Homogeneous Charge Compression Ignition (HCCI) combustion is a potential candidate for dealing with the stringent regulations on vehicle emissions while still providing very good energy efficiency. Despite the promising results obtained in preliminary studies, the lack of autoignition control has delayed its launch in the engine industry. In the development of the HCCI concept, the availability of reliable computer models has proved extremely valuable, due to their flexibility and lower cost compared with experiments using real engines. In order to obtain the best formulation of a fuel surrogate formulated with n-heptane, toluene and cyclohexane that efficiently estimate the autoignition behaviour, regression adjustments are made to the Root-Mean-Square Errors (RMSE) of experimental Starts of Combustion (SOC) from the modeled SOC. The canonical form of the Scheffé polynomials is widely used to fit the data from mixture experiments, however the experimenter might have only partial knowledge. In this paper we present the adaptation of the robust methodology for possibly misspecified blending model and an algorithm to obtain tailor-made optimal designs for mixture experiments, instead of using standard designs which are indiscriminately employed, to make good estimations of the parameters blending model. We maximize the determinant of the mean squared error matrix of the least square estimator over a realistic neighbourhood of the fitted regression mixture model. The maximized determinant is then minimized over the class of possible designs, yielding an optimal design. Thus, the computed desings are robust to the exact form of the true blending model. Standard mixture designs, as the simplex lattice, are around 25% efficient for estimation purposes compared with the designs obtained in this work when deviances from the considered model occur during the experiments. Once an optimal-robust design was selected (based on the level of certainty about model adequacy), we computed the optimal mixture that best reproduces the combustion property to be imitated. Optimal mixtures obtained when the considered model is inadequate agree with the results achieved in empirical studies, which validates the methodology proposed in this work.
Logistic regression models for binary response problems are present in a wide variety of industrial, biological, social and medical experiments; therefore, optimum designs are a valuable tool for experimenters, leading to estimators of parameters with minimum variance. Our interest in this contribution is to provide explicit formulae for the D-optimal designs as a function of the unknown parameters for the logistic model ( )
Many fields including clinical and manufacturing areas usually perform life-testing experiments and accelerated failure time models (AFT) play an essential role in these investigations. In these models the covariate causes an accelerant effect on the course of the event through the term named acceleration factor (AF). Despite the influence of this factor on the model, recent studies state that the form of AF is weakly or partially known in most real applications. In these cases, the classical optimal design theory may produce low efficient designs since they are highly model dependent. This work explores planning and techniques that can provide the best robust designs for AFT models with type I censoring when the form of the AF is misspecified, which is an issue little explored in the literature. Main idea is focused on considering the AF to vary over a neighbourhood of perturbation functions and assuming the mean square error matrix as the basis for measuring the design quality. A key result of this research was obtaining the asymptotic MSE matrix for type I censoring under the assumption of known variance regardless the selected failure time distribution. In order to illustrate the applicability of previous result to a study case, analytical characterizations and numerical approaches were developed to construct optimal robust designs under different contaminating scenarios for a failure time following a log-logistic distribution.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.