Construction of Two-Parameter Procedures for Measuring Control of Batches of Parts with Size Distribution According to the Rayleigh Law

• Published in: Measurement techniques 2022-12, Vol.65 (9), p.642-651
• Main Authors: Grigoriev, S. N., Emelyanov, P. N., Masterenko, D. A., Ped’, S. E.
• Format: Article
• Language: English
• Subjects: Analytical Chemistry; Characterization and Evaluation of Materials; Distribution (Probability theory); Distribution functions; Laws, regulations and rules; Measurement Science and Instrumentation; Parameters; Physical Chemistry; Physics; Physics and Astronomy; Production methods; Quality control; Quality management; Rayleigh distribution; Size distribution; Statistical methods
• ISSN: 0543-1972; 1573-8906
• DOI: 10.1007/s11018-023-02134-8

We consider v arious methods of monitoring technological processes in modern machine-building production, including statistical methods of product quality management. The problem of constructing measurement control procedures for two parameters in those cases where the deviation of the quality index from the nominal value is described by a generalization of the Rayleigh distribution with two parameters is posed and solved. The distributions of control statistics are investigated. Numerical procedures are described that make it possible to calculate the distribution functions of statistics with sufficient accuracy for practical purposes. The operational characteristics of a control plan using statistics that estimate two distribution parameters and a plan for a one-parameter distribution model are compared. It is shown that close values of consumer and producer risks in comparable situations with two-parameter control are provided with a slight increase in the sample size compared to the one-parameter case. The results obtained will be useful in the organization of acceptance control procedures for parts with external and internal cylindrical surfaces.