Thomas L. Saaty
CONFLICTS RESOLUTION AS A GAME WITH PRIORITIES:
MULTIDIMENSIONAL CARDINAL PAYOFFS, PART 1
There are two ways to consider increasing the
effectiveness of the theory of games in applications.
The first is to derive priorities for the payoffs using
a cardinal absolute relative scale instead of an ordinal
or interval scale to do equilibrium analysis. Our
approach using cardinal payoffs is illustrated with one
example in an application to OPEC strategies that the
author published in the International Journal of Game
Theory.
Vyacheslav Abramov
FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE
CLIENT/SERVER COMPUTER NETWORKS
In the recent paper [Abramov, RÒÀ, 2 (2007), pp. 34-42],
confidence intervals have been derived for symmetric
large client/server computer networks with client
servers, which are subject to breakdowns. The present
paper mainly discusses the case of asymmetric network
and provides another representation of confidence
intervals.
Boyan Dimitrov, George Hayrapetyan, Peter Stanchev, Zohel
Khalil
AGING AND LONGEVITY CONTROL OF BIOLOGICAL SYSTEMS VIA DRUGS
- A RELIABILITY MODEL
The treatments in bio-systems correspond to respective
repairs known in reliability. Some treatments may make
the biological objects younger; others may make them
older, or not deteriorate their current age. Such kind
of "maintenance" has some analogous failure/repair
models in reliability. We use it to incorporate some
results of reliability and bio modeling for the
quantitative studies of the aging and resistance of
bio-systems to environmental stress factors. We call
"calendar age" the age of a bio-object which does not
use treatments, or uses it without age improvement, or
deterioration. All bio-objects, which are using
treatments of same strength and direction of effect,
have "virtual age". We explain here what the virtual age
is, and how is it related to age correcting factors. We
illustrate our common results about the virtual ages on
the example of the Gompertz-Makenham law of mortality,
and discuss the relations of the longevity, mechanism of
aging and age affecting control. As a consequence, a
concept of age determination is proposed. Numeric and
graphical examples are provided.
Yakov Genis
RELIABILITY AND RISK ASSESSMENT OF SYSTEMS OF PROTECTION AND
BLOCKING WITH FAST RESTORATION
There is examined a system with fast restoration which
should be operational beginning from some moments of
time. If beginning from these moments of time the system
is defective during the time more than the assigned
random time interval it is considered failed. Such
system includes the models of systems with the
protection and blocking and systems with the discrete
periodic functions. The estimations of indices of
failure-free performance and maintainability of these
systems and the estimation of indices of risk and
losses, connected with the failure (accident) of the
system with protection are obtained. This material was
presented in the Mathematical Methods in Reliability
2007 Conference in Glasgow, UK.
Gurami Tsitsiashvili, A. Losev
AST ALGORITHMS OF ASYMPTOTIC ANALYSIS OF NETWORKS WITH
UNRELIABE ARCS
A problem of a reliability in networks with unreliable
elements naturally origin in technical applications. But
a direct calculation of the reliability demands a number
of operations which increases geometrically dependently
on a number of arcs. So it is necessary to use
approximate methods and particularly asymptotic one. In
other work asymptotic reliability is calculated in
analogous asymptotic suggestions on the network arcs.
Main parameters in these asymptotic are a shortest way
length and a maximal flow in a network. In this paper
different partial classes of networks are considered and
effective algorithms of their parameters calculations
are suggested. These networks are networks originated by
dynamic systems, networks with integer-valued lengths of
arcs, superposition of networks and bridge schemes.
Gurami Tsitsiashvili
BOTTLENECKS IN GENERAL TYPE LOGICAL SISTEMS WITH UNRELIABE
ELEMENTS
In this paper a model of general type logical system
with unreliable elements is considered. An asymptotic
analysis of its work (failure) probability is made in
appropriate conditions on work (failure) probabilities
of the system elements. A concept of bottlenecks of this
system is constructed on a suggestion that an increase
(a decrease) of elements reliabilities lead to an
increase (a decrease) of the system reliability. A
construction of general type logical system is founded
on concepts of disjunctive and conjunctive normal forms
(DNF and CNF) of a logical function.
Mark Kaminskiy, Vasili Krivtsov
AN INTEGRAL MEASURE OF AGING/REJUVENATION FOR REPAIRABLE AND
NON-REPAIRABLE SYSTEMS
This paper introduces a simple index that helps to
assess the degree of aging or rejuvenation of a
non-repairable system. The index ranges from -1 to 1 and
is negative for the class of decreasing failure rate
distributions (or deteriorating point processes) and is
positive for the increasing failure rate distributions
(or improving point processes). The introduced index is
distribution free.
Revaz Kakubava
ANALYSIS OF ALTERNATING RENEWAL PROCESSES WITH DEPENDED
COMPONENTS
In the terms of operational calculus the probability
characteristics of direct and reverse residual renewal
time of alternating renewal process, where renewal time
depends on life-time, are found.
Edward Korczak
COMPUTATION OF FAILURE/REPAIR FREQUENCY OF MULTI-STATE
MONOTONE SYSTEMS
The paper deals with calculation methods for failure and
repair frequencies of multi-state monotone systems, both
for the instantaneous and steady state cases. Being
based on the binary representation of multi-state
structure, new general formula for the failure/repair
frequency is derived. This formula is used to obtain
simple rules for the calculation of failure/repair
frequency. In particular, the use of the algebra of dual
numbers is presented.
Mark Bebbington, Chin-Diew Lai, Ricardas Zitikis
LIFETIME ANALYSIS OF INCANDESCENT LAMPS: THE MENON-AGRAWAL
MODEL REVISITED
The use of the Weibull distribution to model lifetimes
of incandescent lamps was originally suggested by Leff
(1990). Following this suggestion, Agrawal and Menon
have offered and investigated, in a series of papers, an
improved model constructed from physical considerations
and laws of mathematical statistics. In the present
paper we offer supplementary thoughts concerning the
Agrawal-Menon model and its several modifications. In
addition, we discuss the use of Pinelis's l'Hospital-type
calculus rules in the analysis of ageing properties of
lifetime distributions.
