Reliability is a New Science (eBook)

Gnedenko Was Right

Paolo Rocchi (Autor)

eBook Download: PDF

2017 | 1st ed. 2017
XV, 152 Seiten
Springer International Publishing (Verlag)
978-3-319-57472-1 (ISBN)

Infos

This work illustrates research conducted over a ten-year timespan and addresses a fundamental issue in reliability theory. This still appears to be an empirically disorganized field and the book suggests employing a deductive base in order to evolve reliability as a science. The study is in line with the fundamental work by Gnedenko.

Boris Vladimirovich Gnedenko (1912 - 1995) was a Soviet mathematician who made significant contributions in various scientific areas. His name is especially associated with studies of dependability, for which he is often recognized as the 'father' of reliability theory.  In the last few decades, this area has expanded in new directions such as safety, security, risk analysis and other fields, yet the book 'Mathematical Methods in Reliability Theory' written by Gnedenko with Alexander Soloviev and Yuri Bélyaev still towers as a pillar of the reliability sector's configuration and identity.

The present book proceeds in the direction opened by the cultural project of the Russian authors; in particular it identifies different trends in the hazard rate functions by means of deductive logic and demonstrations. Further, it arrives at multiple results by means of the entropy function, an original mathematical tool in the reliability domain. As such, it will greatly benefit all specialists in the field who are interested in unconventional solutions.

Prof. Paolo Rocchi has been recognized as an Emeritus Docent at IBM for his achievements, and is also an Adjunct Professor at Luiss University of Rome. He is still active in various areas of research, including information theory, probability theory, computer science education, and software engineering. Rocchi is no stranger to groundbreaking proposals, having authored over one hundred and thirty works including a dozen volumes.

Inhalt

Contents 6
About the Author 9
Acronyms 10
Introduction 11
1 Background and Motivation 12
1.1 What Is a Principle-Based Theory? 14
1.2 First Cornerstone: Soloviev’s Proof 18
1.3 Comments on the Reliability Function 20
1.4 Questioning the Bathtub Curve 20
1.5 Scopes, Methods and Overview of the Present Work 24
References 25
Functioning Systems 28
2 Old and Novel Tools for the Calculus of the Hazard Rate 29
2.1 The Reliability of What? 29
2.2 Entropic Systems 33
2.3 Boltzmann-like Entropy 36
2.4 Physical Meaning of the Boltzmann-like Entropy 39
References 43
3 How Systems Break Down 45
3.1 Interferences Overlap 45
3.2 Factors Leading to Work Interruption 47
3.3 Systematic Factors of Failure 47
3.4 Simplified Models and Realistic Models 50
3.5 Enduring Obtrusion and Decadence 51
3.6 Comments on the Principle of Progressive Deterioration 52
References 56
4 Constant Decline 58
4.1 Two Introductory Remarks 58
4.2 Comments on the Linearity Assumption 60
4.3 Hazard Rate Caused by Constant Decline 62
4.4 Comments on Theorem 4.1 and Lemma 4.1 64
References 65
5 Random Factors 67
5.1 Random Factors of Failure 67
5.2 Comments on the Principle of Random Accidents 68
5.3 Behavior of Accidents 68
5.4 Hazard Rate Caused by Random Accidents 70
5.5 Comments on Theorem 5.2 and Lemma 5.1 71
5.6 Shock Theories 73
References 75
6 Accelerated Decline 76
6.1 Compound Degradation 77
6.2 Hazard Rate Caused by a Linear Cascade Effect 78
6.3 Comments on Theorem 6.3 and Lemma 6.1 80
6.4 Hazard Rate Caused by Complex Cascade Effect 84
6.5 Comments on Theorem 6.5 and Lemma 6.2 87
6.6 Additional Remarks on the Constant and Accelerated Decline of Systems 92
References 94
7 When the Premises Are Untrue 96
7.1 The Entropy Does not Exist 96
7.2 The Linearity Assumption Is False 97
7.3 The Cascade Effect Is False 102
7.4 Binomial Assumption Is False 103
7.5 The Linearity Assumption Is Alternatively False and True 105
7.6 Intent on Completeness 106
References 106
8 Ideal Hazard Rate 108
8.1 Genericness 108
8.2 Deductive Logic and the Tripartite Curve 109
8.3 Comments on the Bathtub Curve 110
References 113
Reparable Systems 114
9 Properties of Repairable Systems 115
9.1 The Functioning State and the Recovery State 115
9.2 The Reparability Function 116
9.3 Property of the Extreme States 117
9.4 Comments on the Extreme States of the System 118
9.5 Property of the Repair Outcomes 120
9.6 Comments on the Repair Outcomes 123
9.7 Property of the Repair Process 124
9.8 Comments on the Repair Process 124
References 126
Overall Conclusion 128
10 Conclusive Remarks and Comments 129
10.1 What We Meant to Do 129
10.2 What Principles 130
10.3 What We Have Found in Part 1 130
10.4 What We Have Found in Part 2 131
10.5 Overall Discussion of the Results 132
References 136
Appendix A: History of Reliability in Literature 137
Appendix B: Two Sided Estimates of Rate Convergence in Limit Theorem for Minimums of Random Variables 139
B.1. Introduction 139
B.2. Estimates of closeness between limit and pre-limit distributions in scheme of random variables minimum 139
B.3. Upper and Low Bounds for Convergence of ?n to Zero 141
B.4. Conclusion 145
References 145
Appendix C: Mortality Plateau 146
C.1. Experimental Evidence 146
C.2. Simplification Assumption 147
C.3. Comments on Theorem C.1 149
References 153
Index 154

Produkt-Details

• Erscheint lt. Verlag: 13.7.2017
• Zusatzinfo: XV, 152 p. 50 illus.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Schlagworte: arrow of time • Deductive logic • Entropy functions • Foundations of the reliability theory • insurance • Mathematical Modeling • quality control • Quality Control, Reliability, Safety and Risk
• ISBN-10: 3-319-57472-8 / 3319574728
• ISBN-13: 978-3-319-57472-1 / 9783319574721