In this paper, the applications of the multivariate data analysis and optimization on vibration signals from compressors have been tested on the assembly line to identify nonconforming products. The multivariate analysis has wide applicability in the optimization of weather forecasting, agricultural experiments, or, as in this case study, in quality control. The techniques of discriminant analysis and linear program were used to solve the problem. The acceleration and velocity signals used in this work were measured in twenty-five rotating compressors, of which eleven were classified as good baseline compressors and fourteen with manufacturing defects by the specialists in the final acoustic test of the production line. The results obtained with the discriminant analysis separated the conforming and nonconforming groups with a significance level of 0.01, which validated the proposed methodology.
The problem of optimally controlling a Wiener process until it leaves an interval (a; b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = ��1, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.