G. Tsitsiashvili, M.
Osipova
“COLORING” OF MAP BY FINITE NUMBER OF COLORED POINTS USING
FUZZY RECTANGLES
In this paper an
algorithm of a map “coloring” by a finite number of
color points is constructed. This algorithm is based on
the procedure of the interval images recognition and on
the algorithm of a construction of a fuzzy rectangle. It
is significantly simpler and compact than the
triangulation procedure using in the mapping.
Dmitry A. Maevsky, Elena
J. Maevskaya, Oleg P. Jekov, Ludmila N. Shapa
VERIFICATION OF THE SOFTWARE RELIABILITY MODELS
The paper concerns
the verification of the existing Software reliability
models and their comparison to a new one based on the
theory of Software system dynamics. A statistically
significant number of observations over the process of
fault detecting in the fifty different Software systems
has been used for the verification. The results of
comparison of estimation correctness of the nine most
widely used reliability models to the new one based on
the theory of Software system dynamics are represented.
It has been proven the Software system dynamics model
provided 2,7 times higher correctness of reliability
estimation than the existing reliability models.
Mark P. Kaminskiy
CONFIDENCE LIMITS ON PERCENTILES BASED ON TEST RESULTS WITH
A FEW FAILURES – NON-PARAMETRIC VERSUS EXPONENTIAL
The non-parametric
lower confidence limits on percentiles in the classes of
continuous and increasing failure rate distributions are
compared to their parametric exponential counterpart for
the Type II censored data. In opposite to the common
belief that non-parametric estimation procedures are
always less effective than analogous parametric
procedures, in the considered case, it turns out that
the non-parametric procedures provide either better or
the same confidence estimates. In a particular case,
when the data include only one uncensored observation (failure)
and all three estimates (in the classes of continuous
distributions, increasing failure rate distributions and
the exponential distribution) exist, the respective
three lower confidence limits on percentiles coincide.
G. Tsitsiashvili
ASYMPTOTIC OF CYCLY EXISTENCE IN ORIENTED GRAPH WITH LOW
RELIABLE EDGES
In this paper a power
asymptotic of a probability that there is a cycle in a
random oriented graph with n nodes and low reliable
edges is constructed. An accelerated algorithm for a
calculation of asymptotic coefficients with products,
where is an
amount of products in a multiplication of two matrixes
with a size is
constructed.
G. Unnikrishnan, Shrihari,
Nihal A. Siddiqui
APPLICATION OF BAYESIAN METHODS TO EVENT TREES WITH CASE
STUDIES
Event trees are used
extensively to analyze accident scenarios in several
domains. The tree and its branching structures are used
to represent the failure of successive barriers to an
initiating event. The end positions of the branches
indicate the outcome of progression of each scenario.
When probabilities are assigned to success and failure
of each barrier the end probabilities can be calculated
fairly easily. The logical sequence of the events is
clear from the tree structure. However Bayesian networks
(BN) are directed acyclic graphs with the nodes
indicating events and connected arcs indicating the
relationships between the nodes. Initial probabilities
are assigned to the parent nodes and conditional
probabilities of child nodes are worked out using Bayes
Theorem. Bayesian network is a probabilistic modeling
technique. Event trees can be mapped into Bayesian
networks. Once an event tree is mapped as a Bayesian
network, forward (same as in event trees) and backward
analysis (possible but involved in event trees) can be
performed. Additionally BN has the flexibility for
adding causal factors that influence the events. It
offers a different perspective of probabilities and
better understanding of the incident scenarios. This
paper will present mapping of event trees typically
found in process industries to Bayesian networks with
case studies.
G.Sh. Tsitsiashvili
ORIENTED GRAPHS WITH UNRELIABLE NODES
In applications there
are networks with unreliable nodes. To construct models
of such networks and effective algorithms of their
analysis in this paper some elements from the graph
theory, the algebra, the sets theory and the probability
theory are combined. These constructions allow to
investigate oriented graphs with unreliable nodes using
as accuracy so asymptotic formulas. All constructed
algorithms have a linear complexity by a number of graph
nodes.
Farzaliyev Y.Z.
COMPARISON OF WAYS OF NORMALIZATION AT CLASSIFICATION OF
INITIAL DATA
Normalization at
classification of initial data is an indispensable
condition of an opportunity of comparison of technical
and economic characteristics of the equipment and
devices of power supply systems. In work, results of
comparison of efficiency of ways of normalization of
quantitative estimations of analyzed characteristics
used in practice are resulted.
V. M. Chacko
TOTAL TIME ON TEST TRANSFORMS ORDERING OF SEMI-MARKOV SYSTEM
First passage time of
semi-Markov performance process of a multistate system
are considered. TTT (Total time on Test) transform
ordering is discussed.
M.Uspensky, I.Kyzrodev
A SOLUTION CONVERGENCE IN A NEURAL NETWORK, AND AN
ACCOUNTING OF LOAD PRIORITIES AT A POWER SYSTEM RESTORATION
Uniqueness of
solution at a scheme choice for the restorable power
system on the artificial neural network (ANN) base is
shown. The elementary scheme of a power network is used
for this purpose and the subsequent distribution of its
results is applied on any network configuration. The way
of priority accounting for loads is developed at
creation of the restorable power system on the base of
the proof on solution uniqueness for ANN
