Partially replicated two-level fractional factorial designs via semifoldover

Most fractional factorial designs have no replicated points and thus do not provide a reliable estimate for experimental error. The objective of this paper is to study the issue of partially replicated two-level fractional factorial (FF) designs, thereby allowing for the unbiased estimation of the experimental error while maintaining the orthogonality of the main effects. Through the tool of indicator function and the idea of semifoldover, we propose two simple and effective techniques to produce designs with partially replicated points in general two-level FF designs, whether they are regular or not. The related properties of constructed partially replicated designs are investigated. Our results indicate that partially replicated FF are competitive in practice.     

Non-orthogonal designs for measuring dispersion effects in sequential factor screening experiments using search linear models

“Dispersion” effects are considered in addition to “Location” effects of factors in the inferential procedure of sequential factor screening experiments with m factors each at two levels under search linear models. Search designs in measuring "Dispersion" and "Location" effects of factors are presented for both stage one and stage two of factor screening experiments with 4 ≤ m ≤ 10.     

Some inequalities in incomplete beta functions by using statistical techniques

In this paper an inequality concerning incomplete beta functions is stated and proved. From this inequality several other inequalities are derived. The main inequality can be given by using the properties of incomplete beta functions but an interesting derivation by using statistical techniques is given.     

Algorithmic construction of optimal block designs for two-colour cDNA microarray experiments using the linear mixed effects model

ABSTRACT

In this study, methods for efficient construction of A-, MV-, D- and E-optimal or near-optimal block designs for two-colour cDNA microarray experiments with array as the block effect are considered. Two algorithms, namely the array exchange and treatment exchange algorithms together with the complete enumeration technique are introduced. For large numbers of arrays or treatments or both, the complete enumeration method is highly computer intensive. The treatment exchange algorithm computes the optimal or near-optimal designs faster than the array exchange algorithm. The two methods however produce optimal or near-optimal designs with the same efficiency under the four optimality criteria.