Fractional factorial plans represented by orthogonal arrays of
strength two are known to be optimal in a very strong sense under a
model that includes the mean and all the main effects, when all
interactions are assumed to be absent. When a fractional factorial
plan given by an orthogonal array of strength two is not saturated,
one might think of entertaining some two-factor interactions also in
the model. In such a situation, it is of interest to examine which of
the two-factor interactions can be estimated via a plan represented by
an orthogonal array, as also to study the overall efficiency of the
plan when some interactions are in the model alongwith the mean and
all main effects. In this paper, an attempt has been made to examine
these issues by considering some practically useful plans for
asymmetric (mixed level) factorials with small number of runs.