TeAM
YYePG
Digitally signed by TeAM YYePG
DN: cn=TeAM YYePG, c=US,
o=TeAM YYePG, ou=TeAM YYePG,
email=
Reason: I attest to the accuracy and
integrity of this document
Date: 2005.05.28 09:53:55 +08'00'
Scenario Logic and Probabilistic
Management of Risk in Business
and Engineering
Applied Optimization
Volum
e
93
Series
Editors:
Panos M. Pardalos
University of Florida, U.S.A.
Donald W. Hearn
University of Florida, U.S.A.
Scenario Logic and Probabilistic
Management of Risk in Business
and Engineering
by
E.D. Solojentsev
Russian Academy of Sciences, Russia
Springer
eBook ISBN: 1-4020-2978-0

School “Modelling and Analysis of Safety and Risk in complex systems”
(St.Petersburg, IPMash RAN, 2001, 2002, 2003).
E. D. Solojentsev. Scenario logic and probabilistic management
of risk in business and engineering. Pages — 391 p., Figures — 70;
Tables — 40; Refers — 118.
The methodological aspects of the scenario logic and probabilistic
(LP) non-success risk management are considered, following from anal-
ysis of connections between management and risk, personals and risk,
and from study of risk management at stages of design, test and opera-
tion of complex systems.
The theoretical bases of the scenario non-success risk LP-manage-
ment in business and engineering are stated, including LP-calculus, LP-
methods, and LP-theory with groups of incompatible events (GIE). Ex-
amples of risk LP-models with logical connections
OR
,
AND
,
NOT
,
cycles and GIE are given. Methods and algorithms for the scenario risk
LP-management in problems of classification, investment and effective-
ness are described.
Risk LP-models and results of numerical investigations for credit
risks, risk of frauds, security portfolio risk, risk in quality, accuracy, and
risk in multi-state system reliability are given. A rather large number
of new problems of estimation, analysis and management of risk are
considered. In some problems the risk LP-models prove to be showed
almost two times more accurate and seven times more robustness than
other well-known models of risks. Software for risk problems based on

Monitoring and risk
State safety program of Russia
Methods of nonlinear mechanics and probability theory
for accidents
Scenario LP-modelling and management of non-success
risk
11
11
15
17
17
18
20
21
22
24
29
Chapter 2. THE HUMAN BEING AND RISKS
31
2.1.
2.2.
2.3.
2.4.
2.5.
Frauds in business
Errors of personnel
Asymmetric actions of terrorists
Hackers attacks to informational networks
Personnel in modern civilization
31

3.10.
3.11.
3.12.
3.13.
Minimization of the number of decisions
Structural design
Concept of the acceptable risk
Markowitz’s and VaR-approach to investment risk
Active and passive management of risk
Algorithmic calculations
Arithmetical and logical addition
48
50
52
54
57
60
61
Chapter 4. RISK MANAGEMENT AT DEBUGGING
TESTS
4.1.
4.2.
4.3.
4.4.
4.5.
4.6.
4.7.
4.8.
4.9.
Definition of debugging tests

Scenarios of accident appearance
System of monitoring
95
96
98
98
103
Chapter 6. RISK MANAGEMENT ON DANGEROUS
PLANT
107
6.1.
6.2.
Difficult problems
Management of risk
6.2.1.
6.2.2.
6.2.3.
6.2.4.
Period of safe wearing of resource
Risk systematization and classification of problems
The use of risk computation results in exploitation
Principles of work organization for risk decrease
6.3.
6.4.
Financing of the risk management process
Reliability regulation of engineering and a person
107
109
109
111

8.2.
8.3.
8.4.
Basic concepts and definitions of the theory of risk and
safety
151
The basic principles of the LP-method
Transformation of L-function to P-polynomial
“Weight” of the argument in the L-function
8.4.1.
8.4.2.
8.4.3.
Calculation of Boolean difference
Calculation of element’s weight in L-functions
Examples
8.5.
8.6.
“Importance” of elements in a system
Example of construction of the L-function of danger
Chapter 9. AUTOMATED STRUCTURAL AND LOGI-
CAL MODELLING
9.1.
9.2.
9.3.
9.4.
9.5
.
9.6.
9.7.
Problems of LP-modelling

184
185
185
x
Contents
9.8. Calculation of standard probabilistic characteristics of sys-
tems
187
Chapter 10. FOUNDATIONS OF THE RISK LP-THEORY
WITH GROUPS OF INCOMPATIBLE EVENTS
191
10.1.
10.2.
10.3.
10.4.
10.5.
10.6.
10.7.
10.8.
10.9.
Tabular representation of statistical data
Grade-events distribution in GIE
Logical rules of probabilities calculation in GIE
Orthogonality of L-functions for different objects of the
table
Dependent parameter-events
Independent parameter-events
Risk parameters Risk,
Optimization problems
Analysis of risk

Basic equations
Examples of structural, logic and probabilistic risk models
Measure and cost of risk
GIE and the Bayes formula
Dynamic risk LP-models
209
211
212
214
215
216
219
Chapter 12. IDENTIFICATION OF RISK LP-MODELS
WITH GROUPS OF INCOMPATIBLE
EVENTS
223
12.1.
12.2.
12.3.
12.4.
12.5.
Statement of identification problem and algorithm of its
solution
Methods of identification
Choice of initial values and parameters of training
Optimization in identification problems
12.4.1.
12.4.2.
Formulae of optimization
Numerical experiments at optimization

14.2.
14.3.
14.4.
Intellectual Work Station for safety management
Software for identification and analysis of risk LP-models
with GIE
Software for structural and logic modelling
Software for LP-modelling on the basis of cortege algebra
14.4.1.
14.4.2.
Risk analysis of systems with many conditions
Description of Soft Ware
267
270
278
284
285
291
Chapter 15. RISK LP-MODELS IN BUSINESS
295
15.1.
15.2.
15.3.
15.4.
15.5.
Credit risks: scenarios and LP-models
15.1.1.
15.1.2.
15.1.3.
Credit risk problem

Financing of building projects with reservation
311
311
313
Chapter 16.
LOGIC AND PROBABILISTIC THEORY OF
SECURITY PORTFOLIO RISK
315
16.1.
16.2.
Introduction
315
Selection of the optimum portfolio by VaR
317
xii
Contents
16.3.
16.4.
16.5.
Selection and analysis of the optimal security portfolio
by
LP–VaR
319
324
332
Investigation with independent random yields
Investigation with dependent random yields
Chapter 17. RISK LP-MODELS IN ENGINEERING
335
17.1.

364
Finding weights of parameters influential the pa-
rameter of effectiveness
365
Conclusion
371
Bibliography
379
Subject index
389
FOREWORD
In the forewords to the books “Logic and probabilistic valuation of bank-
ing risks and frauds in business” (St. Petersburg, Politechnika, 1996)
and “Logic and probabilistic models of risk in banks, business and qual-
ity” (St. Petersburg, Nauka, 1999) by the author of the presented book
E. D. Solojentsev, and V. V. Karasev, V. E. Solojentsev I already wrote
that they open new fields for application of rigorous analytical methods
of estimation, analysis and investigation of the risk in economics and
engineering. In those forewords I expressed the hope, which I am glad
to express again, that the new logic and probabilistic methods of risk
estimation will have happy fortune.
In many respects the occurrence of this new book is stimulated by
E. D. Solojentsev’s activity for organization of International Scientific
Schools “Modelling and Analysis of Safety and Risk in Complex Sys-
tems” (St. Petersburg: June 18–22, 2001; July 2–5, 2002; August 20–23,
2003). Russian and foreign scientists and experts presented more than
300 papers on the Schools devoted to the problems of safety and risk in
economics and engineering.
For many years the author worked in industry in the field of design-
ing and testing of complex engineering systems. Now he works in an

mathematical logic and the new step in development of the formal logic.
One of the fathers of the mathematical theory of the information
Clod Elwud Shannon succeeded to close the gap between the logic al-
gebraic theory and its practical application. In the D.Sc. dissertation
(1938) he developed principles of the logic model of the computer, by
connecting Boolean algebra with the functioning of electrical circuits.
The success of his ideas concerning connections between the binary cal-
culus, the Boolean algebra and electrical circuits, Shannon explained as
follows: “Simply it is happened so, that nobody else was acquainted
with both areas simultaneously”.
The necessity of quantitative estimation of non-failure operation of
complex technical structures at the beginning of the 60s XX century
stimulated the so-called logic and probabilistic calculus
(LPC)
which is a part of the mathematics treating rules of calculus and operat-
ing with statements of two-value logic. LPC is based on the logic algebra
and rules of replacement of logic arguments in functions of the logic al-
gebra (FAL) by probabilities of their being true and rules of replacement
of the logic operations by the arithmetic ones.
In other words, with the of help of LPC it became possible to connect
the Boolean algebra with the probability theory not only for the elemen-
tary structures, but also for the structures, whose formalization results
in FAL of iterated type (bridge, network, monotonous). This original
“bridge of knowledge” includes some proven theorems, properties and
algorithms, which constitute the mathematical basis of LPC.
Investigation of the safety problem has resulted in development of
the original logic and probabilistic theory of safety (LPTS),
which allows to estimate quantitatively the risk of system (as a mea-
sure of its danger) and to rank the contribution of separate arguments
to the system danger (in the case of an absence of truth probabilities of

LP-management by the risk in economics and engineering, can be ex-
plained the fact that the risk LP-theory and such scientific disciplines
as the LP-calculus, the methods of discrete mathematics and combina-
torics are not usually included into the educational programs of high
schools. Therefore publication of the given monograph devoted to the
LP-management by risk, seems to be actual.
Academician of Russian Academy
of Natural Sciences,
Professor I. A. Ryabinin
This page intentionally left blank
INTRODUCTIO
N
Back to basics, logic and arithmetics,
to solve complex problems.
Author
To the author’s knowledge the risk phenomenon in complex techni-
cal, economic and organizational systems is not completely recognized in
the scientific plane and is not also resolved satisfactory for needs of ap-
plications, despite the fact that in complex systems non-success occurs
rather often with human victims and large economic losses. The man-
agement risk problem is current and challenging; it forces us to carry out
new investigations and to seek new solutions for quantitative estimation
and analysis of risk.
Risk is quantitative measure such fundamental properties of sys-
tems and objects as safety, reliability, effectiveness, quality and accuracy.
Risk is also quantitative measure of non-success of such processes and
actions as classification, investment, designing, tests, operation, train-
ing, development, management, etc.
In the listed subject fields we shall consider three different state-
ments of mathematical tasks of optimization by management of risk —

cycles. Elements of the system under consideration may have several
levels of conditions. The system risk dynamics can be taken into ac-
count by consideration of variation in time of probabilities of condi-
tions.
The basis for construction of the scenario risk LP-management in
complex systems are: the risk LP-theory; the methodology for construc-
tion of scenarios and models of risk; the technology of risk management;
examples of risk modelling and analysis from various fields of economics
and engineering.
In complex systems the technology of the scenario risk LP-manage-
ment is based on the risk estimation by LP-model, the techniques of
the risk analysis, schemes and algorithms of risk management, and the
corresponding software. Generally, it is impossible to control the risk
without quantitative analysis of risk which allows us to trace the con-
tributions of initial events to the risk of the system. Estimation and
analysis of risk as well as finding optimal management are carried out
algorithmically with calculations, which are very time-consuming even
for the modern computers.
The risk LP theory considered in the book unifies: Ryabinin’s LP-
calculus and LP-method, Mojaev’s methodology of automatized struc-
Introduction
ture and logical modelling and Solojentsev’s risk LP-theory with groups
of incompatible events (GIE).
The LP-calculus is a special part of discrete mathematics, which
should not be confused with the probabilistic logic and other sections
of the mathematical logic. Therefore, it is useful to outline briefly the
history of the publications on this subject. To author’s knowledge, the
idea and development of the subject should be attributed to Russian
authors. The contents and formation of LP-calculus originates from
the work by I.A.Ryabinin “Leningrad scientific school of the logic and

3
E.
D. Solojentsev
The present book has of applied importance. The purpose of the
present book is to acquaint economists, engineers and managers with
the bases of the scenario risk LP management, which includes: the risk
LP theory, the methodology of construction of the risk scenario, the
technology of risk management, examples of scenarios and models of
risk in different fields of economy and engineering.
The important feature of suggested presentation is the attempt to
unify knowledge from different fields: discrete mathematics, combinato-
rial theory and Weil’s theorem; nonlinear optimization and algorithmic
calculations, modelling of Monte-Carlo and on modern computers; the
LP-calculus [1,3]; the LP-methods [2,4]; the theories by Markowitz and
VaR for risk of security portfolio [5,6], the risk LP-theory with GIE [7–9].
The novelty and utility of the book consist in the following:
It is the first time when the basic principles of the modern risk LP
theory (the LP-calculus, the LP-methods and the risk LP-theory with
GIE) are stated in one work using uniform methodology and termi-
nology and with practical orientation on use both in engineering and
in economics. With permission of Prof. I. A. Ryabinin, some mathe-
matical results and examples from his book [2] are reproduced. The
technology of the automated construction and analysis of LP-models of
any complexity are presented following works by A. S. Mojaev [4].
The methodology of construction of the non-success risk scenario in
different fields for all stages of the system life cycle is introduced. For this
purpose concepts, principles, experience, scenarios and examples of risk
management in business and engineering at stages of designing, debug-
ging, operational tests and operation are considered and systematized.
It should be emphasized that imperfection of risk management of the

LP-models in different fields of business and engineering with demon-
stration of their effectiveness, high accuracy, robustness, ability for the
risk analysis of one and set of objects and the power in risk management
are considered in the following examples: credit risks of persons and or-
ganizations; bank credit activity analysis; bribes, swindles of managers,
speculations with investments, management of condition and develop-
ment of companies by risk criterion, struggles of buildings companies
for profitable contract; financing construction projects by several banks
with reservation; risk of security portfolio; explosion in a submarine;
management of nuclear power plant safety; risk of resource prolongation
of the power equipment; risk of losses quality, accuracy and efficiency.
The presentation is organized as follows:
In Chapters 1–6 the methodological aspects of the scenario logic
and probabilistic non-success risk management are considered, following
from analysis of connections between management and risk, personals
and risk, and from study of risk management at stages of design, test
and operation of complex systems.
In Chapter 1 the problems of management and risk, management
by risk and insurance, monitoring and risk are considered. Sources of
failures and accidents and fields of applicability of methods of the nonlin-
ear mechanics, the probabilities theory and LP-methods for estimation,
analysis, forecasting and modelling of accidents are discussed.
In Chapter 2 the intentional and unintentional actions of personnel
6
E. D. Solojentsev
resulting in failures and accidents are discussed. The necessity is proved
to take into account behavior of personnel for development of scenarios
of non-successes, failures, incidents and for design of safety systems.
In Chapter 3 principles of risk management for design of complex
systems are stated on the basis of generalization and unification of knowl-

In Chapter 13 techniques of risk LP-analysis in systems with GIE
for problems of classifications are given.
Introduction
In Chapter 14 Software which serves for identification of the risk LP-
models with GIE, for orthogonalization of L-functions and for automated
construction of the risk LP-models is described.
In Chapters 15–18 applications of risk LP-models in business and
engineering are given.
In Chapter 15 examples of application of risk LP-models in business
and results of quantitative modelling and analysis of risk, estimation
of accuracy and robustness of risk models and management by risk are
given.
In Chapter 16 the risk LP-theory of security portfolio is stated.
In contrast to the theories Markowitz and VaR, which use the nor-
mal laws of distribution, the risk LP-theory may involve any discrete
non-parametrical distributions of securities yields.
In Chapter 17 examples of application of risk LP-models in engi-
neering and results of quantitative modelling and analysis of risk are
given.
In Chapter 18 the risk LP-theory with GIE for problems of accuracy,
quality and efficiency is considered.
Conclusion contains a review of applications of risk LP-models in
engineering and business. The differences and similarities of the risk LP-
theory and other methods of risk estimation in problems of classification,
investment and efficiency are discussed.
In writing the book the author proceeds from own his research in
the fields of design and testing of complex technical systems and investi
gation of application of the risk LP-theory in economics [7–9]. Besides
some results of the Scientific School of LP-methods created by I. Rya
binin are used. The author was one of the editors of the book “Theory