Construction of Orthogonal Two-Level Designs of User-Specified Resolution Where N � 2 k

Iyer

1999

Biom. J.

Franklin and Bailey (1977) provided an algorithm for construction of fractional factorial designs for estimating a user specified set of factorial effects. Their algorithm is based on a backtrack procedure. This is computer intensive when the number of factors is not small. We propose a stochastic search method called SEF (sequential elimination of factors) algorithm. The SEF algorithm is a simple modification of the exhaustive approach of the Franklin‐Bailey algorithm since defining contrasts for the design of interest are chosen stochastically rather than choosing them in a systematic and exhaustive manner. Our experience shows the probability of success of obtaining a required design to be sufficiently large to make this a practical approach. The success probability may be expected to be rather small if the required design is close to a saturated design. We suggest the use of this stochastic alternative particularly when the number of factors is large. This can offer substantial savings in computing time relative to an exhaustive approach. Moreover, if the SEF algorithm fails to produce a design even after several attempts, one can always revert back to the Franklin‐Bailey approach.

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

A Stochastic Algorithm for Selecting of Defining Contrasts in Two-Level Experiments

Iyer

1999

Biom. J.

“…1, Liao et al (1996) claimed the simulation result that the 48-run orthogonal designs are plentiful in some median-resolution designs where each two-factor interaction is forced to include one or two of a limited number of specific factors. The theorems presented in the previous section strongly indicate this simulation result.…”

Section: Discussionmentioning

confidence: 99%

“…They presented three classes of two-level orthogonal designs which can be used to estimate the grand mean, all main effects and some specified two-factor interactions. Moreover, Liao et al (1996) developed an algorithm for constructing the median-resolution designs from PFDs. Interestingly, their simulation study showed that the 48-run designs are plentiful in which each two-factor interaction is forced to include one or two of a limited number of specific factors.…”

Section: Introductionmentioning

confidence: 99%

Two-level Orthogonal and Saturated Designs for Estimating Main Effects and Certain Important Interactions

Wang

Liu

Communications in Statistics - Theory and Methods

2013

In a two-level factorial experiment, we consider orthogonal designs that allow joint estimation of the grand mean, all main effects, and certain classes of twolevel interactions, assuming that the remaining effects are all negligible. Based on a judicious allocation of the factorial effects of interest to the columns of a Hadamard matrix, we propose some general classes of orthogonal and saturated designs which include some existing orthogonal main-effect plans of asymmetric factorials as special cases.

“…Then they applied the theorem to generate a series of orthogonal two-level designs. An algorithm for construction of orthogonal two-level PFDs for user-specified resolution can be seen in Liao, Iyer & Vecchia (1996).…”

Section: Introductionmentioning

confidence: 99%

Three Parallel Flats Designs for Two‐level Factorial Experiments

Chai

2001

Aus NZ J of Statistics

This paper investigates the properties of the class of three parallel flats designs for two-level factorial experiments. It shows that the designs constructed from this class of designs can have a very simple correlation structure. The correlation of any pair of best linear unbiased estimators of factorial effects is 0, 1 3 or 1 2 . Furthermore, the designs obtained also have high D-efficiency. Finally, a class of designs is generated with run-size N = 12 to illustrate the use of the theorem.