• Title/Summary/Keyword: Factorial designs

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$ fractional factorial designs of resolution V and taguchi method

  • 김상익
    • The Korean Journal of Applied Statistics
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    • v.5 no.1
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    • pp.19-28
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    • 1992
  • In this paper, minimal balanced $2^t$ fractional factorial designs which permit the estimation of main effects and 2-factor interactions are developed by using a partially balanced array. Such designs are characterized by a minimum number of runs and some balancedness property of the variance-covariance matrix of the estimates. In addition to describing the designs, optimality criteria are discussed and the trace-optimal designs are presented. The proposed designs are especially useful in Taguchi method, where we need to investigate up to 2-factor interactions of the control factors.

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RESIDUALS IN MINIMAL RESOLUTION IV DESIGNS

  • Liau, Pen-Hwang
    • Journal of the Korean Statistical Society
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    • v.32 no.3
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    • pp.235-244
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    • 2003
  • In unreplicated factorial or fractional factorial experiments, the presence of one or more outliers can seriously affect the analysis of variance. Using the normal plot of t residuals to identify outliers in factorial or fractional factorial is an easy method to find these dubious points. In some cases, the t residuals form the identical pairs. One can not tell from the plot which is doubtful. This phenomenon occurs for all minimal designs of resolution IV, which fits the model containing all main effects and some two-factor interactions, whether it is orthogonal or not. In these kinds of models, when we drop one point or two points (not foldover pair) from the fraction, the phenomenon of identical pairs of t residuals may still occur. In this paper, the theoretical background of the phenomenon and its sequences will be investigated in detail.

On ORTHOGONALITY AND BALANCING IN GENERALIZED CYCLIC FACTORIAL EXPERIMENTS

  • Lee, U-Sun
    • Journal of the Korean Statistical Society
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    • v.21 no.1
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    • pp.80-86
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    • 1992
  • The concept of Balanced Factorial Experiment (BFE) was introduced by Shah (1958). The conditions for BFE were set up by Kurkjian and Zelen (1963) and Kshirsagar (1966). Generalized Cyclic Factorial Experiment (GCFE), which is more wide class of designs than BFE, do not satisfy the condition of BFE. So all contrasts belonging to the same interaction are not estimated with equal variance. The main purpose of this paper is to show that GCFE have orthogonal factorial structure and the scheme of the size of variances for all normalized contrasts in GCFE is similar to the original intra-block association scheme.

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A Study on the Construction and Analysis of Fractional Designs by Using Arrays for Factorial Experiments (배열을 이용한 효과적인 일부실시법의 설계 및 분석방법에 관한 연구)

  • Kim, Sang-Ik
    • Journal of Korean Society for Quality Management
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    • v.40 no.1
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    • pp.15-24
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    • 2012
  • For the construction of fractional factorial designs, the various arrays can be widely used. In this paper we review the statistical properties of fractional designs constructed by two arrays such as orthogonal array and partially balanced array, and develop a quick and easy method for analyzing unreplicated saturated designs. The proposed method can be characterized that we control the error rate by experiment-wise way and exploit the multivariate Student $t$-distribution. Especially the proposed method can be used efficiently together with some exploratory analysis methods, such as half normal probability plot method.

Latin Square Type Partially Balanced Incomplete Block Designs

  • Paik, U.B.
    • Journal of the Korean Statistical Society
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    • v.8 no.2
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    • pp.125-130
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    • 1979
  • It is well known that $L_2(m)$ type PBIB designs have the Property A, so they are BNAS PBIB designs. However, $L_3(m)$ type PBIB designs are not of type of Property A but do have the factorial structure (Cotter, John, and Smith(1973)). In this paper, the properties of the $L_3(m)$ type PBIB designs are investigated. Extended Property A and fractional BNAS are defined and a solution formula for the treatment effects in the $L_32(m)$ type designs is obtained.

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Testing on the Existence of Interaction Effects in $3^t$ Resolution IV Factorial Experiments (Resolution IV $3^t$요인실험법에서 교호작용 효과의 존재에 대한 검정 방법 연구)

  • 김상익
    • Journal of Korean Society for Quality Management
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    • v.28 no.3
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    • pp.59-67
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    • 2000
  • In analysis of resolution IV fractional factorial experiments, the main effects only are analyzed, even though we can get some useful information on the confounded 2-factor interactions. In this paper, we introduce an exploiting method of the confounded structure of interactions, especially for the near minimal resolution IV 3$^{t}$ fractional factorial designs developed by Anderson and Thomas (1979). Moreover, in this paper the application way of the proposed method is also discussed by analyzing some simulated data.

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3n-p Fractional Factorial Design Excluded Some Debarred Combinations

  • Park, Byoung -Chul
    • Communications for Statistical Applications and Methods
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    • v.6 no.3
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    • pp.695-706
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    • 1999
  • When fractional factorial experiments contain some infeasible treatment combinations called debarred combinations we should construct experimental designs so that those debarred combinations are to be excluded by selecting defining contrasts appropriately. By applying Franklin(1995)'s procedure for selecting defining contrasts to Cheng and Li(1993)'s method this paper presents a method of selecting defining contrasts to construct orthogonal 3-level fractional factorial experiments which exclude some debarred combinations.

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Evaluation of the Degree of the Orthogonality of 2-level Resolution-V Designs Constructed by Balanced Arrays (균형배열에 의해 설계되는 2-수준 Resolution-V 실험법의 직교성 평가측도)

  • Kim, Sang-Ik
    • Communications for Statistical Applications and Methods
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    • v.15 no.2
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    • pp.235-244
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    • 2008
  • Balanced arrays which are generalized orthogonal arrays, introduced by Chakravarti (1956) can be used to construct the fractional factorial designs. Especially for 2-level factorials, balanced arrays with strength 4 are identical to the resolution-V fractional designs. In this paper criteria for evaluation the degree of the orthogonality of balanced arrays of 2-levels with strength 4 are developed and some application methods of the suggested criteria are discussed. As a result, in this paper, we introduce the constructing methods of near orthogonal saturated balanced resolution-V fractional 2-level factorial designs.

Efficient designs in conjoint analysis (컨조인트 분석에서 효율적인 문항 설계)

  • Chung, Jong Hee;Lim, Yong B.
    • Journal of Korean Society for Quality Management
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    • v.46 no.1
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    • pp.27-38
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    • 2018
  • Purpose: A large number of attributes with mixed levels are often considered in the conjoint analysis. In the cases where attributes have two or three levels, we research on the efficient design of survey questionnaire to estimate all the main effect and two factor interaction effects with a reasonable size of it. Methods: To reduce the number of questions in a questionnaire, the balanced incomplete block mixed level factorial design with minimum aberration was proposed by Lim and Chung (2016). Based on the number of questions and that of the respondents in that design, D-optimality criterion is adopted to find efficient designs where the main effect and two factor interaction effects are estimated. Results: The list of the number of questions and that of the respondents in efficient designs for survey questionnaire are recommended based on the D-efficiency of each design and the proposed selection criteria for the number of both questions and the respondents. By analyzing all the respondents survey data generated by the simulation study, we find the proper model. Conclusion: The proposed methods of designing survey questionnaires seem to perform well in the sense that how often the proper model is found in a simulation study where all the respondents survey data are generated by the simulation model.