journal "Gyroscopy and Navigation" /  Books: 2005 2004 2002 2000-2001 1997-1999   

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.



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


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Last updated September 20, 2002