An Estimation method of flaw distributions reflecting inspection results through Bayesian update

Lu, K. ; Miyamoto, Yuhei*; Mano, Akihiro ; Katsuyama, Jinya  ; Li, Y. 

Nowadays, probabilistic fracture mechanics (PFM) has been utilized in several countries as a rational method for structural integrity assessment of important structural components such as reactor pressure vessels (RPVs). In PFM analyses, potential flaws in target components are used to evaluate the failure probability or frequency. Therefore, flaw distributions (i.e., flaw depth and density distributions) in an RPV shall be rationally set as one of the most important influential factors, which are developed during the manufacturing process such as welding. Recently, a Bayesian updating methodology was applied to reflect the inspection results into flaw distributions, and the likelihood functions applicable to the case when flaws are detected in inspections were proposed. However, there may be no flaw indication as the inspection results of some RPVs. The flaw distributions in this situation are important while the corresponding likelihood functions have not been proposed. Therefore, this study proposed likelihood functions to be applicable for both case when flaws are detected and when there is no flaw indication as the inspection results. Based on the proposed likelihood functions, several application examples were given in which flaw distributions were estimated by reflecting the inspection results through Bayesian update. The results indicate that the proposed likelihood functions are useful for estimating the flaw distribution for the case when there is no flaw indication as the inspection results.