Half-factorial design

Optimization techniques may be classified as parametric statistical methods and nonparametric search methods. Parametric statistical methods, usually employed for optimization, are full factorial designs, half factorial designs, simplex designs, and Lagrangian multiple regression analysis [21]. Parametric methods are best suited for formula optimization in the early stages of product development. Constraint analysis, described previously, is used to simplify the testing protocol and the analysis of experimental results. 

A half factorial design involves reducing the experiments from 2k to 2k l or, in this case, from 32 to 16. 

Example of Half-Factorial Design of Table 3.14 via the D = ABC Alias... 

This notation 2 for the half factorial design for 4 variables at 2 levels indicates the fractional nature of this design. 

Table 15.8 lists a simple design of a two-third factorial design or one-third reduction. This is a more conservative choice than one-half factorial design. Similar to the above option, all time points are tested at Time Zero, end of study, and at submission time (12 months). All other time points are reduced to two-thirds of the configurations to be tested. 

An equally valid half factorial design would be obtained if the values in the last column of Table 20 were merely reversed. 

The digestion procedures for the determination of As in shrimp paste samples were optimised using a two level half factorial design. 

A factorial experiment, by definition, is one consisting of two or more variable factors, whose assigned values are usually called levels. The term appears to have been coined by Ronald Fisher in 1926. If all possible combinations are used, the experiment is referred to as full factorial. Very commonly, half of the possible combinations are used the experiment then designated as half-factoriaL Example 1 uses the half-factorial design. 

The expanded uncertainty of depth measurements was estimated to be 12% of the actual measuring result. Due to the time consuming measurement process, a half-factorial design of experiment (8 different process settings) [5] was performed. 

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