Today, the quantification of the quality of a dynamic structural model remains a major issue, and the number of methods being devised in order to validate a model by comparison with an experimental reference keeps increasing. This paper presents a theory based on the concept of lack of knowledge, which consists in globalizing the various sources of errors on the substructure level by means of a scalar internal variable, called the LOK variable, defined over an interval whose upper and lower bounds follow probabilistic laws. These intervals, which are defined for each substructure, are then propagated rigorously throughout the mechanical model in order to determine intervals with stochastic bounds within which lies a given quantity of interest defined over the whole structure. Then, a general strategy for the reduction of the lack of knowledge is discussed and applied to academic examples as well as industrial cases.