Applications of Generalized Beta-distribution in Quality Control Models

Abstract

Mathematical models of the main stochastic characteristics of the continuous multi-stage control of mechatronic products were created, when the generalized beta-distribution is applied in order to describe the defectivity level. The principles of the stochastic distribution selection according to the empiric data and when applying Johnson and Pearson curve families. The two structures of control schemes are analyzed: one when the flows of discarded products are returned back to the manufacture process and other when the discarded products are repaired in the localized repair operations after each control stage. Mathematical models estimate the first and the second type errors of product classification in control and repair operations, and the efficiency of the control is evaluated according to the transformed densities of defectivity level, defectivity level averages and the magnitudes of the returning flows in the required points of control scheme. It is shown, that the control scheme with localized repair operations performs its functions more efficiently, but the practical implementation of such scheme costs more compare to the scheme in which all the returning flows are directed back to the manufacture. Ill. 5, bibl. 8 (in English; summaries in English, Russian and Lithuanian).