Quality control in machining using order statistics

The quality of surface roughness for machined parts is essential in the manufacturing process. The cutting tool plays an important role in the roughness of the machined parts. The process of determining the number of tolerant faults is problematic; this is due to the fact that the behaviour of the cutting tool is random. In this paper, we use an approach based on order statistics to study the construction of functional and reliability haracteristic for the faults tolerant machined parts in each five batch of ten machined parts. Our experiments show that the number of faulty machined parts will not exceed two and the distribution of the minimum gives the best interval of the surface roughness. We have shown that the distribution of extreme order statistics plays an important role in determining the lower and upper limits of the roughness measurements depending on the reliability of the cutting tool

Prediction of U.S. General Aviation fatalities from extreme value approach

General Aviation is the main component of the United States civil aviation and the most aviation accidents concern this aviation category. Between early 2015 and May 17, 2016, a total of 1546 general aviation accidents in the United States has left 466 fatalities and 384 injured. Hence, in this study, we investigate the risk of U.S. General Aviation accidents by examining historical U.S. General Aviation accidents. Using the Peak Over Threshold approach and Generalized Pareto Distribution, we predict the number of fatalities resulting in extreme GA accidents in the future operations. We use a graphical method and intensive parameters estimates to obtain the optimal range of the threshold. In order to assess the uncertainty in the inference and the accuracy of the results, we use the nonparametric bootstrap approach

Survival analysis in living and engineering sciences

Survival or reliability analysis is one of the most significant advancements of statistics in the last quarter of the 20th century. This domain of statistics takes an important place in biomedical and industrial framework. In this paper, we propose a new baseline hazard function from extreme value theory. The newly suggested function is non-monotone and is named as a generalized extreme values baseline hazard function. We prove that this function satisfies hazard properties. A study of the characteristics of the function related to time is made. Conditions for applicability of the model are obtained

A Stochastic Approach to Modeling Food Pattern

In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in the human organism with a deficient immune system, during consecutive intakes of contaminated food. This process quantifies the exposure to toxins of subjects living with comorbidity (children not breastfed, the elderly, and pregnant women) to food-borne diseases. The Adomian Decomposition Method and the fractional integration of Riemann Liouville are used in the modeling processes

Sampling spatial structures in geostatistical framework

Extreme values geostatistics make it possible to model the asymptotic behaviors of random phenomena which depends on space or time parameters. In this paper, we propose new models of the extremal coefficient within a spatial stationary fields underlied by multivariate copulas. Some models of extensions of the extremogram and the cross-extremogram are constructed in a spatial framework. Moreover, both these two geostatistcal tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.Comment: 16 pages, 3 figure

Spatial Tail Dependence and Survival Stability in a Class of Archimedean Copulas

This paper investigates properties of extensions of tail dependence of Archimax copulas to high dimensional analysis in a spatialized framework. Specifically, we propose a characterization of bivariate margins of spatial Archimax processes while spatial multivariate upper and lower tail dependence coefficients are modeled, respectively, for Archimedean copulas and Archimax ones. A property of stability is given using convex transformations of survival copulas in a spatialized Archimedean family

Estimation of the Value at Risk Using the Stochastic Approach of Taylor Formula

The aim of this paper is to provide an approximation of the value-at-risk of the multivariate copula associated with financial loss and profit function. A higher dimensional extension of the Taylor–Young formula is used for this estimation in a Euclidean space. Moreover, a time-varying and conditional copula is used for the modeling of the VaR

Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT-Based Copulas

In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying