M.S. Finkelstein
Random point processes in reliability
and safety modeling (in Russian)
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
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