Accessible Requires Authentication Published by De Gruyter August 22, 2013

Einsatz der Bayes'schen Statistik in der Zuverlässigkeitsbestimmung von zerstörungsfreien Prüfsystemen

Application of Bayes Statistics for Reliability Assessment of NDT Systems
Daniel Kanzler, Christina Müller, Uwe Ewert and Jorma Pitkänen
From the journal Materials Testing

Abstract

Die Fehlerauffindwahrscheinlichkeit oder “Probability of Detection” ist zu einer wichtigen Qualitätskennzahl von zerstörungsfreien Prüfsystemen geworden. Die Einschätzung von nur künstlichen Fehlern ist jedoch als Bewertungsgrundlage meist nicht ausreichend. Die später verwendeten Prüfobjekte mit den real vorkommenden Fehlern sind die zu betrachtende Basis, für die der Endanwender eine gültige Qualitätseinschätzung der angewandten zerstörungsfreien Prüfung fordert. Jedoch ist bei dem Fall, dass die Datenmenge gering ist, auch die Aussage der POD beschränkt. Es muss daher eine Zwischenlösung gefunden werden, in der die Informationen von beiden Prüfungen kombiniert werden. Die Mathematik ermöglicht mit der Bayes'schen Statistik, diese Informationen miteinander zu kombinieren und somit beide Informationen in die Bewertung einfließen zu lassen. Dabei spielt jedoch der Zusammenhang zwischen Signal und Fehlerausprägung eine wichtige Rolle. Praktisch angewendet und erprobt wird diese Vorgehensweise für die Bewertung der zerstörungsfreien Prüfungen der Firma POSIVA, die sich mit dem Bau eines Endlagers für hochradioaktiven Abfall in Finnland beschäftigt.

Abstract

The assessment of the Probability of Detection (POD) is used to evaluate the reliability of the non-destructive testing (NDT) system. The POD is required in industries, where a missed flaw might cause grave consequences. If only the artificial defects are evaluated, the POD could lead to wrong conclusion or even be invalid. The POD based on real flaws is needed. A small amount of real flaws can lead to a not statistically significant result or even to incorrect results. This work presents an approach to obtain to a significant result for the POD of the current dataset, despite the small amount of real defects. Two steps are necessary to assess a NDT system based on real flaws. First we evaluated the correlation between the NDT signal and the real size of the flaw. Second we use a statistical approach based on the Bayesian statistics to assess a POD in spite of the small amount of data. The approach allows including information of the POD evaluation of artificial defects in the assessment of the POD of real flaws.

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Online erschienen: 2013-08-22
Erschienen im Druck: 2013-04-02

© 2013, Carl Hanser Verlag, München