7 attempts to set out a basic methodology for the estimation of uncertainty based on basic statistical theory. As before chapter 8 deals with the estimation of the various components of uncertainty. Chapter 9 deals with consistency tests and with tests for the goodness of fit for a set of empirical points to a fitted or given curve. Chapter 10 deals with the method of least squares, including curve fitting. A new section has been added dealing with the use of orthogonal polynomials in curve fitting. Chapter 11 deals with the theorems of Besnoulli, Stirling and the binomial, and the distributions of Poisson and the hypergeometric function, together with examples.
