Gnedenko / Belyayev / Solovyev Mathematical Methods of Reliability Theory

1. Auflage 2014
ISBN: 978-1-4832-6351-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 518 Seiten, Web PDF

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.

Autoren/Hrsg.

Gnedenko, B. V.

Belyayev, Yu. K.

Solovyev, A. D.

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematical Methods of Reliability Theory;4
3;Copyright Page ;5
4;Table of Contents;10
5;Preface;6
6;Introduction;14
7;CHAPTER 1. Fundamentals of Probability Theory and Mathematical Statistics;19
7.1;1.1 Concept of a Random Event. Basic Formulas of Probability Theory;19
7.2;1.2 Random Variables and Their Distribution Functions;27
7.3;1.3 Numerical Characteristics of Random Variables;38
7.4;1.4 Some Limit Theorems in Probability Theory;43
7.5;1.5 General Information on the Theory of Random Processes;53
7.6;1.6 Fundamentals of Mathematical Statistics;61
7.7;1.7 The Laplace Transform;74
7.8;Bibliography;80
8;CHAPTER 2. Characteristics of Reliability;82
8.1;2.1 Basic Concepts of Reliability Theory;82
8.2;2.2 Reliability of a Unit Functioning until First Failure;91
8.3;2.3 The Reliability of a "Renewable" Unit;109
8.4;2.4 System Reliability;132
8.5;Bibliography;155
9;CHAPTER 3. Evaluation of Reliability Factors from Experimental Data;156
9.1;3.1 Testing for Reliability;156
9.2;3.2 General Methods of Evaluating Reliability Factors from Experimental Data;162
9.3;3.3 Evaluation of the Parameter of the Exponential Law;181
9.4;3.4 Confidence Intervals for the Parameter of an Exponential Law;195
9.5;3.5 Confidence Intervals and Sets. Case of Many Parameters;208
9.6;Bibliography;224
10;CHAPTER 4. Testing of Reliability Hypotheses;226
10.1;4.1 General Assumptions in the Theory of Testing Statistical Hypotheses;226
10.2;4.2 Tests of Hypotheses on the Exponentiality of the Distribution of Failure-Free Operation Time;242
10.3;4.3 Criteria for Testing Hypotheses on the Values of the Parameter of the Exponential Distribution;254
10.4;4.4 Sequential-Analysis-Type Tests for Hypotheses on the Value of the Parameter . of the Exponential Distribution;266
10.5;4.5 Nonparametric Methods for the Statistical Evaluation of Material Uniformity;280
10.6;Bibliography;288
11;CHAPTER 5. Standby Redundancy without Renewal;290
11.1;5.1 Introduction;290
11.2;5.2 Loaded Standbys;291
11.3;5.3 Birth and Death Processes;299
11.4;5.4 Unloaded Standbys;309
11.5;5.5 Lightly Loaded Standbys;316
11.6;5.6 Switching Unreliabilities;324
11.7;5.7 Certain Fundamental Problems of Standby Redundancy within the System;331
11.8;Bibliography;335
12;CHAPTER 6. Standby Redundancy with Renewal;336
12.1;6.1 Introduction;336
12.2;6.2 Duplication with Renewal;337
12.3;6.3 Birth and Death Processes;347
12.4;6.4 Study of a Nonstationary Period;353
12.5;6.5 Application of Birth and Death Processes to Standby Redundancy with Renewal;367
12.6;Bibliography;374
13;CHAPTER 7. Statistical Methods of Quality Control and Reliability of Mass Production;376
13.1;7.1 Introduction;376
13.2;7.2 Numerical Characteristics of Sampling Inspection Plans;390
13.3;7.3 Standards of Acceptance-Sampling Plans;402
13.4;7.4 Economical Control Plans;414
13.5;7.5 Subsequent Estimates of Quality from Sampling Results;434
13.6;7.6 Introduction to Problems of Continuous Sampling;455
13.7;Bibliography;465
14;Appendix;467
15;Subject Index;514