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In Chap. 10 are presented supplementary facts of probability theory which can be useful in studying error analysis problems. Sections of this chapter contain information on statistical linearization, multidimensional regression, limit theorems of probability theory, and elements of mathematical statistics such as: estimators, testing statistical hypotheses or confidence intervals. The final section...
Chapter 8 is devoted to three-dimensional functions of independent random variables along with applications to an analysis of a positioning accuracy of robot manipulators. Procedure of determining polyhedrons of the positioning accuracy in such cases when tolerance limits of the positioning accuracy of particular joints of the manipulator are given, is described. When the positioning accuracy of joints...
At first in Chap. 3 are described such important notions as characteristic functions of a probability distribution defined as Fourier transform of a probability density function and constants characterizing random variables: an average value, a median value describing the middle of a distribution, a variation ratio closely connected with a standard deviation. Other characteristic constants characterizing...
Chapter 7 presents basic information concerning three-dimensional distributions of random variables. Attention is given to continuous distributions, mainly to a three-dimensional normal distribution of independent random variables. Described is a procedure of determining ellipsoids of probability concentration and their dimensions being determined by a chi-squared distribution with three degrees of...
In Chap. 5 is given basic information concerning two-dimensional distributions of random variables. Starting from a classical problem of the accuracy of artillery fire it is shown that, besides a traditional analytical procedure, components of a covariance tensor may be transformed by means of their representation by Mohr circles. It is shown that this representation, used commonly in mechanics of...
Chapter 9 is devoted to more advanced problems of error analysis: problems described by implicit equations and inequalities. After formulation of the problem, some methods of approximate calculation of the probability that inequalities for random variables and functions of random variables are presented. The powerful method helping to solve such problems, the Rosenblatt transform, is presented along...
At first, in Chap. 4 is given basic information concerning various practical problems in which functions of independent random variables are used in the analysis of the manufacturing or measuring errors. Simple examples illustrate how such functions are used in solving practical problems, among them in non-direct measurements or calculations of tolerance limits in two-dimensional nets of dimensions...
Chapter 6 is devoted to procedures in which two-dimensional functions of independent random variables are used for analysis of positioning accuracy of robot manipulators and various mechanisms. It is shown how the tolerance polygons in complex two-dimensional nets of dimensions can be constructed analytically or with the use of the method of static analogy described in Chap. 4. They can be also obtained...
In Chap. 2 basic information concerning probability and random variables as an introduction to error analysis is given. Such important notions as a probability density function and a cumulative distribution function are defined, along with fundamental parameters of a distribution: an average value, an average deviation, a variance, and a standard deviation. Basic parameters of a normal (Gaussian)...
In Chap. 1 is given introductory basic information concerning the practical aspects of the error analysis. Various examples of histograms show how much information may be deduced from them. Such important parameters deduced from a sample of measurements as a sample average, the sample variance and a sample standard deviation are defined, along with simple examples of practical significance are presented...
This book presents, in the simplest possible manner, those branches of error analysis which find direct applications in solving various problems in engineering. Chapters I, II, III, and IV contain a presentation of the fundamentals of error calculus: basic characteristics of error distributions, histograms and their various applications, basic continuous distributions of errors and functions of...
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