Detection of homegeneous production batches of space electronic components based on separation of a mixture of spherical Gaussian distributions

Separating of homogeneous production batches of the electronic components used in the electronic units of the space systems is one of the most important problems which must be solved for improving quality of such units, their lifetime and reliability of the space systems. The quality of the electronic units is increased due to both more coordinated work of the EEE components which have identical parameters and increase of quality level and the accuracy of the destructive tests due to a new opportunity of guaranteed selecting electronic elements for these destructive tests from each production batch. In this paper, we solve the problem of precipitations of homogeneous batches of industrial products using Gaussian spherical mixture models and the EM algorithm with agglomerative greedy heuristic procedure. The EM (Expectation Maximization) algorithm is an efficient means of splitting a mix of various distributions. However, in case of multi-dimensional Gaussian distributions in a space of very large dimensionality, this algorithm is actually unworkable. In case of large volume of input data, this algorithm demands too complicated calculation for rebuilding its correlation matrices at each iteration. In case of small data volume, algorithm leads to detection of fake correlation in data. In our paper, the shipped lot of the electronic components for space industry is represented by a data set of non-destructive test results which is considered as a mixture of spherical Gaussian distributions (SGD). It is shown that this algorithm allows to efficiently determine homogeneous products batches which are rather large (thousands units) using of high-dimensional array of data (up to some hundreds dimensions). We show that, using this mathematical model in combination with new algorithms is capable to separate the homogeneous batches of the electronic components efficiently and reach more accuracy and stability of results in comparison with random multiple start of the algorithm.