Jacek Malinowski

Reliability evaluation for tree-structured systems with multistate components

A tree-structured system with multistate components consists of a certain number of components which are arranged in a tree structure and are capable of receiving and sending a signal. The signal source is located in the root node, the components located in the leaf nodes can only receive a signal. Each component located in neither a root nor a leaf node is capable of transmitting the received signal directly to a number of components located below it, where this transmission is possible only along arcs linking the nodes, in the direction from upper to lower nodes. A component x is considered to be failed if it cannot transmit a signal to any other component, otherwise it is in the working condition and its state is determined by a set of components receiving a signal directly from x. The whole system is in working condition if each leaf node (which is assumed to be always in working condition) receives the signal from the root node.

Reliability increase of consecutive k-out-of-n:f and related systems through components' rearrangement

In the analysis of consecutive k-out-of-n:F and related systems the optimal ordering of components is an important problem. Simply, if the components are not s-identical, changing their locations may improve the systems reliability. The aim is to find the optimum components arrangement, ie. one for which the systems reliability attains its maximum value. This problem has been studied in several papers, but its solution has been found only for some special cases of systems. The present paper gives a procedure which significantly improves the reliability of the considered systems and does not require laborious computations.

The Deduction Theorem for Quantum Logic--Some Negative Results

We prove that no logic (i.e. consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).

A recursive algorithm evaluating the exact reliability of a circular consecutive k-within-m-out-of-n:F system

Abstract A consecutive κ-within-m-out-of-n:F system consists of n linearly ordered components e1,3.en. The system fails if among any m subsequent components there are k or more failed ones. A recursive algorithm is presented evaluating the reliability of the system whose components are independent and have unequal failure probabilities. This algorithm is computer implementable for “not too large m” (e.g. m ≤ 15 for PC machines).

Reliability of reverse-tree-structured systems with multistate components

We consider a system consisting of components arranged in a reverse tree structure and capable of receiving and sending a signal. The signal sources are located in leaf nodes, the component located in the root node can only receive a signal. Each component located in neither the root nor a leaf node is capable of transmitting the received signal directly to a number of components located below it. The transmission is possible only along arcs linking the nodes, in the direction from upper to lower nodes. A component x is considered to be failed if it cannot transmit a signal to any other component, otherwise it is in working condition and its state is determined by the lowest component reached directly by a signal from x. The whole system is in working condition if the root node (assumed to be always able to receive a signal) receives the signal from each leaf node.

Strong versus weak quantum consequence operations

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic.

Reliability Analysis of a Flow Network with a Series-Parallel-Reducible Structure

We consider a flow network with directed links and three types of nodes: inflow points, transit-only nodes, and outflow points. Its structure can be reduced to a single component by series-parallel aggregation. The components are repairable, they have constant failure and repair rates, and their states are mutually s-independent. Each operable component has an integer throughput; a failed one has zero throughput. The networks performance is measured by the total demand satisfied (TDS) at all the outflow points vs. the total demand required (TDR) at these points. TDS is a r.v. with values in the [0, TDR] interval, where TDR is a constant. The distribution function of TDS is thus the networks basic reliability characteristic. It is computed by an author-developed algorithm operating on integer numbers, its complexity being polynomial w.r.t. certain further defined quantities. A few other reliability parameters, characterizing the dynamically changing ability to satisfy the demands at the outflow points, are also defined. They are calculated using the distribution function of TDS and the d-importances of individual components (a generalization of the Birnbaum importance, defined further in the paper). The presented results can be applied in the reliability analysis of water supply networks, oil or gas pipeline systems, power transmission and/or distribution networks, etc.

The pragmatic interpretation of utterances

The aim of this paper is to analyze the differences and similarities between the linguistic and the logical meaning of a sentence and propose a uniform point of view on the notion of the meaning of utterances. The proposed notion differs from the notion of the logical meaning as well as from the linguistic one. It may be considered to be a kind of composition of both of them.

Reliability of a two-way circular consecutively connected system with multistate components

Abstract A 2-way linear consecutively-connected system with multistate components (2-way LCCSMC) consists of linearly ordered components ei, ie[0,n+1]. e0, can send a signal only in forward direction, each ei, ie[1,n], is capable to send it in both directions, en+1, can send it only in backward direction. All components are capable to receive a signal.The component ei is in state (h,k), he[0,i], ke[0,n+1−i], ie[0,n+1], if it sends a signal directly to h components immediately preceding ei and k components immediately following ei. e0 and en+1 can only be in states (0,·) and (·,0), respectively. The probability that ei is in state (h,k) is assumed to be known for each admissible h and k. The states of all components are mutually s-independent. The 2-way LCCSMC is operating iff a signal is transmitted forward, from e0 to en+1, and backward, from en+1 to e0, possibly indirectly via intermediate components e1, … ,en. The paper gives an algorithm for determining the 2-way LCCSMC reliability.

Reliability Aspects of Multi-commodity Markets

In this paper several reliability aspects of multi-commodity trade are discussed. As it is very often required that trading decisions should be taken both rationally and very quickly, e.g on a short-term electric power market, in such cases trading is performed automatically by multi-agent systems. Thus the question of MAS reliability arises, which is herein considered in two aspects – topological and functional. Interactions of agents in a MAS occur according to a certain topological pattern which can be directly transformed to the structural reliability model of that MAS. A number of such topological patterns are presented along with respective reliability models. In its functional aspect a MAS can be seen as a graph whose nodes process input information and pass it to other nodes thus fulfilling collectively certain task. An agent’s malfunction can lead to a delay, misfulfillment or failure of that task. An interesting model of inter-agent functional dependence based on game-theoretical approach is presented. Apart from reliable execution of trading operations, an important issue is the ability to quickly assess whether the fulfillment of a contract is technically possible. An example is given where the effective conditions which energy suppliers’ capabilities must meet are defined as the constraints of a transportation problem. Also, a non-trivial problem of quickly finding those constraints is addressed.