Non-Orthogonal Designs of Even Resolution

Webb, Steve R.

doi:10.1080/00401706.1968.10490561

Cited by 43 publications

(12 citation statements)

References 6 publications

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“…It is known (Webb, 1968;Margolin, 1969b) that T* must contain at least 2m runs, so that IT* I~2m, the bound being always attainable. Thus a direct product design T must have N~6m, so that N is rather large.…”

Section: Constructionmentioning

confidence: 99%

Resolution Iv Designs of the 2M × 3 Series

Anderson

Srivastava

1972

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary It is shown that a resolution IV 2m × 3 factorial design without blocks permits the estimation of not only the main effects A1, …, Am, B and B2 (which are assumed estimable by definition) but also of (i) the interactions Ai B, and Ai B2 (i = 1, …, m), and (ii) at least one linear combination of the general mean μ and the interactions Ai Ai (i < j; i, j = 1, …, m). Some methods of construction of 2m × 3 designs of resolution IV are discussed and “good” designs of this series with N = 4N* are presented for each m in the range 3 ≤ m ≤ 15, and N ≤ 80. These designs may be conducted in blocks of size 4 or any multiple of 4.

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Section: Constructionmentioning

confidence: 99%

Resolution Iv Designs of the 2M × 3 Series

Anderson

Srivastava

1972

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Fürbringer and Roulet (1995) give a simulation application with k = 24 and p = 16. A different subclass are the non-orthogonal designs derived by Webb (1968). These designs are specified only for k is 3, 5, 6 or 7 with n equal to 2k,.…”

Section: Main Effects Against Two-factor Interactions: Resolution-4 Dmentioning

confidence: 99%

Experimental Design for Sensitivity Analysis, Optimization, and Validation of Simulation Models

Kleijnen

1998

Handbook of Simulation

155

106

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This chapter gives a survey on the use of statistical designs for what-if analysis in simulation, including sensitivity analysis, optimization, and validation/verification. Sensitivity analysis is divided into two phases. The first phase is a pilot stage, which consists of screening or searching for the important factors among (say) hundreds of potentially important factors. A novel screening technique is presented, namely sequential bifurcation. The second phase uses regression analysis to approximate the input/output transformation that is implied by the simulation model; the resulting regression model is also known as a metamodel or a response surface. Regression analysis gives better results when the simulation experiment is well designed, using either classical statistical designs (such as fractional factorials) or optimal designs (such as pioneered by Fedorov, Kiefer, and Wolfowitz). To optimize the simulated system, the analysts may apply Response Surface Methodology (RSM); RSM combines regression analysis, statistical designs, and steepest-ascent hill-climbing. To validate a simulation model, again regression analysis and statistical designs may be applied. Several numerical examples and case-studies illustrate how statistical techniques can reduce the ad hoc character of simulation; that is, these statistical techniques can make simulation studies give more general results, in less time. Appendix 1 summarizes confidence intervals for expected values, proportions, and quantiles, in terminating and steady-state simulations. Appendix 2 gives details on four variance reduction techniques, namely common pseudorandom numbers, antithetic numbers, control variates or regression sampling, and importance sampling. Appendix 3 describes jackknifing, which may give robust confidence intervals.

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“…Finally, Webb's (1968) conjecture that there exist no resolution IV 2 n designs with 2n runs except those constructed by the fold-over technique is proved to be valid.…”

mentioning

confidence: 98%

“…It would seem that a design of resolution III would be a minimal goal for our statistician, that is, hopefully k 1+~(i -1)Ii~N. i=2 One would then like to know, without the effort of trial and error in design construction, whether one can hope to achieve resolution IV for the specified set of factors and N. Previous work by Webb (1968) and Margolin (1969a) determined lower bounds for N for designs of resolution IV for the 2 n and 2 n 3 m , m > 0, series. The bounds are 2n and 3(n +2m -1) respectively.…”

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confidence: 99%

Resolution Iv Fractional Factorial Designs

Margolin

1969

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Fractional factorial designs of resolution IV permit estimation of all the main effects with no aliasing by two-factor interactions. This paper produces a lower bound for the number of observations required for a general fractional factorial design to be of resolution IV. This lower bound agrees with a lower bound obtained by Rao for orthogonal arrays of strength 3. In addition, it is proved that this lower bound is attainable for the t . 2 n factorial design series for t even and n == 3 (mod 4) in plans which permit orthogonal estimation of the main effects. Finally, Webb's conjecture that there exist no resolution IV 2 n factorial designs with 2n runs except for those constructed by the fold-over technique is proved to be valid.

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Non-Orthogonal Designs of Even Resolution

Cited by 43 publications

References 6 publications

Resolution Iv Designs of the 2M × 3 Series

Resolution Iv Designs of the 2M × 3 Series

Experimental Design for Sensitivity Analysis, Optimization, and Validation of Simulation Models

Resolution Iv Fractional Factorial Designs

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