# Failure-Tolerant Computer Design

## 1st Edition

**Authors:**William H. Pierce

**eBook ISBN:**9781483263472

**Imprint:**Academic Press

**Published Date:**1st January 1965

**Page Count:**256

## Description

Failure-Tolerant Computer Design focuses on the use of redundancy theory in improving the reliability of computers.

The book first offers information on redundancy theory and limit theorems. Discussions focus on applications in determining the optimum placement of restoring organs; time asymptotes for log failure probability for exponential survival probability; reliability of multiple-function system with paralleled individual units; and basic concepts for making reliable computers out of unreliable parts. The text then examines decision theory in redundant systems and adaptive decision elements.

The publication examines the interconnection structure for redundant logic and redundant relay theory. Topics include Moore-Shannon limit theorem; systematic groupings of inputs in single-layer error-correcting interwoven redundant logic; interwoven logic with alternating-layer error correction; and interwoven logic with single-layer error correction. The book also elaborates on transition analyses in reliability theory, including Markov chain theory and probability bounds in Markov chains having many states or inexactly known transition matrices.

The manuscript is a vital source of data for engineers and researchers interested in failure-tolerant computer design.

## Table of Contents

Preface

Chapter I. Introduction to Redundancy Theory

A. Basic Concepts for Making Reliable Computers out of Unreliable Parts

B. Error Types and Reliability Types

Chapter II. Limit Theorems: A Foundation for Redundancy Theory

A. Introductory Ideas on Reliability Synthesis

B. Reliability Asymptotes of Paralleled Units

C. Reliability of Multiple-Function System with Paralleled Individual Units

D. A Systematic Procedure for Selecting the Next Improvement in a System

E. Time Asymptotes for Log Failure Probability for Exponential Survival Probability

F. Applications in Determining the Optimum Placement of Restoring Organs

G. Failure Probability Asymptotes for a Fixed System

H. A Short Summary

Problems

Chapter III. Decision Theory in Redundant Systems

A. Concepts and Techniques

B. The Linearly Separable Decision Element

C. Decision Theory and Vote-Taking

D. Reliability Analysis of Vote-Takers

E. Optimum and Optimized Settings of Vote-Weights Using Imperfect Information

F. Summary on Using Decision Theory in Redundant Computers

Problems

Chapter IV. Adaptive Decision Elements

A. Cyclic Error-Counting Adaption Procedures

B. Incremental Adaption Procedures

C. Placement of Decision Elements in Redundant Networks

D. System Reliability

E. Summary

Problems

Chapter

V. Interconnection Structure for Redundant Logic (The Theory of Interwoven Redundant Logic)

A. Vocabulary for Interwoven Logic

B. Restoring Organs

C. Interwoven Logic with Single-Layer Error Correction

D. Interwoven Logic with Alternating-Layer Error Correction

E. Systematic Groupings of Inputs in Alternating-Layer Interwoven Logic

F. Systematic Groupings of Inputs in Single-Layer Error-Correcting Interwoven Redundant Logic

G. Summary and Conclusions

Problems

Chapter VI. Redundant Relay Theory

A. The h(p) Function

B. The Moore-Shannon Limit Theorem

C. Other Reliability Techniques Related to the Moore and Shannon Paper

Problems

Chapter VII. The Place, if Any, of Coding Techniques in Failure Tolerant Digital Networks

A. Historical Background

B. Synthesis Example

C. Placement of Decoders

D. Decoder Complexity

E. Conclusions

Problems

Chapter VIII. Transition Analyses in Reliability Theory

A. Introductory Markov Chain Theory

B. Two Reliability Problems for Nonredundant Systems

C. Reliability Analyses for Chains of Restoring Organs

D. Probability Bounds in Markov Chains Having Many States or Inexactly Known Transition Matrices

E. Applications of Probability Bounds

Problems

Chapter IX. Conclusions, Comparisons, and Unsolved Problems

A. What Is Known

B. What Is Best

C. What Is Unknown

Appendix I. Stability Analysis of Adaption Method II-B

Text

Stability Example

Problems for Appendix 1

Appendix 2. Equilibrium Analysis of Adaption Method III-A

Text

Appendix 3. Optimized Increments for Adaption Methods IV-A and IV-B

Text

Appendix 4. Limitations of all Schemes of Interwoven Alternation Layers

Text

Appendix 5. Reliability Analysis of Alternating Layer Schemes

Text

Appendix 6. Generation of B-Groupings

Text

Appendix 7. Existence of Limits for "Equivalent Error Probability"

Text

References

Bibliography

Author Index

Subject Index

## Details

- No. of pages:
- 256

- Language:
- English

- Copyright:
- © Academic Press 1965

- Published:
- 1st January 1965

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483263472