## 3 Proposed Expanded Triad Model  
In the case of modernising an existing system, it seems more reasonable to expand the triad model (Figure 6a) into a set of related SF models (Figure 6b). Analysis of problem interactions within these models, with ranking by economic or medical-technical criteria, is likely to reveal the most urgent tasks for the improvement of the system under consideration. In triad models, as well as in TOP models, the field is not treated as an individual element (node) of the model, but is defined above the relationship between the substance elements. This is totally justified, since the 'field' is just a way of realising the relationship and its identification, as a particular element complicates the identification of the triad model as a set of three SFs. Subsequently, each of the identified elements of the SFs can be expanded into a new SF (Figure 6c), and so on. Such representation of the triad model allows for the aggregation of all types of SF models, and for the integration of the SF analysis apparatus [27; 28; 31] and standards for engineering problem solving [26; 28; 29; 38] into the 'Triad + Pruning' method. Simultaneously, the most correct and universal model for considering an improvement of the TS by transformation of the prototype is provided by a physical contradiction (PhC) model. It is obvious that aggregating PhC models into triads would allow for the integration  
Figure 6: Expanding the triad model into a set of SFs: (**a**) common triad model; (**b**) expanded triad model in SFA notification; (**c**) expanded triad model in SFA notification with triangles showing the SFs formed as a result of triad element expansion (the fully expanded SF is shown for \(S_{\text{nn}}\)) (developed by authors). of problem-solving tools inherent in bi-triad modelling and PhC modelling (contradiction elimination techniques) into a single algorithm. Analysis of the expanded triad model (Figure 6) shows that each of the real triad elements can be considered as a problem element, incompatible demands to which can be put forward by each pair of interactions in which the element participates. As can be seen from the analysis of these pairs of interactions, the enabling and active elements are actual or potential participants in three pairs of interactions (Figure 7):  
* The enabling element Sen can participate in the following pairs of interactions: 'useful functions \(\mathrm{F_{en1}}\) and \(\mathrm{F_{en2}}\);' useful function \(\mathrm{F_{en1}}\) and accompanying undesirable function \(\mathrm{F_{nd1}}\), which may be generated when attempting to improve \(\mathrm{F_{en1}}\); 'useful function \(\mathrm{F_{en2}}\) and accompanying undesirable function \(\mathrm{F_{nd2}}\), which may be generated when improving \(\mathrm{F_{en1}}\) via the enabling element.' * The active element Sa can participate in the following pairs of interactions: 'useful function \(\mathrm{F_{en2}}\) (for which the active element is a product) and useful function \(\mathrm{F_{a}}\) (for which the active element is a tool)', 'useful function \(\mathrm{F_{a}}\) and accompanying undesirable function \(\mathrm{F_{nd3}}\), which may be generated when attempting to improve \(\mathrm{F_{a}}\); 'useful function \(\mathrm{F_{en2}}\) and accompanying undesirable function \(\mathrm{F_{nd4}}\), which may be generated when attempting to improve \(\mathrm{F_{en2}}\) by changing the active element.' * The passive element \(\mathrm{S_{0}}\) can participate in the following pairs of interactions: 'useful functions \(\mathrm{F_{en1}}\) and \(\mathrm{F_{en2}}\) (when considering the passive element as the problem one)'; 'useful function \(\mathrm{F_{a}}\) and accompanying undesirable function \(\mathrm{F_{nd5}}\), which may originate when attempting to improve \(\mathrm{F_{a}}\) by affecting the passive element'; 'useful function \(\mathrm{F_{en1}}\) and accompanying undesirable function \(\mathrm{F_{nd6}}\), which may originate when attempting to improve \(\mathrm{F_{a}}\) by affecting the passive element'.