Effect of parameters on Geoa/Geob/1 Queues: theoretical analysis and simulation results

This paper analyzes a discrete-time Geoa/Geob/1 queuing system with batch arrivals of fixed size a , and batch services of fixed size b. Both arrivals and services occur randomly following a geometric distribution. The steady-state queue length distribution is obtained as the solution of a system of difference equations. Necessary and sufficient conditions are given for the system to be stationary. Besides, the uniqueness of the root of the characteristic polynomial in the interval (0, 1) is proven which is the only root needed for the computation of the theoretical solution with the proposed procedure. The theoretical results are compared with the ones observed in some simulations of the queuing system under different sets of parameters. The agreement of the results encourages the use of simulation for more complex systems. Finally, we explore the effect of parameters on the mean length of the queue as well as on the mean waiting time

On the construction of experimental designs for a given task by jointly optimizing several quality criteria: Pareto-optimal experimental designs

Experimental designs for a given task should be selected on the base of the problem being solved and of some criteria that measure their quality. There are several such criteria because there are several aspects to be taken into account when making a choice. The most used criteria are probably the so-called alphabetical optimality criteria (for example, the A-, E-, and D-criteria related to the joint estimation of the coefficients, or the I- and G-criteria related to the prediction variance). Selecting a proper design to solve a problem implies finding a balance among these several criteria that measure the performance of the design in different aspects. Technically this is a problem of multi-criteria optimization, which can be tackled from different views. The approach presented here addresses the problem in its real vector nature, so that ad hoc experimental designs are generated with an algorithm based on evolutionary algorithms to find the Pareto-optimal front. There is not theoretical limit to the number of criteria that can be studied and, contrary to other approaches, no just one experimental design is computed but a set of experimental designs all of them with the property of being Pareto-optimal in the criteria needed by the user. Besides, the use of an evolutionary algorithm makes it possible to search in both continuous and discrete domains and avoid the need of having a set of candidate points, usual in exchange algorithms.Projects CTQ2011-26022(SpanishMinisteriodeEconomíayCompetitividad)andBU108A11-2(JuntadeCastillayLeón)

A modified entropy-based performance criterion for class-modelling with multiple classes

The paper presents a new proposal for a single overall measure, the diagonal modified confusion entropy (DMCEN), to assess the performance of class-models jointly computed for several classes, a versatile index regarding sensitivity and specificity, and that supports class weighting. The characteristics of the proposed figure of merit are illustrated as against other usual performance measures and show how the index is more sensitive to the variations in the class-models than similar published indexes. Besides, a benchmark value representing a random modelling is also defined for DMCEN to be used as initial level to assess the quality of the built class-models. Furthermore, systematic comparisons have been conducted by using the degree of consistency C and the degree of discriminancy D when comparing the proposed DMCEN to the usual total efficiency (a geometric mean between sensitivity and specificity). Simulations show that, for a hundred thousand sensitivity/specificity matrices with four categories, C is almost 0.7 on average, well above the needed 0.5, and there is more than 62% probability that DMCEN detects differences when the total efficiency does not. Illustration of the application of the index is shown with an experimental data set with four categories.Spanish Ministerio de Ciencia, Innovaci on y Universidades (AEI) and Consejería de Educaci on de la Junta de Castilla y Le on through projects CTQ2017-88894-R and BU052P20 respectively (both co-financed with European Regional Development Funds

A computational approach to partial least squares model inversion in the framework of the process analytical technology and quality by design initiatives

In the context of the paradigms founding the Quality by Design and Process Analytical Technology initiatives, the work herein presents a computational approach to support the decision-making process, in particular, about the feasibility of a product defined for some a priori given quality characteristics. The approach is based on the computation of the pareto-optimal front when simultaneously minimizing the expected differences between the predicted and the desired characteristics. Thus, the feasibility is tackled as an optimization problem with the novelty of doing so simultaneously for all the characteristics, preserving the correlation structure, but by separately handling each individual characteristic. With data from a low-density polyethylene production process, with fourteen process variables and five measured characteristics of the final polyethylene, solutions are found to define the Design Space for targeted quality characteristics on the product, and without the need of explicitly inverting the PLS (Partial Least Squares) prediction model fitted to the process.Junta de Castilla y León (BU012P17), and also Spanish MINECO and Agencia Estatal de Investigación under research projects CTQ2014-53157-R, and CTQ2017-88894-

A useful tool for computation and interpretation of trading-off solutions through pareto-optimal front in the field of experimental designs for mixtures

An algorithmic implementation is presented to deal with several responses in mixtures problems, without theoretical limits on the number of responses or on the factors to be blended. Also, constrained and unconstrained domains are handled, as well as domains with both mixtures and discrete variables. Besides, an alternative way of interpreting the results coming from the experimental design for mixtures is presented. It is based on the parallel coordinates plots for visualization in more than the usual three-dimensional Cartesian diagrams or the simplex mixture spaces for at most four experimental factors. Specifically, this is done in cases in which more than one experimental response should be handled, tackling the conflict by estimating trading-off solutions via the computation of the pareto-optimal front, which is fully explored with the parallel coordinates plots. The procedure is shown by two case-studies, taken from the literature. The first one deals with several factors in a constrained experimental domain when trying to optimize a detergent by taking into account two severely conflicting characteristics. The second one is about five chemical components blended with different dosage levels for getting a concrete strong enough, experimental results that are re-evaluated by posing a unique blocked design for analysing the data. The joint use of the pareto-optimal front for mixtures designs and the parallel coordinates plots for its visualization provide the researcher a deeper understanding of the problem under study to make accurate decisions.Spanish Ministerio de Economía y Competitividad through project CTQ2014- 53157-R, a national competitive project co-financed with European FEDER funds

Simultaneous class-modelling in chemometrics: A generalization of Partial Least Squares class modelling for more than two classes by using error correcting output code matrices

The paper presents a new methodology within the framework of the so-called compliant class-models, PLS2-CM, designed with the purpose of improving the performance of class-modelling in a setting with more than two classes. The improvement in the class-models is achieved through the use of multi-response PLS models with the classes encoded via Error-Correcting Output Codes (ECOC), instead of the traditional class indicator variables used in chemometrics. The proposed PLS2-CM entails a decomposition of a class-modelling problem into a series of binary learners, based on a family of code matrices with different code length, which are evaluated to obtain simultaneous compliant class-models with the best performance. The methodology develops both a new encoding system, based on multi-criteria optimization to search for optimal coding matrices, and a new decoding system, based on probability thresholds to assign objects to classmodels. The whole procedure implies that the characteristics of the dataset at hand affect the final selection of the coding matrix and therefore of built class-models, thus giving rise to a data-driven strategy. The application of PLS2-CM to a variety of cases (controlled data, experimental data and repository datasets) results in an enhanced class-modelling performance by means of the suggested procedure, as measured by the DMCEN (Diagonal Modified Confusion Entropy) index and by sensitivity-specificity matrices. The predictive ability of the compliant class-models has been evaluated.This work is part of the project with reference BU052P20 financed by Junta de Castilla y Leon, Conserjería de Educacion with the aid of European Regional Development Funds

A new approach based on inversion of a partial least squares model searching for a preset analytical target profile. Application to the determination of five bisphenols by liquid chromatography with diode array detector

The paper shows a procedure for selecting the control method parameters (factors) to obtain a preset ‘analytical target profile’ when a liquid chromatographic technique is going to be carried out for the simultaneous determination of five bisphenols (bisphenol-A, bisphenol-S, bisphenol-F, bisphenol-Z and bisphenol-AF), some of them regulated by the European Union. The procedure has three steps. The first consists of building a D-optimal combined design (mixture-process design) for the control method parameters, which are the composition of the ternary mobile phase and its flow rate. The second step is to fit a PLS2 model to predict six analytical responses (namely, the resolution between each pair of consecutive peaks, and the initial and final chromatographic time) as a function of the control method parameters. The third final step is the inversion of the PLS2 model to obtain the conditions needed for attaining a preset analytical target profile. The computational inversion of the PLS2 prediction model looking for the Pareto front of these six responses provides a set of experimental conditions to conduct the chromatographic determination, specifically 22% of water, mixed with 58% methanol and 20% of acetonitrile, keeping the flow rate at 0.66 mL min−1. These conditions give a chromatogram with retention times of 2.180, 2.452, 2.764, 3.249 and 3.775 min for BPS, BPF, BPA, BPAF and BPZ, respectively, and excellent resolution among all the chromatographic peaks. Finally, the analytical method is validated under the selected experimental conditions, in terms of trueness and precision. In addition, the detection capability for the five bisphenols were: 596, 334, 424, 458 and 1156 μg L−1, with probabilities of false positive and of false negative equal to 0.05.Spanish MINECO (AEI/FEDER, UE) and Consejería de Educación de la JCyL through projects CTQ2017-88894-R and BU052P20, co-financed with European Regional Development Fund

Method operable design region obtained with a partial least squares model inversion in the determination of ten polycyclic aromatic hydrocarbons by liquid chromatography with fluorescence detection

A chromatographic method with the Analytical Quality by Design (AQbD) methodology is developed for the simultaneous determination by HPLC-FLD of ten PAHs (naphthalene, phenanthrene, anthracene, flu- oranthene, pyrene, chrysene, benzo[a]anthracene, perylene, benzo[b]fluoranthene, and benzo[a]pyrene), widely spread in the environment. The construction of the Method Operable Design Region (MODR) is conducted, for the first time, via the inversion of a multiresponse Partial Least Squares (PLS2) model, which is needed to maintain the correlations among the Critical Method Parameters (CMP), among the Critical Quality Attributes (CQA), and the covariance between one another. The five CMP considered were the composition of the mobile phase (water, methanol, acetonitrile), flow rate, and column temperature. The eight CQA were linked to resolution between peaks recorded in the same emission wavelength (greater than 1.4) and the total time (less than 15 minutes). By systematic use of experimental design and parallel coordinates plots to explore the Pareto optimal front obtained with the PLS2 model inversion, the computed MODR is formed by convex combinations of eight specific settings of Critical Method Parameters that have a mobile phase with percentages of water between 37 and 38 %, of methanol from 13 and 22 %, and of acetonitrile between 41 and 49 %, together with a flow rate between 1.47 and 1.50 mL min −1 , and column temperature between 41.9 and 44.0 °C in their adequate combinations. All the chromatographic peaks are well resolved, with total time varying between 12.96 and 15.66 min inside the estimated MODR and the analytical method is accurate with CC βbetween 0.9 and 7.0 μg L −1 with probability of both false positive and false negative equal to 0.05.Research projects CTQ2017-88894-R and BU052P20, financed by the Spanish Ministerio de Ciencia, Inno- vación y Universidades (AEI/FEDER, UE) and Consejería de Edu- cación de la Junta de Castilla y León, both co-financed with Eu- ropean Development Funds. M.M. Arce wishes to thank Junta de Castilla y León for her postdoctoral contract through BU052P20 project

La interdisciplinariedad y el itinerario curricular elegido por el estudiante, ejes fundamentales para desarrollar competencias curriculares en Química

Póster presentado en: V Jornadas de Innovación Docente de la UBU, Burgos, 21-22 de octubre de 2010, organizadas por el Instituto de Formación e Innovación Educativa-IFIE de la Universidad de Burgo

Residual spaces in latent variables model inversion and their impact in the design space for given quality characteristics

The paper contains a discussion about the null spaces associated to linear prediction models for the particular case of Partial Least Squares regression models. The discussion separately considers the two existing null spaces: the one in the input space related to the projection onto the latent space and the null space, coming from the projection space, corresponding to the mapping of the scores onto the predicted responses. The paper also explores the impact of such null spaces in the definition of the design space around some feasible solutions obtained by inverting the prediction model, via several cases with simulated and real data from the literature. The case-studies serve to illustrate the discussion and the need of considering points in the two null spaces, rather than just take into account the null space within the latent space. They also serve to show how to address the use of the resulting vectors in the design space to maintain the desired quality by modifying the tunable (maneuverable) process variables to compensate for variations due to some other feature variables not so easy to control.European Regional Development Fund (FEDER) through Spanish Agencia Estatal de Investigación (project CTQ2017-88894-R