TITLE:
Characterization of Six Categories of Systematic 2n－(n－k) Fractional Factorial Designs
AUTHORS:
Hisham Hilow
KEYWORDS:
Sequential Factorial Experimentation; Trend Resistant Run Orders; Generalized Fold-Over Scheme; Interactions-Main Effects Assignment; Cost of Factor Level Changes; Design Resolution
JOURNAL NAME:
Open Journal of Statistics,
Vol.4 No.1,
February
18,
2014
ABSTRACT: Six categories of systematic 2n－(n－k) designs derivable from the full 2k factorial experiment by the
interactions-main effects assignment are available for carrying out 2n－(n－k) factorial experiments
sequentially run after the other such that main effects are protected against the linear/quadratic time trend and/or such
that the number of factor level changes (i.e. cost) between the runs is
minimal. Three of these six categories are of
resolution at least III and three are of resolution at least IV. The three
categories of designs within each resolution are: 1) minimum cost 2n－(n－k) designs, 2) minimum
cost linear trend free 2n－(n－k) designs and 3) minimum
cost linear and quadratic trend free 2n－(n－k) designs. This paper characterizes these six categories and documents their differences with regard to
either time trend resistance of factor effects and/or the number of factor
level changes. The paper introduces the last category of systematic 2n－(n－k) designs (i.e. the sixth) for the purpose
of extending the design resolution from III into IV and also for raising the level of
protection of main effects from the linear time trend into the quadratic, where a catalog of minimum cost
linear and quadratic trend free 2n－(n－k) designs (of resolution at least IV) will be proposed. The paper provides for
each design in any of the
six categories: 1) the sequence of its runs in
minimum number of factor level changes 2) the defining relation or its 2n－(n－k) alias structure
and 3) the k independent generators
needed for sequencing the 2n－(n－k) runs by the generalized foldover scheme. A comparison among these six categories of designs reveals that when the polynomial degree of the time trend increases from linear into quadratic and/or when the design’s resolution
increases from III to IV, the number of factor level changes between the 2n－(n－k) runs
increases. Also as the number of factors (i.e. n) increases, the
design’s resolution decreases.