The paper is devoted to determining the duration of on-line expensive and unique tests in the presence of parametric uncertainty of the test object model. It is demonstrated that the error in determining this time leads either to an identification error of the object, or to significant resource costs. The relevance of the task is confirmed by cited plural references. An asymptotic critical value is found for the interval criterion what establishes some restrictions in determining the test duration. It is shown that under any accuracy of the critical value, the use of the interval criterion outside the specified parameter range leads to significant dynamic errors during testing which are unacceptable. The paper novelty lies in determining the border between the normal functioning of the interval criterion for online measurement of the transition process duration during testing and the case when this criterion gives a false-positive result. Therefore, the consumer of measurement information cannot be misled; hence, risks of unjustified losses are minimal. The found asymptotic value of the interval criterion can serve as the informational basis for the different criteria, e.g., robust criteria.