scholarly journals Bounds for the Availabilities of Multistate Monotone Systems Based on Decomposition into Stochastically Independent Modules

2012 ◽  
Vol 44 (01) ◽  
pp. 292-308 ◽  
Author(s):  
J. Gåsemyr

Multistate monotone systems are used to describe technological or biological systems when the system itself and its components can perform at different operationally meaningful levels. This generalizes the binary monotone systems used in standard reliability theory. In this paper we consider the availabilities and unavailabilities of the system in an interval, i.e. the probabilities that the system performs above or below the different levels throughout the whole interval. In complex systems it is often impossible to calculate these availabilities and unavailabilities exactly, but it is possible to construct lower and upper bounds based on the minimal path and cut vectors to the different levels. In this paper we consider systems which allow a modular decomposition. We analyse in depth the relationship between the minimal path and cut vectors for the system, the modules, and the organizing structure. We analyse the extent to which the availability bounds are improved by taking advantage of the modular decomposition. This problem was also treated in Butler (1982) and Funnemark and Natvig (1985), but the treatment was based on an inadequate analysis of the relationship between the different minimal path and cut vectors involved, and as a result was somewhat inaccurate. We also extend to interval bounds that have previously only been given for availabilities at a fixed point of time.

2012 ◽  
Vol 44 (1) ◽  
pp. 292-308
Author(s):  
J. Gåsemyr

Multistate monotone systems are used to describe technological or biological systems when the system itself and its components can perform at different operationally meaningful levels. This generalizes the binary monotone systems used in standard reliability theory. In this paper we consider the availabilities and unavailabilities of the system in an interval, i.e. the probabilities that the system performs above or below the different levels throughout the whole interval. In complex systems it is often impossible to calculate these availabilities and unavailabilities exactly, but it is possible to construct lower and upper bounds based on the minimal path and cut vectors to the different levels. In this paper we consider systems which allow a modular decomposition. We analyse in depth the relationship between the minimal path and cut vectors for the system, the modules, and the organizing structure. We analyse the extent to which the availability bounds are improved by taking advantage of the modular decomposition. This problem was also treated in Butler (1982) and Funnemark and Natvig (1985), but the treatment was based on an inadequate analysis of the relationship between the different minimal path and cut vectors involved, and as a result was somewhat inaccurate. We also extend to interval bounds that have previously only been given for availabilities at a fixed point of time.


2017 ◽  
Vol 54 (3) ◽  
pp. 750-762 ◽  
Author(s):  
Jørund Gåsemyr ◽  
Bent Natvig

Abstract Multistate monotone systems are used to describe technological or biological systems when the system itself and its components can perform at different operationally meaningful levels. This generalizes the binary monotone systems used in standard reliability theory. In this paper we consider the availabilities of the system in an interval, i.e. the probabilities that the system performs above the different levels throughout the whole interval. In complex systems it is often impossible to calculate these availabilities exactly, but if the component performance processes are independent, it is possible to construct lower bounds based on the component availabilities to the different levels over the interval. In this paper we show that by treating the component availabilities over the interval as if they were availabilities at a single time point, we obtain an improved lower bound. Unlike previously given bounds, the new bound does not require the identification of all minimal path or cut vectors.


1996 ◽  
Vol 28 (1) ◽  
pp. 270-284 ◽  
Author(s):  
L. Sacerdote ◽  
F. Tomassetti

The series expansion for the solution of the integral equation for the first-passage-time probability density function, obtained by resorting to the fixed point theorem, is used to achieve approximate evaluations for which error bounds are indicated. A different use of the fixed point theorem is then made to determine lower and upper bounds for asymptotic approximations, and to examine their range of validity.


1996 ◽  
Vol 28 (01) ◽  
pp. 270-284 ◽  
Author(s):  
L. Sacerdote ◽  
F. Tomassetti

The series expansion for the solution of the integral equation for the first-passage-time probability density function, obtained by resorting to the fixed point theorem, is used to achieve approximate evaluations for which error bounds are indicated. A different use of the fixed point theorem is then made to determine lower and upper bounds for asymptotic approximations, and to examine their range of validity.


1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.


2016 ◽  
pp. 15
Author(s):  
Mariana Giaretto ◽  
Victoria Naffa

ResumenEn este trabajo analizamos las relaciones entre tomas de tierras y Estado, en elAlto Valle de Río Negro en Argentina. En un contexto general de especulacióninmobiliaria, por la que se encarecen los precios de alquileres y terrenos, y depolíticas de vivienda selectivas y acotadas, los sectores populares acceden aun espacio en la ciudad mediante tomas de tierras. Frente a estos conflictos,el Estado, en sus diferentes niveles y poderes, despliega una forma deintervención basada en la criminalización de las luchas por tierra y vivienda.Al mismo tiempo, el poder ejecutivo nacional crea la Secretaría de Acceso alHábitat, para posibilitar la intervención política orientada a la regularizaciónde los asentamientos. Sin embargo, esta intervención tiende a reinscribir laproblemática habitacional en el campo político, para reducirla a un conflicto“entre partes”, eludiendo la responsabilidad estatal.Desde un enfoque metodológico cualitativo, seleccionamos como referenteempírico el caso del asentamiento de Villa Obrera en Fiske, Menuco (Gral.Roca), y las técnicas de recolección de datos se basan en fuentes secundarias,como expedientes judiciales y normativa, y en fuentes primarias como son losrelatos de los protagonistas mediante entrevistas individuales y colectivas.Palabras clave: tomas de tierras, Estado, criminalización de los conflictos.Conflicts caused by land occupation and modesof State intervention: analysis of an experience ofAlto Valle in Río Negro (Argentina)AbstractThis paper analyzes the relationship between State and land occupation,at Alto Valle in Río Negro, Argentina. In a general context of real estatespeculation, where rents and land prices are expensive, and a policy ofselective and limited housing, popular sectors can have access to a spacein the city through land occupation. In front of these conflicts, the Statein its different levels and powers, displays a form of intervention basedon the criminalization of struggles for land and housing. At the sametime, the national executive creates the Secretariat of Access to Habitat,oriented to allow political intervention for the regularization of settlements.However, this intervention tends to re-register the housing problems in thepolitical arena, reducing it to a conflict “between parties” and eluding theresponsibility of the State.From a qualitative methodological approach, we selected as empirical referencethe case of the settlement of Villa Obrera in Fiske, Menuco (GeneralRoca). The techniques of data collection are based on secondary sources, suchas policy and legal records, and primary sources as the stories of protagoniststhrough individual and collective interviews.Keywords: land occupation, State, criminalization of conflicts.Conflitos sobre ocupações de terras e modos deintervenção do estado: análise de uma experiênciado Alto Valle do Rio Preto (Argentina)ResumoEste trabalho analisa as relações entre a posse de terra e o Estado, no AltoValle do Rio Preto, na Argentina. Num contexto geral da especulaçãoimobiliária, por qual se encarecem os preços do aluguel e das terras, e depolíticas de habitação seletivas e limitadas, os setores populares acedem aum espaço na cidade através de ocupações de terras. Frente a estes conflitos,o Estado, em seus diferentes níveis e poderes, desenvolve uma forma deintervenção com base na criminalização das lutas pela terra e vivenda. Aomesmo tempo, o poder executivo nacional cria a Secretaria de Acesso àHabitat para possibilitar à intervenção política orientada a regularização dosassentamentos. No entanto, esta intervenção tende a registrar os problemasde habitação no campo político, para reduzi-la a um conflito “entre aspartes”, iludindo a responsabilidade do Estado.A partir de uma abordagem metodológica qualitativa, foi selecionado comoreferência empírica o caso do Assentamento de Villa Obrera em Fiske,Menuco (Gral. Roca), e as técnicas de recolecção de dados são baseados emfontes secundárias, como expedientes judiciais e normativos, e em fontes primárias como são as histórias dos protagonistas através de entrevistasindividuais e coletivas.Palavras-chave: tomada de terras, Estado, criminalização dos conflitos.


Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.


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