The correct behavior of control and protection schemes is basically determined by the availability of accurate information on the system status. For economical reasons the distribution networks are just partially monitored networks. The few real measurements and all the a priori data provide information for distribution system state estimation (DSSE) techniques. An incorrect evaluation of the accuracy of the DSSE results creates decision risks in network management. For this reason, it is fundamental to take into account all the possible uncertainty sources. Furthermore, possible decays of the metrological characteristics of the measurement system elements have to be considered. Such eventualities may significantly affect the trustworthiness of the results. In this connection, this paper focuses on the robustness of the DSSE results. The paper proposes an optimization algorithm suitable to choose the optimal number and position of the measurement devices so that the estimator is robust with respect to possible malfunctions in measurement system components. The results obtained on a small portion of an Italian distribution network are presented and discussed.