According to statistics, the actual execution time of most jobs on a supercomputer cluster differs significantly from the time requested by the user. Investigation of distributions of supercomputer job execution times using statistical or machine learning methods allows optimizing the operation of a supercomputer cluster. We study the results of computational jobs processing in the supercomputer center of Peter the Great St. Petersburg Polytechnic University. We have developed a nonparametric approach for detection and statistical confirmation of weak stochastic orders based on categorical nonparametric framework of contrasts obtained from the Kaplan–Meier estimators obtained from independent groups of right-censored observations. To adjust the confidence level of the detected weak stochastic orders, we apply the Bonferroni correction to all the comparisons under consideration. We perform comparative statistical analysis of the distributions of required execution times to complete successfully the job in different groups of right-censored observations; detect and confirm available weak stochastic orders.