ERROR ANALYSIS WITH APPLICATIONS IN ENGINEERING IBD

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1 Basic characteristics of error distribution, histograms 1 .I Introductory remarks, histograms, 1.2 The average of a sample of measurements , 1.3 Dispersion measures in error analysis , 1.4 Cumulative frequency distribution , 1.5 Examples of empirical distributions , 1.6 Parameters obtained from the measured data and their theoretical values , Problems , References , 2 Random variables and probability, normal distribution , 2.1 Probability and random variables , 2.2 The cumulative distribution function, the probability density function, 2.3 Moments, 2.4 The normal probability distribution , 2.5 Two-dimensional gravity flow of granular material , Problems, References , 3 Probability distributions and their characterizations , 3.1 The characteristic function of a distribution , 3.2 Constants characterizing the random variables , 3.3 Deterministic functions of random variabies, 3.4 Some other one-dimensionat distributions , 3.4.1 Discrete probability distributions , 3.4.2 Corttinuous probability distribuhoas , 3.4.3 Remarks on other probability distributions , 3.4.4 Measures of deviation from the normal distribution , 3.5 Approximate methods for constructing a probability density function , 3.6 Multi-dimensional probability distributions , Problerns , References , 4 Functions of independent random variables , 4.1 Basic relations.. , 4.2 Simple examples of applications , 4.3 Examples of applications in non-direct measuremenis , 4.4 Remarks on applications in the calculus of tolerance limits , 4.5 Statical analogy in the analysis of complex dimension nets , Problems , References , 5 Two-dimensional Distributions , 5.1 Introductory remarks , 5.2 Linear regression of experimental observations , 5.2.1 Nonparametric regression , 5.2.2 The method of least squares for determining the linear regression line , 5.2.3 The method of moments for determining the linear regression line l 5.3 Litlear correlation between experimentally determined quantities , 5.4 Two-dimensional continuous random variables , 5.5 The two-dimensional normal distribution , 5.5.1 The case of independent random variables , 5.5.2 The circular normal distribution , 5 5.3 Three-dimensional gravity flow of granular media , 5.5.4 The case of dependent randoin variables , Problems , References , 6 Two-dimeosional functions of independent random variables , 6 .1 Basic relations , 6.2 The rectangillar distribution of independent random variables , 6.2.1 Analytical method for determining two-dimensional tolerance limits polygons , .2.2 Statical analogy method for determining two-dimensional tolerance limit polygons , 6.2.3 Graphical method for determining two-dimensional tolerance limits polygon . Williot?s diagram , 6.3 The normal distribution of independent random variables , 6.4 Indirect deternlination of the ellipses of probability concentration, Problems , References , 7 Three-dimensional distributions, 7.1 General remarks, 7.2 Continuous three-dimensional random variables , 7.3 Thc three-dimensional normal distribution , 7.3.1 Independent random variables , 7.3.2 The spherical normd distribution , 7.3.3 The case of dependent random variables , Problems , References , 8 Three-dimensional functions of independent random variables , 8.1 Basic relations , 8.2 The rectangular distribution of independent random variables , 8.3 The normal distribution of independent random variables , 8.4 Indirect determination of the ellipsoids of probability concentmtion, Problems , References, 9 Problems described by implicit equations: 9.1 Introduction , 9.2 Statistically independent random variables , 9.2.1 Two independent random variables, 9.2.2 A function of independent random variables , 9.3 Statistically dependent random variables , 9.3.1 Two dependent random variables , 9.3.2 The case of Gaussian random variables , 9.3.3 More random variables: the Rosenblatt transformation , 9.4 Computational problems , References , 10 Useful defini