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Reliability theory has become one of the important areas in
Operational Research and Systems Engineering. Any system analysis,
in order to be complete, must give due consideration to system
reliability and availability. A system deSigner is often faced with
the problems of evaluation and improvement of system relia bility
and determination of optimum preventive maintenance schedule. In
the solution of these problems, he is largely aided by mathematical
mOdels. These models have received consi derable attention in the
past several years following the satel lite era. The monographs of
Gnedenko, Belyayev and Solovyev, and Barlow and Proschan describe
the state of art of the subject upto 1965 and are largely
responsible for the further work in the subject. The large number
of papers and surveys that have appeared subsequently in journals
devoted to Operational Research, Industrial Engineering and
Statistical Quality Control amply demonstrate the overwhelming
importance of the subject in contexts other than satellite and
space craft research. While there are very many important problems
that stem from these models, atten tion has been largely confined
to calculations of reliability of the system. In a lighter vein the
authors feel that the original papers in the area have a common
feature-oBJECTIVE ORIENTEDNES- the general theme of Operational
Research and in general, it is carried too far and to a high degree
of meticulousness. Thus there is a general need for a cogent
account of all the results that have appeared in the literature."
1 Some basic neurophysiology 4 The neuron 1. 1 4 1. 1. 1 The axon 7
1. 1. 2 The synapse 9 12 1. 1. 3 The soma 1. 1. 4 The dendrites 13
13 1. 2 Types of neurons 2 Signals in the nervous system 14 2. 1
Action potentials as point events - point processes in the nervous
system 15 18 2. 2 Spontaneous activi~ in neurons 3 Stochastic
modelling of single neuron spike trains 19 3. 1 Characteristics of
a neuron spike train 19 3. 2 The mathematical neuron 23 4
Superposition models 26 4. 1 superposition of renewal processes 26
4. 2 Superposition of stationary point processe- limiting behaviour
34 4. 2. 1 Palm functions 35 4. 2. 2 Asymptotic behaviour of n
stationary point processes superposed 36 4. 3 Superposition models
of neuron spike trains 37 4. 3. 1 Model 4. 1 39 4. 3. 2 Model 4. 2
- A superposition model with 40 two input channels 40 4. 3. 3 Model
4. 3 4. 4 Discussion 41 43 5 Deletion models 5. 1 Deletion models
with 1nd~endent interaction of excitatory and inhibitory sequences
44 VI 5. 1. 1 Model 5. 1 The basic deletion model 45 5. 1. 2
Higher-order properties of the sequence of r-events 55 5. 1. 3
Extended version of Model 5. 1 - Model 60 5. 2 5. 2 Models with
dependent interaction of excitatory and inhibitory sequences -
MOdels 5. 3 and 5.
Stochastic Point Processes are interesting from many points of
view. From and abstract point of view, point process is a simple
version of random measure; these processes have acquired importance
mainly due their viability in modeling a variety of phenomena
spanning physical, biological, economic and engineering sciences.
This volume with contributions from leading probabilists contains,
besides surveys on the state-of-art of the theory, papers dealing
with problems of queues, inventory, reliability and population
evolution. There are also papers dealing with practical aspects
like statistical inference and nonlinear filtering. The book will
be of interest to a wide spectrum of people including those working
in the area of operations research, signal processing, electrical
communications & control and neural network.
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