Reliability of systems with dependent components based on lattice polynomial description

Reliability of a system is considered where the components' random lifetimes may be dependent. The structure of the system is described by an associated "lattice polynomial" function. Based on that descriptor, general framework formulas are developed and used to obtain direct results for the cases where a) the lifetimes are "Bayes-dependent", that is, their interdependence is due to external factors (in particular, where the factor is the "preliminary phase" duration) and b) where the lifetimes' dependence is implied by upper or lower bounds on lifetimes of components in some subsets of the system. (The bounds may be imposed externally based, say, on the connections environment.) Several special cases are investigated in detail

Tests for exponentiality against NBUE alternatives: a Monte Carlo comparison

Testing of various classes of life distributions has been addressed in the literature for more than 45 years. In this paper, we consider the problem of testing exponentiality (which essentially implies no ageing) against positive ageing which is captured by the fairly large class of new better than used in expectation (NBUE) distributions. These tests of exponentiality against NBUE alternatives are discussed and compared. The empirical size of the tests is obtained by simulations. Power comparisons for different popular alternatives are done using Monte Carlo simulations. These comparisons are made for both small and large sample sizes. The paper concludes with a discussion in which suggestions are made regarding the choices of the test when a particular alternative is suspected

Modified Paouris inequality

The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of l_r-norms and suprema of norms of coordinate projections of isotropic log-concave vectors.Comment: 14 page

Observable structure functions.

Considers the concept of structure function in reliability theory. Complete lattices are considered in order to model the space of performance levels for both system and components, leading to a general concept of structure function. Measurability with respect to the associate order topology is also assumed. On one hand, some basic concepts in classical reliability theory are translated into this context, where a particular measure has been defined over the space of components. On the other hand, the idea of duality is analysed in this context

Semiparametric frailty models for zero-inflated event count data in the presence of informative dropout

Recurrent events data are commonly encountered in medical studies. In many applications, only the number of events during the follow-up period rather than the recurrent event times is available. Two important challenges arise in such studies: (a) a substantial portion of subjects may not experience the event, and (b) we may not observe the event count for the entire study period due to informative dropout. To address the first challenge, we assume that underlying population consists of two subpopulations: a subpopulation nonsusceptible to the event of interest and a subpopulation susceptible to the event of interest. In the susceptible subpopulation, the event count is assumed to follow a Poisson distribution given the follow-up time and the subject-specific characteristics. We then introduce a frailty to account for informative dropout. The proposed semiparametric frailty models consist of three submodels: (a) a logistic regression model for the probability such that a subject belongs to the nonsusceptible subpopulation; (b) a nonhomogeneous Poisson process model with an unspecified baseline rate function; and (c) a Cox model for the informative dropout time. We develop likelihood-based estimation and inference procedures. The maximum likelihood estimators are shown to be consistent. Additionally, the proposed estimators of the finite-dimensional parameters are asymptotically normal and the covariance matrix attains the semiparametric efficiency bound. Simulation studies demonstrate that the proposed methodologies perform well in practical situations. We apply the proposed methods to a clinical trial on patients with myelodysplastic syndromes

Remarks on the KLS conjecture and Hardy-type inequalities

We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily vanishing on the boundary $\partial \Omega$. This reduces the study of the Neumann Poincar\'e constant on $\Omega$ to that of the cone and Lebesgue measures on $\partial \Omega$; these may be bounded via the curvature of $\partial \Omega$. A second reduction is obtained to the class of harmonic functions on $\Omega$. We also study the relation between the Poincar\'e constant of a log-concave measure $\mu$ and its associated K. Ball body $K_\mu$. In particular, we obtain a simple proof of a conjecture of Kannan--Lov\'asz--Simonovits for unit-balls of $\ell^n_p$, originally due to Sodin and Lata{\l}a--Wojtaszczyk.Comment: 18 pages. Numbering of propositions, theorems, etc.. as appeared in final form in GAFA seminar note

Exotic Smooth Structures on Small 4-Manifolds

Let M be either CP^2#3CP^2bar or 3CP^2#5CP^2bar. We construct the first example of a simply-connected symplectic 4-manifold that is homeomorphic but not diffeomorphic to M.Comment: 11 page

Efficient exploration of availability models guided by failure distances

Recently, a method to bound the steady-state availability using the failure distance concept has been proposed. In this paper we refine that method by introducing state space exploration techniques. In the methods proposed here, the state space is incrementally generated based on the contributions to the steady-state availability band of the states in the frontier of the currently generated state space. Several state space exploration algorithms are evaluated in terms of bounds quality and memory and CPU time requirements. The more efficient seems to be a waved algorithm which expands transition groups. We compare our new methods with the method based on the failure distance concept without state exploration and a method proposed by Souza e Silva and Ochoa which uses state space exploration but does not use the failure distance concept. Using typical examples we show that the methods proposed here can be significantly more efficient than any of the previous methods.Postprint (published version

Identificación del índice de vulnerabilidad territorial a partir de modelos jerárquicos y heurísticos aplicando SOA

Auxiliar de InvestigaciónEn el proyecto se realiza el diseño y desarrollo de 4 servicios web implementando los modelos de toma de decisión (AHP, AHP FUZZY, ELECTRE y PROMETHEE), encargados de procesar datos obtenidos en campo en la primera fase del proyecto que se realizó a través de encuestas, formatos de entrevistas, talleres y metodologías de análisis. Los datos se procesaran de acuerdo al modelo de toma de decisión seleccionado, generando como resultado final un indicador de vulnerabilidad territorial.PregradoIngeniero de Sistema