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1
Content available Optimal allocation of reliability improvement target based on multiple correlation failures and risk uncertainty
Jia Shuoguo, Yan Changfeng, Kang Jianxiong, Xie Heping, Wei Yongqiao
Eksploatacja i Niezawodność
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2023
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Vol. 25, no. 1
art. no. 8
EN
Optimal allocation of the reliability improvement target is essential for the system optimization design. In order to solve the problems that the optimization model is with loss of generality and the validity of the optimal solution is weakened, an optimal allocation method is proposed by considering multiple correlation failures and risk uncertainty in this paper. Two new concepts are presented, such as independent failure results in basic risk, and correlation failure leads to disturbance risk. A risk assessment machinery of “actual risk = basic risk + disturbance risk” is proposed. The action mechanisms of the three correlation failures are studied based on the cooperation game theory, and the generalized risk models are given under probability measure. Considering the improvement cost, the expectation and the variance of the reduction of system risk, a multi-objective optimal allocation model is developed, which is solved by using the PSO algorithm. Finally, the proposed optimal allocation is implemented at the 2-stage NGW planetary reducer, and the results show that it is more efficient and feasible for engineering practice.
2
Content available Probability measures and logical connectives on quantum logics
Nánásiová Oľga, Valášková Ľubica, Čerňanová Viera
Journal of Automation Mobile Robotics and Intelligent Systems
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2019
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Vol. 13, No. 3
64--73
EN
The present paper is devoted to modelling of a probabi‐ lity measure of logical connectives on a quantum logic via a G‐map, which is a special map on it. We follow the work in which the probability of logical conjunction (AND), dis‐ junction (OR), symmetric difference (XOR) and their nega‐ tions for non‐compatible propositions are studied. Now we study all remaining cases of G‐maps on quantum lo‐ gic, namely a probability measure of projections, of impli‐ cations, and of their negations. We show that unlike clas‐ sical (Boolean) logic, probability measures of projections on a quantum logic are not necessarilly pure projections. We indicate how it is possible to define a probability me‐ asure of implication using a G‐map in the quantum logic, and then we study some properties of this measure which are different from a measure of implication in a Boolean algebra. Finally, we compare the properties of a G‐map with the properties of a probability measure related to logical connectives on a Boolean algebra.
3
Content available remote Multigranulation Decision-theoretic Rough Set in Ordered Information System
Li W., Xu W.
Fundamenta Informaticae
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2015
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Vol. 139, nr 1
67--89
EN
The decision-theoretic rough set model based on Bayesian decision theory is a main development tendency in the research of rough sets. To extend the theory of decision-theoretic rough set, the article devotes this study to presenting multigranulation decision-theoretic rough set model in ordered information systems. This new multigranulation decision-theoretic rough set approach is characterized by introducing the basic set assignment function in an ordered information system. It is addressed about how to construct probabilistic rough set and multigranulation decision-theoretic rough set models in an ordered information system. Moreover, three kinds of multigranulation decision-theoretic rough set model are analyzed carefully in an ordered information system. In order to explain probabilistic rough set model and multigranulation decision-theoretic rough set models in an ordered information system, an illustrative example is considered, which is helpful for applying these theories to deal with practical issues.
4
Content available remote Probabilistic models of random behaviours of concurrent systems
Winkowski J.
Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk
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2012
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Nr 1024
1--42
EN
The paper presents a theoretical basis for describing and analysing random behaviours of concurrent systems of a broad class.
PL
Praca zawiera podstawy teoretyczne opisu i analizy losowych zachowań systemów współbieżnych dowolnej natury.
5
Content available remote Generating functions of orthogonal polynomials and Szegö-Jacobi parameters
Asai N., Kubo I., Kuo H.-H.
Probability and Mathematical Statistics
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2003
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Vol. 23, Fasc. 2
273--291
EN
In this paper, we present a more direct way to compute the Szegö-Jacobi parameters from a generating function than that in [5] and [6]. Our study is motivated by the notions of one-mode interacting Fock spaces defined in[1] and Segal-Bargmann transform associated with non-Gaussian probability measures introduced in [2]. Moreover, we examine the relationships between the representations of orthogonal polynomials in terms of differential or difference operators and our generating functions. The connections provide practical criteria to determine when functions of a certain form are orthogonal polynomials.
6
Content available remote On central sets relatively measures - a simple proof of the Sonneborn theorem
Krasinkiewicz J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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Vol. 50, no 1
21-24
EN
We present a simple proof of an extension of the Sonneborn theorem [3] about fibers of functions defined on higher dimensional spheres.
7
Content available remote Discrete probability measures on 2 × 2 stochastic matrices and a functional equation on [0, 1]
Mukherjea A., Ratti J. S.
Probability and Mathematical Statistics
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2000
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Vol. 20, Fasc. 2
359--372
EN
In this paper, we consider the following natural problem: suppose μ1 and μ2 are two probability measures with finite supports S(μ1), S(μ2) respectively, such that |S(μ1)| = |S(μ2)| and S(μ1) U S(μ2) ⊂ 2 × 2 stochastic matrices, and μn1 (the n-th convolution power of μ1 under matrix multiplication), as well as μn 2 , converges weakly to the same probability measure λ, where S(λ) ⊂ 2 × 2 stochastic matrices with rank one. Then when does it follow that μ1 = μ2? What if S(μ1) = S(μ2)? In other words, can two different random walks, in this context, have the same invariant probability measure? Here, we consider related problems.
8
Content available remote Independent marginals of operator-semistable and operator-stable probability measures
Łuczak A.
Probability and Mathematical Statistics
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1998
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Vol. 18, Fasc. 1
173--183
EN
We investigate independent marginals of full operator-semistable and operator-stable probability measures on finite-dimensional vector spaces. In particular, it is shown that for purely Poissonian operator-semistable and operator-stable distributions their independent marginals have decomposability properties of the same kind. Operator-semistability and operator-stability of independent marginals of Gaussian measures are studied in detail, and a description of independent marginals of an arbitrary operator-semistable or operator-stable distribution is obtained.
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