• Communications for Statistical Applications and Methods
• /
• 제7권3호
• /
• pp.741-757
• /
• 2000

In may experimental situations, whenever a block design is used, the block effect is usually considered to be fixed. There are, however, experimental situations in which it should be treated as random. The choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response and on the size of he prediction variance even if the experimental runs re the same. Therefore, care should be exercised in the selection of blocks. In this paper, in the presence of a random block effect, we propose a graphical method or evaluating the effect of blocking in response surface designs using cuboidal regions. This graphical method can be used to investigate how the blocking has influence on the prediction variance throughout all experimental regions of interest when this region is cuboidal, and compare the block effects in the cases of the orthogonal and non-orthogonal block designs, respectively.

• Communications for Statistical Applications and Methods
• /
• 제5권3호
• /
• pp.607-621
• /
• 1998

When fitting a response surface model, the least squares estimates of the model's parameters and the prediction variance will generally depend on how the response surface design is blocked. That is, the choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response and on the size of the prediction variance even if the experimental runs are the same. Therefore, care should be exercised in the selection of blocks. In this paper, we prognose a graphical method for evaluating the effect of blocking in a response surface designs using cuboidal regions in the presence of a fixed block effect. This graphical method can be used to investigate how the blocking has influence on the prediction variance throughout the entire experimental region of interest when this region is cuboidal, and compare the block effect in the cases of the orthogonal and non-orthogonalblockdesigns, resfectively.

• 산업공학
• /
• 제23권2호
• /
• pp.118-125
• /
• 2010

The determination of a regression model is important in using statistical designs of experiments. Generally, the exact regression model is not known, and experimenters suppose that a certain model form will be fit. Then an experimental design suitable for that predetermined model form is selected and the experiment is conducted. However, the initially chosen regression model may not be correct, and this can result in undesirable statistical properties. We develop model-robust experimental designs that have stable prediction variance for a family of candidate regression models over a cuboidal region by using genetic algorithms and the desirability function method. We then compare the stability of prediction variance of model-robust experimental designs with those of the 3-level face centered cube. These model-robust experimental designs have moderately high G-efficiencies for all candidate models that the experimenter may potentially wish to fit, and outperform the cuboidal design for the second-order model. The G-efficiencies are provided for the model-robust experimental designs and the face centered cube.

• Communications for Statistical Applications and Methods
• /
• 제9권3호
• /
• pp.799-808
• /
• 2002

This paper aims at selecting the multi-response design with γ responses minimizing the bias error caused by fitting inadequate models to responses, where the first order models are fitted to Ρ responses fearing the quadratic bias, while to other γ- Ρ responses, the quadratic models are fitted fearing the cubic biases in the cuboidal region of interest. Under the assumption of symmetric design, by minimizing the criterion which represents the amount of error caused by fitting inadequate models, the optimum design was found to be the one having the design moments of second order and the fourth order as 1/3 and l/5, respectively. Examples of the design meeting the required conditions are given for illustration.

• 응용통계연구
• /
• 제25권1호
• /
• pp.215-223
• /
• 2012

반응표면 방법론은 어떤 공정을 개선하거나 최적화하는데 이용되는 아주 유용한 통계적방법이다. 이러한 최적조건을 추정하기 위하여 최적조건이 있으리라 예상되는 실험구역을 탐색하여 실험을 실시한다. 그런데 이 실험구역은 실험의 환경의 제약 그리고 연구자의 선택 등으로 그 모습이 다양하게 달라질 수 있다. 반응표면 설계는 실험구역의 모양에 따라 보통 둥그런 모양의 "구형설계"와 육면체 모양의 "입방형설계"로 구분한다. 구형설계는 회전성을 만족하거나 회전성에 상당히 근접하는 "유사회전성"을 갖는 특징이 있다. 반응표면 설계에서 가장 많이 사용되는 중심합성설계는 실험구역이 구형인 5수준 실험설계이다. 이 때, 축점의 ${\alpha}$값을 ${\alpha}=\sqrt{k}$ 대신 ${\alpha}=1$로 조정하면 5-수준이 아닌 3-수준 입방형 중심합성설계를 얻을 수 있다. 그러나 입방형 중심합성설계는 실험구역이 구형이 아니므로 회전성을 만족하지 못하는 문제가 있다. 이러한 이유로, 변수들의 수준 수를 3으로 제한하면서 실험구역은 구형인 실험설계가 필요할 때가 많다. 이에 대한 대표적 실험설계가 바로 박스-벤켄 실험설계이다. 이 실험설계는 구형의 실험구역으로 회전성을 만족하나 실험구역의 크기가 변수의 개수가 증가해도 제자리 수준으로 좁은 특징이 있다. 현실적으로 실험구역의 가상 자리 부분에 대한 예측에 관심이 있을 경우 변수의 개수가 많아지면 이에 비례하여 실험구역이 커지는 실험설계가 바람직하다. 본 논문은 3-수준 입방형설계에 비하여 실험구역이 유달리 좁은 박스-벤켄 실험설계를 보완하여 구형설계를 만족하면서도 다른 한편으로는 변수 수에 따라 실험반경이 커지는 3-수준 구형 반응표면 설계를 소개하고자 한다. 이 방법을 기존의 실험설계들과 비교한 결과 변수수가 비교적 작을 경우 실험횟수 등을 고려하여 응용가치가 있음을 확인하였다.

• 품질경영학회지
• /
• 제27권1호
• /
• pp.59-79
• /
• 1999

The fitting of a response surface model and the subsequent exploration of the response surface are usually based on the assumption that the experimental runs are carried out under homogeneous conditions. This, however, may be quite often difficult to achieve in many experiments. To control such an extraneous source of variation, the response surface design should be arranged in several blocks within which homogeneity of conditions can be maintained. In this case, when fitting a response surface model, the least squares estimates of the model's parameters and the prediction variance will generally depend on how the response surface design is blocked. That is, the choice of a blocking arrangement for a response surface design can have a considerable effect on estimating the mean response and on the size of the prediction variance. In this paper, we propose a measure for evaluating the effect of blocking of response surface designs using cuboidal regions.

• 품질경영학회지
• /
• 제29권1호
• /
• pp.24-40
• /
• 2001

Response surface designs can be classified, according to the shape of the experimental region, into spherical designs and cuboidal designs. Among the central composite design(CCD)s and the Box-Behnken design(BBD)s that are popular in practice, when the number of factors is k, spherical designs are tile CCDs with the axial value being $\sqrt{\textit{k}}$ and the BBDs, and cuboidal designs are the CCDs with the axial value being 1. With the CCDs having $\sqrt{\textit{k}}$ as the axial value, the radius of the experimental region varies with number of factors, but these designs are the 5-level designs. With the BBDs that are 3-level designs, the radius of the experimental region does not vary with the number of factors. In this article, we propose tile 3-level spherical designs which are constructed so that tile radius of the experimental region varies with the number of factors.

• Communications for Statistical Applications and Methods
• /
• 제16권1호
• /
• pp.195-208
• /
• 2009

A conventional single design optimality criterion has been used to select an efficient experimental design. But, since an experimental design is constructed with respect to an optimality criterion pre specified by investigators, an experimental design obtained from one optimality criterion which is superior to other designs may perform poorly when the design is evaluated by another optimality criterion. In other words, none of these is entirely satisfactory and even there is no guarantee that a design which is constructed from using a certain design optimality criterion is also optimal to the other design optimality criteria. Thus, it is necessary to develop certain special types of experimental designs that satisfy multiple design optimality criteria simultaneously because these multi-optimal designs (MODs) reflect the needs of the experimenters more adequately. In this article, we present a heuristic approach to construct second-order response surface designs which are more flexible and potentially very useful than the designs generated from a single design optimality criterion in many real experimental situations when several competing design optimality criteria are of interest. In this paper, over cuboidal design region for $3\;{\leq}\;k\;{\leq}\;5$ variables, we construct multi-optimal designs (MODs) that might moderately satisfy two famous alphabetic design optimality criteria, G- and IV-optimality criteria using a GA which considers a certain amount of randomness. The minimum, average and maximum scaled prediction variances for the generated response surface designs are provided. Based on the average and maximum scaled prediction variances for k = 3, 4 and 5 design variables, the MODs from a genetic algorithm (GA) have better statistical property than does the theoretically optimal designs and the MODs are more flexible and useful than single-criterion optimal designs.

• 한국CDE학회논문집
• /
• 제20권4호
• /
• pp.357-366
• /
• 2015

We review recent research results on coupled line cameras (CLC) as a new geometric tool to reconstruct a scene quadrilateral from image quadrilaterals. Coupled line cameras were first developed as a camera calibration tool based on geometric insight on the perspective projection of a scene rectangle to an image plane. Since CLC comprehensively describes the relevant projective structure in a single image with a set of simple algebraic equations, it is also useful as a geometric reconstruction tool, which is an important topic in 3D computer vision. In this paper we first introduce fundamentals of CLC with reals examples. Then, we cover the related works to optimize the initial solution, to extend for the general quadrilaterals, and to apply for cuboidal reconstruction.