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A Measure of Robust Rotatability for Second Order Response Surface Designs
Rabindra Nath Das,박성현 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.4
In Response Surface Methodology (RSM), rotatability is a natural andhighly desirable property. For second order general correlated regressionmodel, the concept of robust rotatability was introduced by Das (1997). Inthis paper a new measure of robust rotatability for second order responsesurface designs with correlated errors is developed and illustrated with anexample. A comparison is made between the newly developed measure withthe previously suggested measure by Das (1999).
On efficient robust first order rotatable designs with autocorrelated error
Rabindra Nath Das,Sung Hyun Park 한국통계학회 2008 Journal of the Korean Statistical Society Vol.37 No.2
Generally, it is very difcult to derive optimal or at least efcient designs for linear models with correlated observations, and forsome correlation structure, an exactD-optimal design does not exist. In this paper we have developed the notion of aD-optimalrobust rst order design(D-ORFOD) for linear model with a general correlated error structure. We have shown thatD-optimalrobust rst order designs are always robust rst order rotatable designs (RFORDs)butthe converse is not always true. For a rstorder linear model with autocorrelated error, we have developed a set ofefcientRFORDs with efciency around ninety percentand the developed designs are very close toD-ORFODs. We have also developed a new method of analysis that is the estimationof regression parameters, correlation parameter and error variance, assuming the correlation parameter involved in the correlationstructure is unknown.
Log-Normal Versus Gamma Models for Analyzing Data from Quality-Improvement Experiments
Das, Rabindra Nath,Lee, Youngjo Taylor Francis 2008 Quality engineering Vol.20 No.2
<P> Recently, log-normal and gamma models are of interest in fitting data arising from quality-improvement experiments. It is known that the gamma model with the constant coefficient of variation and the log-normal model with constant variance often give similar analyzes. However, in the analysis of data from quality improvement experiments, neither the coefficient of variation nor the variance needs to be constant, so that the two models do not necessarily give similar results. A choice needs to be made between the gamma and the log-normal models.</P>
A MEASURE OF ROBUST ROTATABILITY FOR SECOND ORDER RESPONSE SURFACE DESIGNS
Das, Rabindra Nath,Park, Sung-Hyun The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.4
In Response Surface Methodology (RSM), rotatability is a natural and highly desirable property. For second order general correlated regression model, the concept of robust rotatability was introduced by Das (1997). In this paper a new measure of robust rotatability for second order response surface designs with correlated errors is developed and illustrated with an example. A comparison is made between the newly developed measure with the previously suggested measure by Das (1999).
Sanatan Das,Bhola Nath Barman,Rabindra Nath Jana 한국유변학회 2021 Korea-Australia rheology journal Vol.33 No.4
This article intends to conduct an analytical simulation for the electroosmosis modulated peristaltic transport of ionic hybrid nano-liquid with Casson model through a symmetric vertical microchannel occupying a homogeneous porous material in the existence of the dominant magnetic field, Hall, and ion-slip currents. The hybrid nano-liquid is acquired by the suspension of silver and silicon dioxide nanoparticles into pure water. The wall slip and convective heating impacts are imposed. The Casson fluid (CF) model is adopted to mimic the rheological behaviour accounting for hybrid nano-liquid. Darcy’s law is applied to evaluate the impact of a porous medium. The Poisson-Boltzmann equation is engaged to accommodate the electric double layer (EDL) in the microchannel. Assumptions of low Reynolds number (LRN), long wavelength (LWL), and Debye-Hückel linearization (DHL) are undertaken to simplify the normalized constitutive equations. Closed-form solutions for the linearized dimensionless resulting equations are achieved by ND-solve code in Mathematica. For a comprehensive physical investigation of the problem under simulation, several graphs are furnished to evaluate the role of emerging thermal and physical parameters in developing the flow patterns and thermal characteristics. Outcomes envisage that Hall, ion-slip, and electro-osmotic parameters have a marked impact on the velocity of the ionic liquid. A decrement in the EDL thickness corresponds to an augmentation in the axial velocity profile in the locality of the channel walls. An increment in radiation parameter results in a demotion in the temperature profile. The pressure gradient is elevated with higher Hall and ion-slip parameters, thermal Grashof number, and electro-osmotic parameter, whereas it is dropped due to higher estimates of Hartmann number. The trapping phenomena under the flow factors are also outlined in brief. The bolus formation is deeply affected by Hall, ion-slip, and electro-osmotic parameters. Outcomes achieved here are expected to shed light on the design and analysis of electroosmotic pumps, microchannel devices, water filtration and purification processes, DNA analyzers, nanoscale electro-fluid thruster designs in-space propulsion, and many more.
Robust second-order rotatable designs invariably applicable for some lifetime distributions
Kim, Jinseog,Das, Rabindra Nath,Singh, Poonam,Lee, Youngjo The Korean Statistical Society 2021 Communications for statistical applications and me Vol.28 No.6
Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.