Mathematical Methods of Reliability Theory - 1st Edition - ISBN: 9781483230535, 9781483263519

Mathematical Methods of Reliability Theory

1st Edition

Authors: B. V. Gnedenko Yu. K. Belyayev A. D. Solovyev
Editors: Z. W. Birnbaum E. Lukacs
eBook ISBN: 9781483263519
Imprint: Academic Press
Published Date: 1st January 1969
Page Count: 518
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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.

Table of Contents


Translation Editor's Note


Chapter 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


Chapter 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


Chapter 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


Chapter 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 λ of the Exponential Distribution

4.5 Nonparametric Methods for the Statistical Evaluation of Material Uniformity


Chapter 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


Chapter 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


Chapter 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



Subject Index


No. of pages:
© Academic Press 1969
Academic Press
eBook ISBN:

About the Author

B. V. Gnedenko

Yu. K. Belyayev

A. D. Solovyev

About the Editor

Z. W. Birnbaum

E. Lukacs

Affiliations and Expertise

Bowling Green State University

Ratings and Reviews