In this work, we present a new approach that considers orthogonal mixed models, under situations of stability, when the sample dimensions are not known in advance. In this case, sample sizes are considered realizations of independent random variables. We apply this methodology to the case where there is an upper bound for the sample dimensions, which may not be attained since failures may occur. Based on this, we assume that sample sizes are binomially distributed. We consider an application on the incidence of unemployed persons in the European Union to illustrate the proposed methodology. A simulation study is also conducted. The obtained results show the relevance of the proposed approach in avoiding false rejections.

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