Balanced prime basis factorial fixed effects model with random number of observations

Factorial designs are in general more efficient for experiments that involve the study of the effects of two or more factors. In this paper we consider a $$ factorial model with U factors, each one having a p prime number of levels. We consider a balanced (r replicates per treatment) prime factorial with fixed effects. Our goal is to extend these models to the case where it is not possible to known in advance the number of treatments replicates, r. In these situations is more appropriate to consider r as a realization of a random variable R, which will be assumed to be geometrically distributed. The proposed approach is illustrated through an application considering simulated data.