In the individual risk processes of an insurance company with dependent claim sizes, determination of the ruin probability and time to ruin are very important. Exact computing of theses probabilities, because of it's complex structure, is not easy. In this paper, Monte Carlo simulation method is used to obtain the ruin probabilities estimates, times to ruin and confidence interval for the ruin probability estimates of the mentioned process for different dependence level of claims. In this simulation the multivariate Frank copula function and Marshall and Olkin's algorithm are provided to generate the dependent claims. Then it has shown that with increasing the dependence level of claim sizes the ruin probability of the risk process increases, while its time to ruin decreases