On the Problem of Correctness and Stability of Composite Indices of Complex Systems

The construction of the integral characteristic of the system can be considered as a problem signal-to-noise discrimination. The signal in this case is the weight coefficients of the linear convolution of indicators. Composite index weights should reflect the structure of the system being evaluated. The successful application of principal component analysis in different systems structure description allows us to suggest that the method will also provide adequate results for social systems description. However, principal component analysis and factor analysis determine the structure of principal components and principal factors differently for different observations. The reason for this may be the presence of inevitable errors in the used data. As a method of avoiding this, a modification of the principal component analysis method is proposed, taking into account the presence of errors in the data used. A solution of the problem requires a detailed understanding of input data errors’ influence on the calculated model’s parameters. Therefore, the question of the problem correctness is essential. A clarification of the concept of computation a system’s quality changes composite index problem correctness is proposed. The consequence of the stability is on average a slight change (increment) of objects Rank for different measurements. This increment can be estimated a posteriori using a number of observations of the proposed variance criterion. The results of different composite index evaluation stability according to this criterion are presented. The integral indicators calculated using the author’s method have a good stability.