Thus, the experiment features a split double factorial with additional treatment in the plot (3x3+1) x 4, under 3 replications.

Let a triple factorial experiment conducted in CRD with factors [alpha], [beta] and [gamma] considered in a, b and c levels, respectively, replicated J times.

As a first result of this research, it was sketched the layout of the randomization of the experiment (Figure 1) which has a split double factorial in CRD with an additional factor.

CONSTRUCTION OF px3x2 ASYMMETRICAL FACTORIAL EXPERIMENTS BY SARDANA AND DAS:

Following steps are used in the construction of the asymmetrical factorial experiments of type px3x2.

Here our aim is to construct principle block for the asymmetrical factorial experiments of the type px3x2 in 3x2 i.e.

Having removed the 1!, 2 is now a factor is all remaining factorials, and is the final factor in 2!, hence

The basic pattern created in this paper also allows for the rapid calculation of other Smarandache-like functions based on the sum of factorials function.

Or we can define the sum of factorials squared function as

This full two-level factorial would reveal 31 effects: five main effects, 10 two-factor interactions, 10 three-factor interactions, five four-factor interactions, and the one five-factor interaction.

Notice that the first four factor columns form a full factorial with 16 runs.