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Let $ X_{\lambda_1},\ldots,X_{\lambda_n}$ be a set of dependent andnon-negative random variables share a survival copula and let $Y_i=I_{p_i}X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ beindependent Bernoulli random variables independent of $X_{\lambda_i}$'s, with${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences, $Y_i$corresponds to the claim amount in a portfolio of risks. This paper considerscomparing the smallest claim amounts from two sets of interdependentportfolios, in the sense of usual and likelihood ratio orders, when thevariables in one set have the parameters $\lambda_1,\ldots,\lambda_n$ and$p_1,\ldots,p_n$ and the variables in the other set have the parameters$\lambda^{*}_1,\ldots,\lambda^{*}_n$ and $p^*_1,\ldots,p^*_n$. Also, we presentsome bounds for survival function of the smallest claim amount in a portfolio.To illustrate validity of the results, we serve some applicable models.

Ordering the smallest claim amounts from two sets of interdependent heterogeneous portfolios