arXiv subjects

Jorge Navarro

Publications and source records attributed to Jorge Navarro.

16 recordsLinked to original sources

arXiv2026

Simple repair policies and decompositions for semi-coherent systems with simultaneous failures

We consider semi-coherent binary systems that are subject to simultaneous failures of its components. These are systems whose components can be either working or failed; the system can also be working or failed depending on the state of the components; and repairing a component cannot cause the system to fail. We consider that one or more components can fail simultaneously, allowing us to model external shocks and disasters. For this, we use the L\'evy-frailty Marshall-Olkin (LFMO) multivariate distribution to model the failure times of the components. We aim to answer in which states of the system we should repair the components. This is a challenging question, as the number of repair policies grows super-exponentially in the number of components. To tackle this, we propose a simple family of repair policies, which we call $r$-out-of-$n$:R repair policies, where one repairs all failed components when the system fails or when there are $r$ or more failed components. Our main contribution is that we derive exact and simple expressions for key performance-evaluation quantities of the system operating under our proposed repair policies. That is, we give explicit expressions for the mean time-to-failure of the system, mean time-to-repair, probability of system-failure before repair, and component- and system-repair rate. We also give expressions for the expected cost and long-term average cost, when there are components' and system repair cost. The only relevant parameters involved in the derived expressions are the structural signature of the system, and the Laplace exponent associated to the LFMO distribution.

math.PR↗

arXiv2025

Stochastic dominance of sums of risks under dependence conditions

We provide conditions for the stochastic dominance comparisons of a risk $X$ and an associated risk $X+Z$, where $Z$ represents the uncertainty due to the environment and where $X$ and $Z$ can be dependent. The comparisons depend on both the copula $C$ between the distributions of $X$ and $Z$ and on the distribution of $Z$. We provide two different conditions for $C$ which represents new positive dependence properties. Regarding $Z$, we need some symmetry or asymmetry (skew) properties. Some illustrative examples are provided.

math.ST↗

arXiv2024

Comparisons of coherent systems under the time-transformed exponential model

The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and $k$-ou-of-$n$ systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. In this paper we study them by assuming a Time Transformed Exponential (TTE) model for the joint distribution of the component lifetimes. This model is equivalent to the frailty model which assumes that they are conditionally independent given a common risk parameter (which represents the common environment risk). Under this model, we obtain explicit expressions for the system reliability functions and comparison results for the main stochastic orders. The system residual lifetime (under different assumptions) is studied as well.

math.ST↗

arXiv2024

On sums of dependent random lifetimes under the Time Transformed Exponential model

Considered a pair of random lifetimes whose dependence is described by a Time Transformed Exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of the joint distribution in terms of multivariate distortions, which is an alternative approach to the classical copula representation. Since this approach allows to obtain conditional distributions and their inverses in simple form, then it is also shown how it can be used to predict the value of the sum from the value of one of the variables (or vice versa) by using quantile regression techniques.

math.ST↗

arXiv2024

Predicting failure times of coherent systems

The article is focused on studying how to predict the failure times of coherent systems from the early failure times of their components. Both the cases of independent and dependent components are considered by assuming that they are identically distributed (homogeneous components). The heterogeneous components' case can be addressed similarly but more complexly. The present study is for non-repairable systems, but the information obtained could be used to decide if a maintenance action should be carried out at time t. Different cases are considered regarding the information available at time t. We use quantile regression techniques to predict the system failure times and to provide prediction intervals. The theoretical results are applied to specific system structures in some illustrative examples.

stat.AP↗

arXiv2024

A variance-based importance index for systems with dependent components

This paper proposes a variance-based measure of importance for coherent systems with dependent and heterogeneous components. The particular cases of independent components and homogeneous components are also considered. We model the dependence structure among the components by the concept of copula. The proposed measure allows us to provide the best estimation of the system lifetime, in terms of the mean squared error, under the assumption that the lifetime of one of its components is known. We include theoretical results that are useful to calculate a closed-form of our measure and to compare two components of a system. We also provide some procedures to approximate the importance measure by Monte Carlo simulation methods. Finally, we illustrate the main results with several examples.

stat.AP↗

arXiv2024

New multivariate Gini's indices

The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian line and the Lorenz curve. Both are dispersion indices because they quantify how far a random variable and its independent copy are. Aiming to measure dispersion in the multivariate case, we define and study new Gini's indices. For the bivariate case we provide several results and we point out that they are "dependence-dispersion" indices. Covariance representations are exhibited, with an interpretation also in terms of conditional distributions. Further results, bounds and illustrative examples are discussed too. Multivariate extensions are defined, aiming to apply both indices in more general settings. Then, we define efficiency Gini's indices for any semi-coherent system and we discuss about their interpretation. Empirical versions are considered in order as well to apply multivariate Gini's indices to data.

math.PR↗

arXiv2021

A theoretical look at ordinal classification methods based on reference sets composed of characteristic actions

From a theoretical view, this paper addresses the general problem of designing ordinal classification methods based on comparing actions with subset of actions, which are representative of their classes (categories). The basic demand of the proposal consists in setting a relational system (D, S), where S is a reflexive relation compatible with the preferential order of the set of classes, and D is a transitive relation such that D is a subset of S. Different ordinal classification methods can be derived from diverse model of preferences fulfilling the basic conditions on S and D. Two complementary assignment procedures compose each method, which correspond through the transposition operation and should be used complementarily. The methods work under relatively slight conditions on the representative actions and satisfy several fundamental properties. ELECTRE TRI-nC, INTERCLASS-nC, and the hierarchical ELECTRE TRI-nC with interacting criteria, can be considered as particular cases of this general framework.

econ.TH↗

arXiv2021

a theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes

This paper addresses the general problem of designing ordinal classification methods based on comparing actions with limiting boundaries of ordered classes (categories). The fundamental requirement of the method consists of setting a relational system (D,S), where S and D are reflexive and transitive relations, respectively, S should be compatible with the order of the set of classes, and D is a subset of S. An asymmetric preference relation P is defined from S. Other requirements are imposed on the actions which compose the limiting boundaries between adjacent classes, in such a way that each class is closed below and above. The paper proposes S-based and P-based assignment procedures. Each of them is composed of two complementary assignment procedures, which correspond through the transposition operation and should be used conjointly. The methods work under several basic conditions on the set of limiting boundaries. Under other more demanding separability requirements, each procedure fulfills the set of structural properties established for other outranking-based ordinal classification methods. Our proposal avoids the conflict between the required correspondence through the transposition operation and the assignment of limiting actions to the classes to which they belong. We thus propose very diverse S and P-based ordinal classification approaches with desirable properties, which can be designed by using decision models with the capacity to build preference relations fulfilling the basic requirements to S and D.

econ.TH↗

arXiv2020

Distortion Representations of Multivariate Distributions

The univariate distorted distribution were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks. Later they were also applied to represent distributions of order statistics, coherent systems, proportional hazard rate (PHR) and proportional reversed hazard rate (PRHR) models, etc. In this paper we extend this concept to the multivariate setup. We show that, in some cases, they are a valid alternative to the copula representations especially when the marginal distributions may not be easily handled. Several relevant examples illustrate the applications of such representations in statistical modeling. They include the study of paired (dependent) ordered data, joint residual lifetimes, order statistics and coherent systems.

math.ST↗

arXiv2019

Ultrafast Relativistic Electron Nanoprobes

One of the frontiers in electron scattering is to couple ultrafast temporal resolution with highly localized probes to investigate the role of microstructure on material properties. Here, taking advantage of the unprecedented average brightness of the APEX electron gun providing relativistic electron pulses at high repetition rates, we demonstrate for the first time the generation of ultrafast relativistic electron beams with picometer-scale emittance and their ability to probe nanoscale features on materials with complex microstructures. At the sample plane, the APEX beam is tightly focused by a custom in-vacuum lens system based on permanent magnet quadrupoles, and its evolution around the waist is tracked by a knife-edge technique, allowing accurate reconstruction of the beam shape and local density. We then use the focused beam to characterize a Ti-6 wt\% Al polycrystalline sample by correlating the diffraction and imaging modality, showcasing the capability to locate grain boundaries and map adjacent crystallographic domains with sub-micron precision. This work provides a new paradigm for ultrafast electron instrumentation, demonstrating the ability to generate relativistic beams with ultrasmall transverse phase space volumes enabling novel characterization techniques such as relativistic ultrafast electron nano-diffraction and ultrafast scanning transmission electron microscopy.

physics.app-ph↗

arXiv2017

Joint signature of two or more systems with applications to multistate systems made up of two-state components

The structure signature of a system made up of $n$ components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the $n$-tuple whose $k$-th coordinate is the probability that the $k$-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order $n$ whose $(k,l)$-entry is the probability that the $k$-th failure causes the first system to fail and the $l$-th failure causes the second system to fail. This concept was successfully used to derive a signature-based decomposition of the joint reliability of the two systems. In the first part of this paper we provide an explicit formula to compute the joint structure signature of two or more systems and extend this formula to the general non-i.i.d. case, assuming only that the distribution of the component lifetimes has no ties. We also provide and discuss a necessary and sufficient condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. In the second part of this paper we show how our results can be efficiently applied to the investigation of the reliability and signature of multistate systems made up of two-state components. The key observation is that the structure function of such a multistate system can always be additively decomposed into a sum of classical structure functions. Considering a multistate system then reduces to considering simultaneously several two-state systems.

math.PR↗

arXiv2013

A simple proof for the multivariate Chebyshev inequality

In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the population of an arbitrary random vector X with finite mean E(X) and a positive definite covariance matrix V=Cov(X) whose Mahalanobis distance with respect to V to the mean E(X) is less than a fixed value. The proof is based on the calculation of the principal components.

math.ST↗

arXiv2010

Symmetry restoration at finite temperature with weak magnetic fields

We study symmetry restoration at finite temperature in the standard model during the electroweak phase transition in the presence of a weak magnetic field. We compute the finite temperature effective potential up to the contribution of ring diagrams, using the broken phase degrees of freedom, and keep track of the gauge parameter dependence of the results. We show that under these conditions, the phase transition becomes stronger first order.

hep-ph↗

arXiv2010

The Bonds of Laughter: A Multidisciplinary Inquiry into the Information Processes of Human Laughter

A new core hypothesis on laughter is presented. It has been built by putting together ideas from several disciplines: neurodynamics, evolutionary neurobiology, paleoanthropology, social networks, and communication studies. The hypothesis contributes to ascertain the evolutionary origins of human laughter in connection with its cognitive emotional signaling functions. The new behavioral and neurodynamic tenets introduced about this unusual sound feature of our species justify the ubiquitous presence it has in social interactions and along the life cycle of the individual. Laughter, far from being a curious evolutionary relic or a rather trivial innate behavior, should be considered as a highly efficient tool for inter-individual problem solving and for maintenance of social bonds.

q-bio.NC↗

arXiv2008

Minimal Standard Model self-energies at finite temperature in the presence of weak magnetic fields: towards a full symmetry restoration study

The study of the universe's primordial plasma at high temperature plays an important role when tackling different questions in cosmology, such as the origin of the matter-antimatter asymmetry. In the Minimal Standard Model (MSM) neither the amount of CP violation nor the strength of the phase transition are enough to produce and preserve baryon number during the Electroweak Phase Transition (EWPT), which are two of the three ingredients needed to develop baryon asymmetry. In this talk we present the first part of the analysis done within a scenario where it is viable to have improvements to the aforementioned situation: we work with the degrees of freedom in the broken symmetry phase of the MSM and analyze the development of the EWPT in the presence of a weak magnetic field. More specifically, we calculate the particle self-energies that include the effects of the weak magnetic field, needed for the MSM effective potential up to ring diagrams.

hep-ph↗