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