The stochastic approach strategy to realize the robotized insertion of low-clearance, chamferless parts is studied in both the analytical and experimental contexts. The analytical approach is discussed in terms of stochastic differential equations that involve Gaussian white and colored noises processes to model a planar radom search. Special attention is devoted to characterize the time required for the insertion, a random variable whose first moment calculation (i.e., the mean) is dealt with. In the mathematical modelization context adopted, it is remarkable that the calculated mean mating time grows slowly (i.e., logarithmically), with the precision required to perform an insertion. The theoretical results are validataed on a robotized assembly system, also presented in this article. In this experimental system, the random movements are generated by pseudorandom binary sequences that, for the time scale considered to substain the logarithmic behavior obtained analytically. Hence, in addition to its simiplicity and flexibility, the random strategy approach appears to be very efficient when high mating precision is required.