Abstract : System reliability is a measure of the performance of an engineering system. High-tech industrial processes increase in complexity and at the same time, system failures are having more significant impacts on society than ever before. Hence, the importance of reliability in modern engineering processes, can hardly be overstated.
The reliable performance of complex systems depends on the performance of their components and the system's structure. In recent years, advanced statistical, probabilistic and algebraic methods and techniques have been applied to system reliabilty. This minisymposium brings together recent developments of mathematical methods applied to industrial system reliability.
Organizer(s) : Fatemeh Mohammadi, Eduardo Sáenz-de-Cabezón, Henry Wynn
Abstract : Domination functions has been studied extensively in the context of binary systems, where the structure function is a sum of products of the component states, and with coefficients given by the domination function. Using matroid theory, properties of the domination function can be derived. We generalise these results to multistate systems. The domination is determined by the poset generated by the minimal paths, and two systems with isomorphic posets also have the same domination function.
[01419] Mathematical analysis of the reliability of stable systems
Format : Talk at Waseda University
Author(s) :
Eduardo Sáenz-de-Cabezón (University of La Rioja)
Abstract : One of the main characteristics of coherent systems is redundancy. In this talk we define stability as a way to encode redundancy in a way that generalizes well known systems like k-out-of-n and variants. We furthermore provide a complete algebraic analysis of the reliability of these systems and design based on stability.
[01422] Algebraic probability: the case of system reliability
Format : Online Talk on Zoom
Author(s) :
Henry Wynn (London School of Economics)
Abstract : Algebra arises in probability because of additivity over set disjointness and multiplication with independence. With
systems such as those in causal analysis, data analysis and reliability we can have rich algebraic structures. In
reliability, under coherence, failure patterns give rise to monomial ideals and from there Betti numbers and Hilbert
series lead to efficient identities and bounds for failure probabilities. Structures such as mixed series-parallel systems and multi state systems have special features.
[01425] Algebraic analysis of importance measures of coherent systems
Format : Online Talk on Zoom
Author(s) :
Patricia Pascual-Ortigosa (University of La Rioja)
Eduardo Sáenz-de-Cabezón (University of La rioja)
Rodrigo Iglesias (University of La Rioja)
Abstract : The aim of this talk is to do an analysis of importance measures of coherent systems using an algebraic approach.
First of all, we introduce what importance measures are, providing a classification of them and some background for all of them. Then, we will show how Algebra can help us to study structural measures of importance of coherent systems. Finally, we present some examples explaining the advantages and disadvantages of this approach.
[01455] New exactly solvable architecture for system reliability and safety
Format : Talk at Waseda University
Author(s) :
Christian Tanguy (Orange)
Abstract : Network reliability is a crucial performance index for telecommunication operators. In the general case, the calculation of the two-terminal reliability is known to be #P-complete, even for identical links and perfect nodes of the network's underlying graph. Exact solutions have nonetheless been found for a few recursive architectures. We present a new example of such an architecture, which could be of interest to reliability practitioners and graph theorists.
[01469] Application of Logic Differential Calculus in Reliability Analysis
Format : Online Talk on Zoom
Author(s) :
Michal Mrena (University of Zilina)
Abstract : Logic differential calculus – specifically logic derivatives – provides an efficient way to investigate the reliability of systems described by a structure function. The structure function captures the topology of the system and the derivatives describe the behavior of the system when the state of a component changes. Consequently, they allow us to calculate importance measures for individual components. In this contribution, we present a comprehensive framework for the evaluation of various system reliability characteristics.
[03092] Stochastic comparisons of coherent systems with active redundancy at component level and system level
Format : Talk at Waseda University
Author(s) :
Pradip Kundu (XIM University, Bhubaneswar)
Arindam Panja (Indian Statistical Institute)
Biswabrata Pradhan (Indian Statistical Institute)
Abstract : An effective way to increase system reliability is to use redundancies (spares) into the systems. In this paper, we derive sufficient conditions under which a coherent system with a set of active redundancy at the component level or the system level provides better system reliability than that of the system with another set of redundancy, with respect to some stochastic orders. We have derived the results for the component lifetimes following accelerated life (AL) model.
