Comparative Analysis of Mathematical Models of User Response Time in Knowledge Testing System

Abstract

The paper provides a description of the mathematical models of the user's response time to test tasks. The basis for the comparative analysis of the main mathematical models of the user's response time to the tasks was lognormal V. van der Linden's model. A description of the Discrete Response Time Model is given, when test tasks are performed by a group of testees. A discrete response time model and a gamma-distributed time model are proposed, since in the case of a log-normal distribution of response time to tasks for a group of testees, it is difficult to obtain a close to reliable estimate of the total time to complete the entire test. An algorithm is proposed for estimating the parameters of the gamma distribution for each task, assuming that the complexity of the tasks is determined either by an expert or using appropriate algorithms based on the Rash model.