Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore, certain theoretical results concerning estimators of distribution function and quantiles under censoring are recalled and then utilized to prove consistency of solution based on estimates. Behavior of solutions for finite data sizes is studied with the aid of randomly generated example of a newsvendor problem.