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Barrera, J., Homem-De-Mello, T., Moreno, E., Pagnoncelli, B. K., & Canessa, G. (2016). Chance-constrained problems and rare events: an importance sampling approach. Math. Program., 157(1), 153–189.
Abstract: We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sampling (IS) techniques, combined with a Sample Average Approximation (SAA) approach, can be effectively used in such situations, provided that variance can be reduced uniformly with respect to the decision variables. We give sufficient conditions to obtain such uniform variance reduction, and prove asymptotic convergence of the combined SAA-IS approach. As it often happens with IS techniques, the practical performance of the proposed approach relies on exploiting the structure of the problem under study; in our case, we work with a telecommunications problem with Bernoulli input distributions, and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the IS distributions. Although some of the results are specific to this problem, we are able to draw general insights that can be useful for other classes of problems. We present numerical results to illustrate our findings.
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Beltran, J. F., Nunez, E., Nunez, F., Silva, I., Bravo, T., & Moffat, R. (2018). Static response of asymmetrically damaged metallic strands: Experimental and numerical approach. Constr. Build. Mater., 192, 538–554.
Abstract: In this study, the effect of the presence of broken wires (damage) asymmetrically distributed on metallic strands surfaces on their static response is assessed. To this end, a general mechanical model for multi layered strands is presented, in which damaged strands are treated as a 1D nonlinear beam under uncoupled biaxial bending and axial load (NLBM). The NLBM is validated by comparisons with the results obtained from an experimental program especially designed for studying the effect of surface damage distribution on strands response and 3D nonlinear finite element simulations. Analyses are carried out on two strand constructions: 1 x 7 and 1 x 19, in which the damage levels and strand diameters vary from 5% to 40% and from 3.5 mm to 22.2 mm, respectively. Results indicate that the NLBM accurate predicts the static response (residual strength, stiffness, axial strain field, and deformed configuration) of the asymmetrically damaged strands, achieving good computational efficiency and numerical robustness. (C) 2018 Elsevier Ltd. All rights reserved.
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Benitez-Llambay, P., Krapp, L., Ramos, X. S., & Kratter, K. M. (2023). RAM: Rapid Advection Algorithm on Arbitrary Meshes. Astron. J., 952(2), 106.
Abstract: The study of many astrophysical flows requires computational algorithms that can capture high Mach number flows, while resolving a large dynamic range in spatial and density scales. In this paper we present a novel method, RAM: Rapid Advection Algorithm on Arbitrary Meshes. RAM is a time-explicit method to solve the advection equation in problems with large bulk velocity on arbitrary computational grids. In comparison with standard upwind algorithms, RAM enables advection with larger time steps and lower truncation errors. Our method is based on the operator splitting technique and conservative interpolation. Depending on the bulk velocity and resolution, RAM can decrease the numerical cost of hydrodynamics by more than one order of magnitude. To quantify the truncation errors and speed-up with RAM, we perform one- and two-dimensional hydrodynamics tests. We find that the order of our method is given by the order of the conservative interpolation and that the effective speed-up is in agreement with the relative increment in time step. RAM will be especially useful for numerical studies of disk-satellite interaction, characterized by high bulk orbital velocities and nontrivial geometries. Our method dramatically lowers the computational cost of simulations that simultaneously resolve the global disk and potential well inside the Hill radius of the secondary companion.
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Bustos, C., Herrera, C. G., Celentano, D., Chen, D. M., & Cruchaga, M. (2016). Numerical Simulation and Experimental Validation of the Inflation Test of Latex Balloons. Lat. Am. J. Solids Struct., 13(14), 2357–2378.
Abstract: Experiments and modeling aimed at assessing the mechanical response of latex balloons in the inflation test are presented. To this end, the hyperelastic Yeoh material model is firstly characterized via tensile test and, then, used to numerically simulate via finite elements the stress-strain evolution during the inflation test. The numerical pressure-displacement curves are validated with those obtained experimentally. Moreover, this analysis is extended to a biomedical problem of an eyeball under glaucoma conditions.
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Castaneda, P., & Reus, L. (2019). Suboptimal investment behavior and welfare costs: A simulation based approach. Financ. Res. Lett., 30, 170–180.
Abstract: We propose a representation of suboptimal investment behavior based on the stochastic discount factor (SDF) paradigm. Suboptimal investment behavior is rationalized as being the investor's optimal decision under a wrong SDF, while wealth trajectories and budget constraints are based on the true SDF. We develop a novel Monte Carlo simulation approach to compute the welfare costs for this suboptimal behavior. We study the suboptimal portfolio choice under CRRA preferences using two financial market models. The Monte Carlo simulation delivers comparable welfare losses to those computed in the original studies, which are based on partial differential equations (PDE) and – finite-difference schemes.
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Comisso, L., & Asenjo, F. A. (2021). Magnetic reconnection as a mechanism for energy extraction from rotating black holes. Phys. Rev. D., 103(2), 023014.
Abstract: Spinning black holes store rotational energy that can be extracted. When a black hole is immersed in an externally supplied magnetic field, reconnection of magnetic field lines within the ergosphere can generate negative energy (relative to infinity) particles that fall into the black hole event horizon while the other accelerated particles escape stealing energy from the black hole. We show analytically that energy extraction via magnetic reconnection is possible when the black hole spin is high (dimensionless spin a similar to 1) and the plasma is strongly magnetized (plasma magnetization sigma(0) > 1/3). The parameter space region where energy extraction is allowed depends on the plasma magnetization and the orientation of the reconnecting magnetic field lines. For sigma(0) >> 1, the asymptotic negative energy at infinity per enthalpy of the decelerated plasma that is swallowed by a maximally rotating black hole is found to be epsilon(infinity)(-) similar or equal to – root sigma(0)/3. The accelerated plasma that escapes to infinity and takes away black hole energy asymptotes the energy at infinity per enthalpy epsilon(infinity)(+) similar or equal to root 3 sigma(0).. We show that the maximum power extracted from the black hole by the escaping plasma is P-extr(max) similar to 0.1M(2) root sigma(0)w(0) (here, M is the black hole mass and w(0) is the plasma enthalpy density) for the collisionless plasma regime and one order of magnitude lower for the collisional regime. Energy extraction causes a significant spindown of the black hole when a similar to 1. The maximum efficiency of the plasma energization process via magnetic reconnection in the ergosphere is found to be eta(max) similar or equal to 3/2. Since fast magnetic reconnection in the ergosphere should occur intermittently in the scenario proposed here, the associated emission within a few gravitational radii from the black hole is expected to display a bursty nature.
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Cortes, C. E., Jara-Moroni, P., Moreno, E., & Pineda, C. (2013). Stochastic transit equilibrium. Transp. Res. Pt. B-Methodol., 51, 29–44.
Abstract: We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing in-vehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic common-lines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic common-lines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a real-size network case as the next step of this research. (C) 2013 Elsevier Ltd. All rights reserved.
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de la Cruz, R., Salinas, H. S., & Meza, C. (2022). Reliability Estimation for Stress-Strength Model Based on Unit-Half-Normal Distribution. Symmetry, 14(4), 837.
Abstract: Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. We propose a novel estimation procedure of stress-strength reliability in the case of two independent unit-half-normal distributions can fit asymmetrical data with either positive or negative skew, with different shape parameters. We obtain the maximum likelihood estimator of the reliability, its asymptotic distribution, and exact and asymptotic confidence intervals. In addition, confidence intervals of model parameters are constructed by using bootstrap techniques. We study the performance of the estimators based on Monte Carlo simulations, the mean squared error, average bias and length, and coverage probabilities. Finally, we apply the proposed reliability model in data analysis of burr measurements on the iron sheets.
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During, G., Josserand, C., & Rica, S. (2017). Wave turbulence theory of elastic plates. Physica D, 347, 42–73.
Abstract: This article presents the complete study of the long-time evolution of random waves of a vibrating thin elastic plate in the limit of small plate deformation so that modes of oscillations interact weakly. According to the wave turbulence theory a nonlinear wave system evolves in longtime creating a slow redistribution of the spectral energy from one mode to another. We derive step by step, following the method of cumulants expansion and multiscale asymptotic perturbations, the kinetic equation for the second order cumulants as well as the second and fourth order renormalization of the dispersion relation of the waves. We characterize the non-equilibrium evolution to an equilibrium wave spectrum, which happens to be the well known Rayleigh-Jeans distribution. Moreover we show the existence of an energy cascade, often called the Kolmogorov-Zakharov spectrum, which happens to be not simply a power law, but a logarithmic correction to the Rayleigh Jeans distribution. We perform numerical simulations confirming these scenarii, namely the equilibrium relaxation for closed systems and the existence of an energy cascade wave spectrum. Both show a good agreement between theoretical predictions and numerics. We show also some other relevant features of vibrating elastic plates, such as the existence of a self-similar wave action inverse cascade which happens to blow-up in finite time. We discuss the mechanism of the wave breakdown phenomena in elastic plates as well as the limit of strong turbulence which arises as the thickness of the plate vanishes. Finally, we discuss the role of dissipation and the connection with experiments, and the generalization of the wave turbulence theory to elastic shells. (C) 2017 Elsevier B.V. All rights reserved.
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Fierro, R., & Leiva, V. (2017). A stochastic methodology for risk assessment of a large earthquake when a long time has elapsed. Stoch. Environ. Res. Risk Assess., 31(9), 2327–2336.
Abstract: We propose a stochastic methodology for risk assessment of a large earthquake when a long time has elapsed from the last large seismic event. We state an approximate probability distribution for the occurrence time of the next large earthquake, by knowing that the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a nonhomogeneous Poisson process. As it is not possible to obtain an empirical cumulative distribution function of the waiting time for the next large earthquake, an estimator of its cumulative distribution function based on existing data is derived. We conduct a simulation study for detecting scenario in which the proposed methodology would perform well. Finally, a real-world data analysis is carried out to illustrate its potential applications, including a homogeneity test for the times between earthquakes.
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Fustos-Toribio, I., Manque-Roa, N., Vasquez Antipan, D., Hermosilla Sotomayor, M., & Gonzalez, V. L. (2022). Rainfall-induced landslide early warning system based on corrected mesoscale numerical models: an application for the southern Andes. Nat. Hazards Earth Syst. Sci., 22(6), 2169–2183.
Abstract: Rainfall-induced landslides (RILs) are an issue in the southern Andes nowadays. RILs cause loss of life and damage to critical infrastructure. Rainfall-induced landslide early warning systems (RILEWSs) can reduce and mitigate economic and social damages related to RIL events. The southern Andes do not have an operational-scale RILEWS yet. In this contribution, we present a pre-operational RILEWS based on the Weather and Research Forecast (WRF) model and geomorphological features coupled to logistic models in the southern Andes. The models have been forced using precipitation simulations. We correct the precipitation derived from WRF using 12 weather stations through a bias correction approach. The models were trained using 57 well-characterized RILs and validated by ROC analysis. We show that WRF has strong limitations in representing the spatial variability in the precipitation. Therefore, accurate precipitation needs a bias correction in the study zone. We used accurate precipitation simulation and slope, demonstrating a high predicting capacity (area under the curve, AUC, of 0.80). We conclude that our proposal could be suitable at an operational level under determined conditions. A reliable RIL database and operational weather networks that allow real-time correction of the mesoscale model in the implemented zone are needed. The RILEWSs could become a support to decision-makers during extreme-precipitation events related to climate change in the south of the Andes.
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Garcia-Papani, F., Uribe-Opazo, M. A., Leiva, V., & Aykroyd, R. G. (2017). Birnbaum-Saunders spatial modelling and diagnostics applied to agricultural engineering data. Stoch. Environ. Res. Risk Assess., 31(1), 105–124.
Abstract: Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered-which is extremely important for agricultural management.
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Girard, A., Gago, E. J., Muneer, T., & Caceres, G. (2015). Higher ground source heat pump COP in a residential building through the use of solar thermal collectors. Renew. Energy, 80, 26–39.
Abstract: This article investigates the feasibility of achieving higher performance from ground-source heat-pumps (GSHP) in space heating mode through the use of solar thermal collectors. A novel simulation tool for solar-assisted ground-source heat-pumps (SGSHP) is presented with an analysis of the influence of solar collectors on the improvement of heat pump performance. Solar radiation and climate temperature data of 19 European cities were used to perform simulations of SGSHP and GSHP systems considering a typical residential house. Overall performance coefficients (COPsys) varied from northern to southern locations between 4.4 and 5.8 for SGSHP and between 4.3 and 5.1 for GSHP. Results show that solar collectors coupling has more impact on performance improvement in regions that benefit from higher irradiance. However, greater running cost savings are achieved in milder climate conditions. Both heat-pump systems are able to effectively contribute to carbon footprint reductions for residential buildings, especially in countries where fossil fuels are the primary source of electricity generation. SGSHP payback periods are found between 8.5 and 23 years from northern to southern localities, making such heating system an economic heating option. SGSHPs are best suited for high irradiance and cool climate locations such as the mountainous regions in southern Europe. (C) 2015 Elsevier Ltd. All rights reserved.
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Girard, A., Muneer, T., & Caceres, G. (2014). A validated design simulation tool for passive solar space heating: Results from a monitored house in West Lothian, Scotland. Indoor Built Environ., 23(3), 353–372.
Abstract: Determining the availability of renewable sources on a particular site would result in increasing the efficiency of buildings through appropriate design. The overall aim of the project is to develop a pioneering software tool allowing the assessment of possible energy sources for any building design project. The package would allow the user to simulate the efficiency of the Passive Solar Space Heating referred in the Low and Zero Carbon Energy Sources (LZCES) Strategic Guide stated by the Office of the Deputy Prime Minister (2006) and the Building Regulations. This research paper presents the tool for modelling the passive solar sources availability in relation to low-carbon building. A 3-month experimental set up monitoring a solar house in West Lothian, Scotland, was also undertaken to validate the simulation tool. Experimental and simulation results were found in good agreement following a one-to-one relationship demonstrating the ability of the newly developed tool to assess potential solar gain available for buildings. This modelling tool is highly valuable in consideration of the part L of the Building Regulations (updated in 2010).
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Jimenez, D., Barrera, J., & Cancela, H. (2023). Communication Network Reliability Under Geographically Correlated Failures Using Probabilistic Seismic Hazard Analysis. IEEE Access, 11, 31341–31354.
Abstract: The research community's attention has been attracted to the reliability of networks exposed to large-scale disasters and this has become a critical concern in network studies during the last decade. Earthquakes are high on the list of those showing the most significant impacts on communication networks, and simultaneously, they are the least predictable events. This study uses the Probabilistic Seismic Hazard Analysis method to estimate the network element state after an earthquake. The approach considers a seismic source model and ground prediction equations to assess the intensity measure for each element according to its location. In the simulation, nodes fail according to the building's fragility curves. Similarly, links fail according to a failure rate depending on the intensity measure and the cable's characteristics. We use the source-terminal, and the diameter constrained reliability metrics. The approach goes beyond the graph representation of the network and incorporates the terrain characteristics and the component's robustness into the network performance analysis at an affordable computational cost. We study the method on a network in a seismic region with almost 9000 km of optical fiber. We observed that for source-terminal that are less than 500 km apart the improvements are marginals while for those that are more than 1000 km apart, reliability improves near a 30% in the enhanced designs. We also showed that these results depend heavily on the robustness/fragility of the infrastructure, showing that performance measures based only the network topology are not enough to evaluate new designs.
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Kosterhon, M., Müller, A., Rockenfeller, R., Aiyangar, A. K., Gruber, K., Ringel, F., et al. (2024). Invasiveness of decompression surgery affects modeled lumbar spine kinetics in patients with degenerative spondylolisthesis. Front. Bioeng. Biotechnol., 11, 1281119.
Abstract: Introduction: The surgical treatment of degenerative spondylolisthesis with accompanying spinal stenosis focuses mainly on decompression of the spinal canal with or without additional fusion by means of a dorsal spondylodesis. Currently, one main decision criterion for additional fusion is the presence of instability in flexion and extension X-rays. In cases of mild and stable spondylolisthesis, the optimal treatment remains a subject of ongoing debate. There exist different opinions on whether performing a fusion directly together with decompression has a potential benefit for patients or constitutes overtreatment. As X-ray images do not provide any information about internal biomechanical forces, computer simulation of individual patients might be a tool to gain a set of new decision criteria for those cases.
Methods: To evaluate the biomechanical effects resulting from different decompression techniques, we developed a lumbar spine model using forward dynamic-based multibody simulation (FD_MBS). Preoperative CT data of 15 patients with degenerative spondylolisthesis at the level L4/L5 who underwent spinal decompression were identified retrospectively. Based on the segmented vertebrae, 15 individualized models were built. To establish a reference for comparison, we simulated a standardized flexion movement (intact) for each model. Subsequently, we performed virtual unilateral and bilateral interlaminar fenestration (uILF, bILF) and laminectomy (LAM) by removing the respective ligaments in each model. Afterward, the standardized flexion movement was simulated again for each case and decompression method, allowing us to compare the outcomes with the reference. This comprehensive approach enables us to assess the biomechanical implications of different surgical approaches and gain valuable insights into their effects on lumbar spine functionality.
Results: Our findings reveal significant changes in the biomechanics of vertebrae and intervertebral discs (IVDs) as a result of different decompression techniques. As the invasiveness of decompression increases, the moment transmitted on the vertebrae significantly rises, following the sequence intact -> uILF -> bILF -> LAM. Conversely, we observed a reduction in anterior-posterior shear forces within the IVDs at the levels L3/L4 and L4/L5 following LAM.
Conclusion: Our findings showed that it was feasible to forecast lumbar spine kinematics after three distinct decompression methods, which might be helpful in future clinical applications.
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Krapp, L., Garrido-Deutelmoser, J., Benítez-Llambay, P., & Kratter, K. M. (2024). A Fast Second-order Solver for Stiff Multifluid Dust and Gas Hydrodynamics. Astrophys. J. Suppl. Ser., 271(1), 7.
Abstract: We present MDIRK: a multifluid second-order diagonally implicit Runge-Kutta method to study momentum transfer between gas and an arbitrary number (N) of dust species. The method integrates the equations of hydrodynamics with an implicit-explicit scheme and solves the stiff source term in the momentum equation with a diagonally implicit, asymptotically stable Runge-Kutta method (DIRK). In particular, DIRK admits a simple analytical solution that can be evaluated with O(N) operations, instead of standard matrix inversion, which is O(N)3 . Therefore, the analytical solution significantly reduces the computational cost of the multifluid method, making it suitable for studying the dynamics of systems with particle-size distributions. We demonstrate that the method conserves momentum to machine precision and converges to the correct equilibrium solution with constant external acceleration. To validate our numerical method we present a series of simple hydrodynamic tests, including damping of sound waves, dusty shocks, a multifluid dusty Jeans instability, and a steady-state gas-dust drift calculation. The simplicity of MDIRK lays the groundwork to build fast high-order, asymptotically stable multifluid methods.
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Lagos, R., Canessa, E., & Chaigneau, S. E. (2019). Modeling stereotypes and negative self-stereotypes as a function of interactions among groups with power asymmetries. J. Theory Soc. Behav., 49(3), 312–333.
Abstract: Stereotypes is one of the most researched topics in social psychology. Within this context, negative self-stereotypes pose a particular challenge for theories. In the current work, we propose a model that suggests that negative self-stereotypes can theoretically be accounted for by the need to communicate in a social system made up by groups with unequal power. Because our theory is dynamic, probabilistic, and interactionist, we use a computational simulation technique to show that the proposed model is able to reproduce the phenomenon of interest, to provide novel accounts of related phenomena, and to suggest novel empirical predictions. We describe our computational model, our variables' dynamic behavior and interactions, and link our analyses to the literature on stereotypes and self-stereotypes, the stability of stereotypes (in particular, gender and racial stereotypes), the effects of power asymmetries, and the effects of intergroup contact.
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Leiva, V., Ferreira, M., Gomes, M. I., & Lillo, C. (2016). Extreme value Birnbaum-Saunders regression models applied to environmental data. Stoch. Environ. Res. Risk Assess., 30(3), 1045–1058.
Abstract: Extreme value models are widely used in different areas. The Birnbaum-Saunders distribution is receiving considerable attention due to its physical arguments and its good properties. We propose a methodology based on extreme value Birnbaum-Saunders regression models, which includes model formulation, estimation, inference and checking. We further conduct a simulation study for evaluating its performance. A statistical analysis with real-world extreme value environmental data using the methodology is provided as illustration.
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Leiva, V., Marchant, C., Ruggeri, F., & Saulo, H. (2015). A criterion for environmental assessment using Birnbaum-Saunders attribute control charts. Environmetrics, 26(7), 463–476.
Abstract: Assessing environmental risk is useful for preventing adverse effects on human health in highly polluted cities. We design a criterion for environmental monitoring based on an attribute control chart for the number of dangerous contaminant levels when the concentration to be monitored follows a Birnbaum-Saunders distribution. This distribution is being widely applied to environmental data. We provide a novel justification for its usage in environmental sciences. The control coefficient and the minimum inspection concentration for the designed criterion are determined to yield the specified in-control average run length, whereas the out-of-control case is obtained according to a shift in the target mean. A simulation study is conducted to evaluate the proposed criterion, which reports its performance to provide earlier alerts of out-of-control processes. An application with real-world environmental data is carried out to validate its coherence with what is reported by the health authority. Copyright (c) 2015 John Wiley & Sons, Ltd.
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