The Optimality Criteria For Mixed Level Blocked Designs

Design of experiments has played a fundamental role in the statistical curriculum, practice and research ever since R.A. Fisher founded the modern discipline. It has been successfully applied in many fields of scientific investigation, such as agriculture, biology, chemistry and so on. One of the main tasks in experimental designs is to find good designs and analyze experimental data effectively, so that more effects and more possible models related to the effects in experiments can be estimated.Blocking designs are useful when the experimental units are not homogeneous. Systematic sources of variations in experiments can be effectively eliminated by properly grouping the runs into blocks. In some block designs, there may be some treatment factors which have different numbers of levels. Among fractional factorial block designs with factors at different numbers of levels, those with factors at two and four levels have the simplest mathematical structure. We refer to these designs as mixed level blocked designs, denoted by 2^n-m4¹ : 2^r, where n is the number of treatment factors, m is the number of independent treatment defining words and r is the number of independent block factors.This paper studies the optimality criteria for selecting the mixed level blocked designs. Chapter 1 introduces the existing optimality criteria for regular fractional factorial designs. Some notations are also given in this chapter.Chapter 2 classifies the words in the defining contrast subgroup of a 2^n-m4¹ : 2^r design into four types and based on them discusses the minimum aberration criterion for such designs.Chapter 3 extends the results of Chen and Hedayat (1998) for 2^m-p fractional factorial designs with resolution III or IV containing clear two-factor interactions to mixed level blocked designs.Baaed on the aliased effect-number pattern introduced by Zhang, Li, Zhao and Ai (2008), Chapter 4 introduces a new aliasing pattern (MBAP) for 2^n-m4¹ : 2^r designs. And based on MBAP, we give the general minimum lower-order confounding criterion for selccting good 2^n-m4¹ : 2^r designs.