Acceptance testing procedure equivalence

Abstract

This article addresses the issues of comparing different acceptance testing systems in an industrial setting, specifically in the dairy industry. The issues were two-fold: how to demonstrate that two different product testing systems were equivalent; and how to ensure that testing done by a customer or consumer on delivery of the product does not reject product deemed acceptable by the producer's testing system. Our comparison of sampling systems was focused around Operating Characteristic curves. Our results suggest that previous approaches are sound when data are normally distributed, although some refinement is possible. When data are not distributed normally, especially with multi-parameter distributions, the usual one dimensional Operating Characteristic curve method fails. In such cases, test methods can be compared by comparing acceptance surfaces in three dimensional plots. To address discrepancies between producer and consumer testing systems, especially if these arise because of different levels of variability between the two systems, an approach involving confidence intervals has the most appeal. References

• L. J. Bain and M. Engelhardt. Introduction to Probability and Mathematical Statistics. Duxbury Press, 2000.
• N. N. Cencov. Statistical Decision Rules and Optimal Inference. American Mathematical Society, 2000.
• J. Cohen. A coefficient of agreement for nominal scales. Educational and Psychological Measurement. 20, 1960, 37--46.
• D. R. Cox and D. V. Hinkley. Theoretical Statistics. Chapman and Hall/CRC, 1979.
• P. Grzegorzewski. Acceptance sampling plans by attributes with fuzzy risks and quality levels. In: P-Th. Wilrich and H. J. Lenz, editors, Frontiers in statistical quality control, Vol. 6, pages 36--46. Physica-Verlag, 2001.
• K. Gwet. Handbook of Inter-Rater Reliability. Advanced Analytics, LLC., 2010.
• A. Hald. Statistical theory of sample inspection by attributes. Academic, 1981.
• {ISO 8196-1:2009} Milk---Definition and evaluation of the overall accuracy of alternative methods of milk analysis.
• {ISO 8196-2:2000} Milk---Definition and evaluation of the overall accuracy of indirect methods of milk analysis.
• N. A. Nechval, K. N. Nechval, E. K. Vasermanis. Statistical decision equivalence principle and its applications. Proceedings of International Conference RelStat04, 2004, 81--89.
• S. K. Niazi. Handbook of Bioequivalence Testing. Informa Healthcare, 2007.
• NIST/SEMATECH e-Handbook of Statistical Methods. http://www.itl.nist.gov/div898/handbook/pmc/section2/pmc21.htm
• H. D. Patterson and R. Thompson. Recovery of inter-block information when block sizes are unequal. Biometrika, 58 (3), 1971, 545--554. http://www.ams.org/mathscinet-getitem?mr=0319325
• S. Wellek. Testing Statistical Hypotheses of Equivalence. Chapman and Hall/CRC, 2002.
• P.-Th. Wilrich. Single sampling plans for the inspection by variables in the presence of measurement error. Allgermeines Statistisches Archiv, 84, 2000, 239--250.
• P.-Th. Wilrich. Statistical concepts of capability of detection. Appl. Stochastic Models Bus. Ind. 18, 2002, 339--346. http://www.ams.org/mathscinet-getitem?mr=1932646