Error Analysis with Applications in Engineering

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