Application of functionally dependent statistics for assessing product quality risks

In today's environment of fierce competition and high product quality requirements, risk assessment is becoming an integral part of the quality management system at enterprises. Particular attention should be paid to the risk of low-quality products, which directly affects the image, financial performance and overall competitiveness of the enterprise. Effective management of such risks requires the implementation of sound, reliable and quantifiable quality assessment methods. One of the most promising areas in this context is the use of a multi-criteria approach to assessing qualimetric objects. Since quality indicators may have different units of measurement, there is a need to bring them to a dimensionless form to create a single integrated assessment. This task requires use of mathematical dependencies that can provide a quantitative definition of quality with sufficient accuracy. However, the formation of such models is a complex process that requires a detailed analysis of the research object. In this regard, the paper proposes to investigate the possibility of using functionally dependent statistics, in particular the error function, to obtain dimensionless estimates of single dimensional quality indicators. This function is widely used in mathematical physics and statistics and has significant potential in the context of practical evaluation. The development of computing technology has greatly simplified its use in applied problems. In addition, based on the analysis of the density function of estimates, it is proposed to determine the probability of these estimates falling into critical intervals, which allows developing an effective methodology for assessing the risks of producing low-quality products.