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Abstract: The simple assembly line balancing problem type E (abbreviated as SALBP-E) occurs when the number of workstations and the cycle time are variables and the objective is to maximise the line efficiency. In contrast with other types of SALBPs, SALBP-E has received little attention in the literature. In order to solve optimally SALBP-E, we propose a mixed integer liner programming model and an iterative procedure. Since SALBP-E is NP-hard, we also propose heuristics derived from the aforementioned procedures for solving larger instances. An extensive experimentation is carried out and its results show the improvement of the SALBP-E resolution.
Keywords: Assembly line balancing, SALBP, manufacturing optimisation.
Pages: 227– 242
Abstract: This article is directed at the problem of reliability estimation using ranked set sampling. A nonparametric estimator based on kernel density estimation is developed. The estimator is shown to be superior to its analog in simple random sampling. Monte Carlo simulations are employed to assess performance of the proposed estimator. Two real data sets are analysed for illustration.
Keywords: Bandwidth selection, Judgment ranking, Stress-strength model.
Pages: 243– 266
Abstract: We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller number of parameters. The resulting processes are linear combinations of Ornstein-Uhlenbeck processes all driven by the same Lévy process. This provides a straightforward computation of covariances, a state-space model representation and methods for estimating parameters. Furthermore, the discrete and equally spaced sampling of the process turns to be an ARMA(p, p−1) process. We propose methods for estimating the parameters of the iterated Ornstein-Uhlenbeck process when the noise is either driven by a Wiener or a more general Lévy process, and show simulations and applications to real data.
Keywords: Ornstein-Uhlenbeck process, Lévy process, Continuous ARMA, stationary process.
Pages: 267– 302
Abstract: The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection algorithm. One of the main contributions is to extend the methodology based on moments to all distributions, even without finite moments. These techniques are applied to euro/dollar daily exchange rates and to Danish fire insurance losses.
Keywords: Statistics of extremes, heavy tails, high quantile estimation, value at risk.
Pages: 303– 320
Abstract: This study proposes two methods for detecting outliers in functional time series. Both methods take dependence in the data into account and are based on robust functional principal component analysis. One method seeks outliers in the series of projections on the first principal component. The other obtains uncontaminated forecasts for each data set and determines that those observations whose residuals have an unusually high norm are considered outliers. A simulation study shows the performance of these proposed procedures and the need to take dependence in the time series into account. Finally, the usefulness of our methodology is illustrated in two real datasets from the electricity market: daily curves of electricity demand and price in mainland Spain, for the year 2012.
Keywords: Functional data analysis, functional principal component analysis, functional time series, outlier detection, electricity demand and price.
Pages: 321– 348
Abstract: When traditional methods are applied to compositional data misleading and incoherent results could be obtained. Finite mixtures of multivariate distributions are becoming increasingly important nowadays. In this paper, traditional strategies to fit a mixture model into compositional data sets are revisited and the major difficulties are detailed. A new proposal using a mixture of distributions defined on orthonormal log-ratio coordinates is introduced. A real data set analysis is presented to illustrate and compare the different methodologies.
Keywords: Compositional data, Finite Mixture, Log ratio, Model-based clustering, Normal distribution, Orthonormal coordinates, Simplex.
Pages: 340– 374
Abstract: One important goal in clinical applications of multi-state models is the estimation of transition probabilities. Recently, landmark estimators were proposed to estimate these quantities, and their superiority with respect to the competing estimators has been proved in situations in which the Markov condition is violated. As a weakness, it provides large standard errors in estimation in some circumstances. In this article, we propose two approaches that can be used to reduce the variability of the proposed estimator. Simulations show that the proposed estimators may be much more efficient than the unsmoothed estimator. A real data illustration is included.
Keywords: Kaplan-Meier, Multi-state model, Nonparametric estimation, Presmoothing, Survival Analysis.
Pages: 375– 398