Mathematical Methods of Reliability Theory
Published on 20. June 2014
518 pages
978-1-4832-6351-9 (ISBN)
Description
Mathematical Methods of Reliability Theory discusses fundamental concepts of probability theory, mathematical statistics, and an exposition of the relationships among the fundamental quantitative characteristics encountered in the theory. The book deals with the set-theoretic approach to reliability theory and the central concepts of set theory to the phenomena. It also presents methods of finding estimates for reliability parameters based on observations and methods of testing reliability hypotheses. Based on mathematical statistics, the book also explains formulation of some selected results. It presents a method that increases the reliability of manufactured articles-redundancy. An important part of product quality control is the standards of acceptance-sampling plans which require simplicity, wide content for flexibility, comprehensive characteristics, and variability. The book also tackles economical and rational methods of sampling inspections, highlighting the need for a correct evaluation of environmental conditions-the factors which predetermine the choice of the inspection method. The book then explains how to estimate the efficiency of the operation of the sampling plan after its selection. The book can be helpful for engineers, mathematicians, economists, or industrial managers, as well as for other professionals who work in the technological, political, research, structural, and physico-chemical areas.
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Content
PrefaceTranslation Editor's NoteIntroductionChapter 1. Fundamentals of Probability Theory and Mathematical Statistics 1.1 Concept of a Random Event. Basic Formulas of Probability Theory 1.2 Random Variables and Their Distribution Functions 1.3 Numerical Characteristics of Random Variables 1.4 Some Limit Theorems in Probability Theory 1.5 General Information on the Theory of Random Processes 1.6 Fundamentals of Mathematical Statistics 1.7 The Laplace Transform BibliographyChapter 2. Characteristics of Reliability 2.1 Basic Concepts of Reliability Theory 2.2 Reliability of a Unit Functioning until First Failure 2.3 The Reliability of a "Renewable" Unit 2.4 System Reliability BibliographyChapter 3. Evaluation of Reliability Factors from Experimental Data 3.1 Testing for Reliability 3.2 General Methods of Evaluating Factors by the Results of Testing 3.3 Evaluation of the Parameter of the Exponential Law 3.4 Confidence Intervals for the Parameter of an Exponential Law 3.5 Confidence Intervals and Sets. Case of Many Parameters BibliographyChapter 4. Testing of Reliability Hypotheses 4.1 General Assumptions in the Theory of Testing Statistical Hypotheses 4.2 Tests of Hypotheses on the Exponentiality of the Distribution of Failure-Free Operation Time 4.3 Criteria for Testing Hypotheses on the Values of the Parameter of the Exponential Distribution 4.4 Sequential-Analysis-Type Tests for Hypotheses on the Value of the Parameter ¿ of the Exponential Distribution 4.5 Nonparametric Methods for the Statistical Evaluation of Material Uniformity BibliographyChapter 5. Standby Redundancy without Renewal 5.1 Introduction 5.2 Loaded Standbys 5.3 Birth and Death Processes 5.4 Unloaded Standbys 5.5 Lightly Loaded Standbys 5.6 Switching Unreliabilities 5.7 Certain Fundamental Problems of Standby Redundancy within the System BibliographyChapter 6. Standby Redundancy with Renewal 6.1 Introduction 6.2 Duplication with Renewal 6.3 Birth and Death Processes 6.4 Study of a Nonstationary Period 6.5 Application of Birth and Death Processes to Standby Redundancy with Renewal BibliographyChapter 7. Statistical Methods of Quality Control and Reliability of Mass Production 7.1 Introduction 7.2 Numerical Characteristics of Sampling Inspection Plans 7.3 Standards of Acceptance-Sampling Plans 7.4 Economical Control Plans 7.5 Subsequent Estimates of Quality from Sampling Results 7.6 Introduction to Problems of Continuous Sampling BibliographyAppendixSubject Index
