• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.595-610
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• 2021

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.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.557-578
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• 2007

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).

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 춘계 학술발표회 논문집
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• pp.95-100
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• 2005

In this paper a class of multifactor designs for estimating the slope of second order response surface regression models with correlated errors is considered. General conditions for second order slope rotatability over all directions and also with respect to the maximum directional variance in case of k=2 have been derived assuming errors have a general correlated error structure. And we consider the measures for evaluating slope rotatability with correlated errors similar to in case of uncorrelated error structures.

• 한국축산식품학회지
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• 제43권2호
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• pp.374-381
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• 2023

In a previous study, 'response surface methodology (RSM) using a fullest balanced model' was proposed to improve the optimization of food processing when a standard second-order model has a significant lack of fit. However, that methodology can be used when each factor of the experimental design has five levels. In response surface experiments for optimization, not only five-level designs, but also three-level designs are used. Therefore, the present study aimed to improve the optimization of food processing when the experimental factors have three levels through a new approach to RSM. This approach employs three-step modeling based on a second-order model, a balanced higher-order model, and a balanced highest-order model. The dataset from the experimental data in a three-level, two-factor central composite design in a previous research was used to illustrate three-step modeling and the subsequent optimization. The proposed approach to RSM predicted improved results of optimization, which are different from the predicted optimization results in the previous research.

• 품질경영학회지
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• 제40권4호
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• pp.431-440
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• 2012

Purpose: In this paper we propose modified Notz designs which are useful to experimenters who want to adopt the sequential experimentation strategy and to estimate second-order regression model with as few experimental points as possible. Methods: We first present the design matrices and design points in two or three dimensional spaces for such small sized second-order designs as small composite, hybrid, and Notz designs. Modified Notz designs are proposed and compared with some response surface designs in terms of the total number of experimental points, the estimation capability criteria such as D- and A-optimality. Results: When sequential experimentation is necessary, the modified Notz designs are recommendable. Conclusion: The result of this paper will be beneficial to experimenters who need to do experiments more efficiently, especially for those who want to reduce the time of experimentation as much as possible to develop cutting-edge products.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.253-264
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• 2005

Hader and Park(l978) suggested the concept of slope-rotatability in axial directions for second order response surface designs. In this paper, the moment conditions for slope-rotatability in axial directions are shown and the measures for evaluating slope-rotatability in axial directions are proposed.

• 품질경영학회지
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• 제23권3호
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• pp.102-112
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• 1995

Estimation of each of mean response, difference between mean responses and derivatives of the response function is a possible objective of a response surface design. These objectives are to be achieved simultaneously when an experiment is designed to improve mean response. For the situations where departure from the assumed model is suspected, first and second order designs for improving mean response are obtained by combining minimum bias designs for the individual design objectives. D- and A-optimalities are used for selecting specific second order designs. The results are applied to central composite designs.

• Journal of the Korean Statistical Society
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• 제34권2호
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• pp.153-160
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• 2005

In this paper, modified second order slope rotatable designs are introduced and modified slope rotatable central composite designs (SRCCD) are constructed for $2 {\le} v {\le} 17$ (v: the number of factors). Further, it can be shown for certain values of 'v', the modified SRCCD can be viewed as SRCCD constructed as with the technique of augmentation of second order rotatable design (SORD) using central composite design to SRCCD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.

• Journal of the Korean Statistical Society
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• 제31권2호
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• pp.153-161
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• 2002

A new method of construction of second order slope rotatable designs (SOSRD) using symmetrical unequal block arrangements (SUBA) with two unequal block sizes is suggested. The proposed method may sometimes lead to designs with less number of design points than those available in the literature. Further, bounds for the parameters of SOSRD are also obtained.

• Journal of the Korean Statistical Society
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• 제35권2호
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• pp.179-192
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• 2006

In this paper, a new method of modified second order slope rotatable designs (SOSRD) using balanced incomplete block designs (BIBD) for $4{\le}v{\le}16$ is presented. In this method the number of design points required is in some cases less than the number required in Victorbabu (2305) modified slope rotatable central composite designs. Further, a new method of construction of three level modified SOSRD using BIBD is presented. The modified SOSRD can be viewed as SOSRD constructed with the technique of augmentation of second order rotatable design (SORD) using BIBD to SOSRD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.