Reliability Is a New Science: Gnedenko Was Right

155 Pages·2017·2.882 MB·English

by  Paolo Rocchi (auth.)

Paolo Rocchi
Reliability Is A
New Science
Gnedenko Was Right
Reliability Is A New Science
Paolo Rocchi
Reliability Is A New Science
Gnedenko Was Right
With an Appendix by Gurami Sh. Tsitsiashvili
123
PaoloRocchi
IBM
Rome
Italy
and
LUISS GuidoCarli University
Rome
Italy
ISBN978-3-319-57471-4 ISBN978-3-319-57472-1 (eBook)
DOI 10.1007/978-3-319-57472-1
LibraryofCongressControlNumber:2017943205
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Onfaitlascienceavecdesfaits,commeonfait
une maison avec des pierres: mais une
accumulationdefaitsn’estpasplusunescience
qu’un tas de pierres n’est une maison.
Henri Poincaré
Contents
1 Background and Motivation... .... .... .... .... .... ..... .... 1
1.1 What Is a Principle-Based Theory?.. .... .... .... ..... .... 3
1.2 First Cornerstone: Soloviev’s Proof . .... .... .... ..... .... 7
1.3 Comments on the Reliability Function ... .... .... ..... .... 9
1.4 Questioning the Bathtub Curve. .... .... .... .... ..... .... 9
1.5 Scopes, Methods and Overview of the Present Work..... .... 13
References. .... .... .... ..... .... .... .... .... .... ..... .... 14
Part I Properties of Functioning Systems
2 Old and Novel Tools for the Calculus of the Hazard Rate.... .... 19
2.1 The Reliability of What? . .... .... .... .... .... ..... .... 19
2.2 Entropic Systems .. ..... .... .... .... .... .... ..... .... 23
2.3 Boltzmann-like Entropy .. .... .... .... .... .... ..... .... 26
2.4 Physical Meaning of the Boltzmann-like Entropy... ..... .... 29
References. .... .... .... ..... .... .... .... .... .... ..... .... 33
3 How Systems Break Down .... .... .... .... .... .... ..... .... 35
3.1 Interferences Overlap .... .... .... .... .... .... ..... .... 35
3.2 Factors Leading to Work Interruption.... .... .... ..... .... 37
3.3 Systematic Factors of Failure .. .... .... .... .... ..... .... 37
3.4 Simplified Models and Realistic Models.. .... .... ..... .... 40
3.5 Enduring Obtrusion and Decadence . .... .... .... ..... .... 41
3.6 Comments on the Principle of Progressive Deterioration .. .... 42
References. .... .... .... ..... .... .... .... .... .... ..... .... 46
4 Constant Decline... .... ..... .... .... .... .... .... ..... .... 49
4.1 Two Introductory Remarks.... .... .... .... .... ..... .... 49
4.2 Comments on the Linearity Assumption.. .... .... ..... .... 51
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viii Contents
4.3 Hazard Rate Caused by Constant Decline. .... .... ..... .... 53
4.4 Comments on Theorem 4.1 and Lemma 4.1... .... ..... .... 55
References. .... .... .... ..... .... .... .... .... .... ..... .... 56
5 Random Factors ... .... ..... .... .... .... .... .... ..... .... 59
5.1 Random Factors of Failure.... .... .... .... .... ..... .... 59
5.2 Comments on the Principle of Random Accidents .. ..... .... 60
5.3 Behavior of Accidents ... .... .... .... .... .... ..... .... 60
5.4 Hazard Rate Caused by Random Accidents ... .... ..... .... 62
5.5 Comments on Theorem 5.2 and Lemma 5.1... .... ..... .... 63
5.6 Shock Theories.... ..... .... .... .... .... .... ..... .... 65
References. .... .... .... ..... .... .... .... .... .... ..... .... 67
6 Accelerated Decline. .... ..... .... .... .... .... .... ..... .... 69
6.1 Compound Degradation .. .... .... .... .... .... ..... .... 70
6.2 Hazard Rate Caused by a Linear Cascade Effect ... ..... .... 71
6.3 Comments on Theorem 6.3 and Lemma 6.1... .... ..... .... 73
6.4 Hazard Rate Caused by Complex Cascade Effect... ..... .... 77
6.5 Comments on Theorem 6.5 and Lemma 6.2... .... ..... .... 80
6.6 Additional Remarks on the Constant and Accelerated
Decline of Systems. ..... .... .... .... .... .... ..... .... 85
References. .... .... .... ..... .... .... .... .... .... ..... .... 87
7 When the Premises Are Untrue .... .... .... .... .... ..... .... 89
7.1 The Entropy Does not Exist... .... .... .... .... ..... .... 89
7.2 The Linearity Assumption Is False.. .... .... .... ..... .... 90
7.3 The Cascade Effect Is False ... .... .... .... .... ..... .... 95
7.4 Binomial Assumption Is False . .... .... .... .... ..... .... 96
7.5 The Linearity Assumption Is Alternatively False and True. .... 98
7.6 Intent on Completeness... .... .... .... .... .... ..... .... 99
References. .... .... .... ..... .... .... .... .... .... ..... .... 99
8 Ideal Hazard Rate.. .... ..... .... .... .... .... .... ..... .... 101
8.1 Genericness... .... ..... .... .... .... .... .... ..... .... 101
8.2 Deductive Logic and the Tripartite Curve. .... .... ..... .... 102
8.3 Comments on the Bathtub Curve ... .... .... .... ..... .... 103
References. .... .... .... ..... .... .... .... .... .... ..... .... 106
Part II Properties of Reparable Systems
9 Properties of Repairable Systems... .... .... .... .... ..... .... 109
9.1 The Functioning State and the Recovery State. .... ..... .... 109
9.2 The Reparability Function .... .... .... .... .... ..... .... 110
9.3 Property of the Extreme States. .... .... .... .... ..... .... 111
9.4 Comments on the Extreme States of the System.... ..... .... 112
9.5 Property of the Repair Outcomes ... .... .... .... ..... .... 114
Contents ix
9.6 Comments on the Repair Outcomes. .... .... .... ..... .... 117
9.7 Property of the Repair Process. .... .... .... .... ..... .... 118
9.8 Comments on the Repair Process... .... .... .... ..... .... 118
References. .... .... .... ..... .... .... .... .... .... ..... .... 120
Part III Overall Conclusion
10 Conclusive Remarks and Comments .... .... .... .... ..... .... 125
10.1 What We Meant to Do... .... .... .... .... .... ..... .... 125
10.2 What Principles ... ..... .... .... .... .... .... ..... .... 126
10.3 What We Have Found in Part 1.... .... .... .... ..... .... 126
10.4 What We Have Found in Part 2.... .... .... .... ..... .... 127
10.5 Overall Discussion of the Results... .... .... .... ..... .... 128
References. .... .... .... ..... .... .... .... .... .... ..... .... 132
Appendix A: History of Reliability in Literature .. .... .... ..... .... 133
Appendix B: Two Sided Estimates of Rate Convergence in Limit
Theorem for Minimums of Random Variables. ..... .... 135
Appendix C: Mortality Plateau .... .... .... .... .... .... ..... .... 143
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 151
About the Author
Paolo Rocchi has been recognized as an Emeritus Docent at IBM for his
achievements,andservesasanAdjunctProfessoratLuissUniversityofRome.He
isstillactiveinvariousareasofresearch,includinginformationtheory,probability
theory, computer science education, and software engineering. Rocchi is a solitary
‘pathfinder’whoisnostrangertogroundbreakingproposals.Hehasauthoredover
one hundred and thirty works including a dozen volumes.
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Acronyms
AAP Advanced Aging Period
ABAO As-Bad-As-Old
AGAN As-Good-As-New
ALT Accelerated Life Testing
CF Continuous Factors
CSE Continuous Side Effects
DfR Design for Reliability
DRM Degradation Reliability Methods
IDL International Database on Longevity
MOF Multi-Organ Failure
MTBF Mean Time Between Failure
MTTF Mean Time To Failure
NAP Normal Aging Period
NTA Network Theory of Aging
PHM Proportional Hazard Model
POF Physics of Failure
PM Preventive Maintenance
RF Random Factors
TS Thermodynamic System
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