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Random point processes in reliability and safety modeling (in Russian)

M.S. Finkelstein

176 p.
Saint-Petersburg, CSRI "Elektropribor"

The simplest random point processes are considered for solving problems of reliability and safety assessment. The basic processes are the nonhomogeneous Poisson and the renewal process.

The developed methods are applied to modeling the reliability of software performance, to safety at sea assessment and to some other practical settings.

The systematic mathematical treatment of the general repair theory is performed for the first time in the literature. It is based on the notion of the generalized renewal process. A detailed description of applications of this theory is presented for solving the problems of planning accelerated testing and estimating the influence of random environment on a lifetime random variable to name a few.

The monograph can be helpful to those involved in reliability and safety analyses of various objects at different stages.

References: 146. Fig.10. Tab. 2.


CONTENTS

Introduction

Chapter 1. Probabilistic description of the simplest point processes
1.1 The lifetime distribution and the failure rate
1.2. Some definitions
1.3. Three ways of point processes description
1.4. The Poisson process
1.5. The renewal process
1.7. The Markov point processes
1.8. Some generalizations

Chapter 2. Terminating point processes in reliability and safety modeling
2.1. Reliability and safety of engineering systems
2.2. The terminating Poisson point process
2.3. The multiple availability
2.4. The terminating renewal process
2.5. The simplest spatial point processes
2.6. The planar model of point influences with fixed coordinates
2.7. The planar model of point influences with moving coordinates
2.8. The random paths process
2.9. The safety at sea application

Chapter 3. Point processes in some models of software reliability
3.1. Software reliability indexes
3.2. The review of conventional models in software reliability
3.3. The general definition of software reliability
3.4 Independence of history
3.5. One-dimensional model of the input space

Chapter 4. Introduction to the theory of general repair
4.1. Perfect, imperfect and general repair in engineering systems
4.2. Imperfect repair with 2 types of failures
4.3. The general repair function
4.4. The main asymptotic result
4.5. The stochastic process of general repair
4.6. The monotonicity properties
4.7. The degrading process of general repair

Chapter 5. Some applications of the theory of general repair
5.1. The virtual age in accelerated testing
5.2. The recalculation of characteristics for different environment
5.3. The lifetime distribution function in arbitrary environment
5.4. The virtual age of the distribution functions
5.5. The renewal process in changing environment
5.6. Shocks and general repair

Conclusion

166 p.
Saint-Petersburg, CSRI "Elektropribor", 1997
ISBN 5-900780-14-7


The principles and methodology are stated for the systems engineering of precision vacuum diffusion welding as a process component for developing objects of new technology. The technical solutions obtained on this basis are described, including techniques, methods, equipment facilities and algorithms for the welding technology design.

The book is intended for engineers and scientists engaged in precise instrument engineering.


CONTENTS

Introduction 3
Chapter 1. Precision vacuum diffusion welding as a means forrealization of permanent assemblies of precise instrument engineering joints (PIEJ) 7
1.1. Permanent assemblies in PIEJ -
1.2. Characteristics and features of construction materials 12
1.3. Welding features of materials used in PIEJ 18
1.4. Block diagram for solving problems of precision vacuum diffusion welding (PVDW) 27
Chapter 2. PVDW technology design 34
2.1. System of problem solution models for developing PVDW technology -
2.2. Multilevel iterative method for precision welding process development 50
2.3. Information-logical model for PVDW technology designing 58
Chapter 3. Theory and technological fundamentals for PVDW process 68
3.1. Investigation of control principles for PVDW thermomechanical parameters and factors 69
3.2. Development of PVDW process with regulated load of external drive and under thermal tightness pressure 74
3.3. Development of initial conditions and estimation criteria for assembly formation possibility 87
3.4. Software and design procedure for process of wire intermediate layers formation 97
Chapter 4. PVDW process equipment facilities 107
4.1. Set for diffusion welding with local electron-beam heating 108
4.2. Set for multiposition PVDW of elements on parts of rotation body form 110
4.3. Welding module with combined pressure 113
4.4. Set for multiposition PVDW with thermal tightness pressure 115
4.5. PVDW module for thin-walled hemispherical shells 117
Chapter 5. Technology development and practical PVDW realization when producing joints for precise instrument engineering 120
5.1. Assembly units of gyro devices -
  5.1.1. Beryllium rotors of electrostatic gyro -
  5.1.2. Metal-ceramic joints of sensor gyrohousing 141
  5.1.3. Joints and elements for spherical gyro with gas aerodynamic suspension, floated gyro and gravimeter core 153
5.2. Products of ionizing radiation technique154
5.3. Joints with long-length capillary channels for products of analytical instrument engineering 157
Conclusion 159
References 160
V.E. Dzhashitov, V.M. Pankratov / Under the general editorship of the RAS Academician V.G. Peshekhonov

150 p.
St. Petersburg: SRC of Russia - CSRI "Elektropribor", 2001
ISBN 5-900780-30-9


Mathematical models of classical and promising gyroscopic inertial data sensors of various physical principles and laws of operation have been considered. Principles of operation and dynamics fundamentals of thermally disturbed inertial gyroscopic sensors, devices and systems based on them are stated. Mathematical models of thermal drift of float, dynamically tuned, electrostatic non-contact, wave solid-state, micromechanical and fiber-optic gyros have been constructed and investigated. Particular attention has been given to the new mathematical models of thermal drift making it possible to investigate the phenomenon of deterministic chaos in non-linear thermally disturbed dynamic systems with inertial sensors.

The book is intended for scientists, engineers and technicians. Also it can be useful for post-graduates and students of higher education institutes.

Bibliography: 16 references. 34 illustrations. 1 table.


CONTENTS

Introduction5
Chapter 1. Models of bound physical processes of mechanical motion, heat-mass exchange, thermoelasticity, hydromechanics and optics for sensors of various principles of operation10
1.1. Problems of mathematical models construction and their solution strategy-
1.2. Mathematical models and investigation methods for thermal processes in gyroscopic sensors of inertial systems15
1.3. Mathematical models and investigation methods for mechanical motion processes in gyroscopic sensors of inertial systems24
1.4. Mathematical models and thermoelasticity theory methods in investigation of stressed and deformed state of gyroscopic sensors of inertial systems27
1.5. Mathematical models and investigation methods for hydromechanical processes in gyroscopic sensors of inertial systems30
1.6. Mathematical models and investigation methods for optic processes in fiber paths of gyroscopic sensors of inertial systems33
Chapter 2. Inertial data sensors of various physical principles of operation38
2.1. Float inertial sensors - principle of operation, mathematical models, investigation problems -
2.2. Rotor vibratory dynamically tuned inertial sensors - principle of operation, mathematical models, investigation problems 48
2.3. Electrostatic spherical inertial sensors - principle of operation, mathematical models, investigation problems57
2.4. Wave solid-state inertial sensors - principle of operation, mathematical models, investigation problems63
2.5. Micromechanical inertial sensors - principle of operation, mathematical models, investigation problems74
2.6. Fiber-optic inertial sensors - principle of operation, mathematical models, investigation problems108
2.7. Systematization of mathematical models of thermally disturbed inertial sensors118
Chapter 3. Special construction and investigation problems of mathematical models of thermally disturbed inertial data sensors 128
3.1. Deterministic chaos in disturbed non-linear gyroscopic systems - general approach -
3.2. Deterministic chaos in thermally disturbed fiber-optic inertial sensors139
Conclusions148
References149
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Journal "Giroskopiya i Navigatsiya" website (in Russian)
• based on fiber-optic gyros (FOG)
• based on micromechanical gyros (MMG)
• Shipborne speed and depth meters
• Magnetic compasses
• Communication complex Distancia-E
• Integrated Shipborne Communication and Broadcasting Complex P-409
• Trailing towed array device K-697E
• Equipment for shipborne self-powered telephone communication BTS
• Shipborne automatic digital telephone exchange P-443E
• Floating information assemblies for submarines
• Mobile aeromarine gravimeter Chekan-AM
• Multi-purpose bottomhole remote sensing system UZTS-90
• Micromechanical gyro MMG-2
• Micromechanical gyro MMG-EPTRON
• Multi-channel micro-acceleration measurement system SINUS
• Autonomous attitude control system for low-orbiting spacecrafts