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, RТА, 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.