Abstract
The conformity of products is usually assessed on the basis of Gaussian distributions of the test results. For wire screen products, as an example, this assumption is only valid if the apertures are quite close to the nominal value and if the dispersion of the apertures is small compared to the tolerance band. In cases where these provisions are not given beta distributions are better distribution approaches. The application of a modified beta distribution leads to significantly lower producer’s and consumer’s risks allowing to expand safeguard limits without changing the levels of confidence. A financial model enables the user to create scenarios for such different input data as the effort for testing, the number of products in line with the production target, the prices of products and scrap prices as well as quality classifications of products. The pivots chosen for the model are the producer’s and consumer’s risks. For reasons of comparison the risks were determined both on the basis of normal and modified beta distributions. Product-specific conformity assessment procedures may have apparent financial benefits if the parameters of the model can be well defined.
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Notes
The term conformity is used for final products, whereas conformance refers to internal criteria. The term ‘conformity assessment’ in this contribution is used with reference to ISO/IEC 17000 [1].
In contrast to measurement tests are often not traceable to SI units.
A Type II error is a false negative error. The test result is ‘no’ but due to the uncertainty of the test the product conforms with the requirement (=producer’s risk).
A negative profit: a profit that would not have been realized if loss preventive measures had not been implemented yet. So the profit would still contribute to the company’s overall profit.
References
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Acknowledgments
This project (15464/N) was sponsored by the German Federal Ministry of Economics and Technology (BMWi), managed by the German Federation of Industrial Research Associations (AiF) and supported by the German Wire Weavers Association (VDD), Düsseldorf.
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Hinrichs, W. Product-specific adaption of conformity assessment criteria and their financial consequences. Prod. Eng. Res. Devel. 5, 549–556 (2011). https://doi.org/10.1007/s11740-011-0329-7
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DOI: https://doi.org/10.1007/s11740-011-0329-7