Full Factorial Designs- to Full Factorial Designs with Two-Level Factors- Analysis of Full Factorial Experiments- Common Randomization Restrictions- More Full Factorial Design Examples- Fractional Factorial Designs- Fractional Factorial Designs: The Basics- Fractional Factorial Designs for Estimating Main Effects- Designs for Estimating Main Effects and Some Two-Factor Interactions- Resolution V Fractional Factorial Designs- Augmenting Fractional Factorial Designs- Fractional Factorial Designs with Randomization Restrictions- More Fractional Factorial Design Examples- Additional Topics- Response Surface Methods and Second-Order Designs- Special Topics Regarding the Design- Special Topics Regarding the Analysis- Appendices and Tables- Upper Percentiles of t Distributions, t- Upper Percentiles of F Distributions, F- Upper Percentiles for Lenth t Statistics, and- Computing Upper Percentiles for Maximum Studentized Residual- Orthogonal Blocking for Full 2 Factorial Designs- Column Labels of Generators for Regular Fractional Factorial Designs- Tables of Minimum Aberration Regular Fractional Factorial Designs- Minimum Aberration Blocking Schemes for Fractional Factorial Designs- Alias Matrix Derivation- Distinguishing Among Fractional Factorial Designs

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A Comprehensive Guide to Factorial Two-Level Experimentation

11 – Response Surface Methods

Randomizing the order of experimentation in a factorial design does not always achieve the desired effect of neutralizing the influence of unknown factors. In fact, with some very reasonable assumptions, an important proportion of random orders achieve the same degree of protection as that obtained by experimenting in the design matrix standard order. In addition, randomization can induce a large number of changes in factor levels and thus make experimentation expensive and difficult. De Leon et al. [Experimentation order in factorial designs with 8 or 16 runs, J. Appl. Stat. 32 (2005), pp. 297–313] proposed experimentation orders for designs with eight or 16 runs that combine an excellent level of protection against the influence of unknown factors, with the minimum number of changes in factor levels. This article presents a new methodology to obtain experimentation orders with the desired properties for designs with any number of runs.

Experimentation order with good properties for 2 k factorial designs

Under some very reasonable hypotheses, it becomes evident that randomizing the run order of a factorial experiment does not always neutralize the effect of undesirable factors. Yet, these factors do have an influence on the response, depending on the order in which the experiments are conducted. On the other hand, changing the factor levels is many times costly; therefore it is not reasonable to leave to chance the number of changes necessary. For this reason, run orders that offer the minimum number of factor level changes and at the same time minimize the possible influence of undesirable factors on the experimentation have been sought. Sequences which are known to produce the desired properties in designs with 8 and 16 experiments can be found in the literature. In this paper, we provide the best possible sequences for designs with 32 experiments, as well as sequences that offer excellent properties for designs with 64 and 128 experiments. The method used to find them is based on a mixture of algorithm...

Experimentation order in factorial designs: new findings

We need extra runs to design two-level factorial experiments in blocks of size two to estimate all the available effects, as is possible in experiments without blocking. The number of runs suggested is (n - p)2 n - p for 2 n - p fractional factorial experiments. In designing such an experiment, two issues need to be considered. First, the precision of estimates is usually different because different numbers of observations are used for estimation in the analysis of the resulting data. It is important to have more precise estimates of the effects with which we are most concerned. Second, the trade-off between run-size reduction and the possibly negligible effects is of significance, especially when the number of factors is large. To deal with these two issues, several assignment rules are suggested for designing good experiments.

Designing two-level fractional factorial experiments in blocks of size two

Often industrial experiments require good fractional factorial designs to examine the effects of many factors by using only a small number of experimental runs. These experimental runs can be determined by assigning factors to the columns of appropriate orthogonal arrays. When the experimental runs are carried out in a time order sequence, the responses can depend on the run order. Frequently level changes are more expensive for some factors in the study than for others. To avoid unwanted time effects and to reduce costs, information is needed about the columns of the orthogonal arrays to assign factors to appropriate columns. In this paper, we review some useful properties of columns in the arrays and present several rules for the assignments. These are helpful in designing experiments using orthogonal arrays. For illustration, several examples are given after these rules have been presented.

Designing Two‐Level Factorial Experiments Using Orthogonal Arrays When the Run Order is Important

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Designing Two‐Level Factorial Experiments Using Orthogonal Arrays When the Run Order is Important