The numerical approach of data collaboration is extended to address the mutual consistency of experimental observations. The analysis rests on the concept of a dataset, which represents an organization of pertinent experimental observations, their uncertainties, and mechanistic knowledge of the subject of interest. The numerical foundation of data collaboration lies in constrained optimization, utilizing solution mapping tools and robust control algorithms. A rigorous measure of dataset consistency is developed, and Lagrange multipliers are used to identify factors that influence consistency. The new analysis is demonstrated on a real-world example, taken from the field of combustion. In performing the consistency test, the new procedure identifies two major outliers of the dataset, which were corrected upon re-examination of the raw experimental data. The results of the analysis suggest a sequential procedure with step-by-step identification of outliers and inspection of the causes. Altogether, the new numerical approach offers an important tool for assessing experimental observations and model building.