###### Abstract
In their work, [PERSON] and al. developed the Cognitive Reliability and Error Analysis Method (CREAM) to achieve the interpretation of radiograms. Data were collected through a survey conducted with operators in a nuclear power plant [20]. In the case of the nuclear industry, it has been necessary to create reliable, large-scale benchmarks to study the reliability of NDT methods. The PISC (Programme for the Inspection of Steel Components) started in 1976 with the PISC I programme and was continued with PISC II (1980-1986) and PISC III (1988). These are major international programmes involving fifteen countries and some fifty NDT teams worldwide. Other trials of this type have also taken place on a smaller scale, such as the Defect Detection Trial (DDT, 1983), or in the aeronautical and offshore fields [21]. The need to create standard parts for NDT is still relevant today in every industrial field, as is the case for bonding in aeronautics [22; 23]. These standard parts are essential to assess the efficiency of novelties in NDT techniques. In general, ultrasonic methods have a fairly good average accuracy of defect sizing, but with a fairly high standard deviation [24]. This trend is confirmed in the PISC III tests where five out of seven teams overestimate the defects. The average sizing error in these tests is only 0.5 mm for a maximum crack size of 30% of the wall thickness. Such an average value may seem good, but this performance should be put into perspective, because the correlation between the size assessed by the nondestructive examination and the real size still shows a large dispersion [25]. In general, if the checks by different teams are multiplied, the risk of leaving an unacceptable defect undetected drops considerably. The best sizing results are obtained by using the crack tip diffraction echo, which encourages the use of focused sensors [26]. The poor fatigue crack detection performance is due to the material structure of the steels used. The best performances are obtained in ferritic forged steels with easy access. The performance decreases with accessibility difficulties and becomes even worse in welds sometimes at very low levels [25]. The best results are obtained in welds for automatic processes and for detection methods just above the noise level. Conversely, this configuration often leads to more false alarms [25; 27; 28]. With the beginning of numerical simulations for NDT applications, it was understandable that an alternative to standard blocks was to build simulators which took into account the many causes of amplitude variations and signal noise [15]. Year after year, numerous physical laws have been progressively included in specialised software, such as the CIVA code [29], and the POD (probability of detection) is now a part of research work in NDT science [30]. In the last twenty years, mechanical integrity assessment has been progressing, with a better understanding of the physical and mechanical phenomena underlying nondestructive characterisation. This has required bringing together many scientific skills. We are contributing to the understanding of ultrasonic testing in anisotropic and heterogeneous welds by developing welded material modelling as well as by developing experimental set-ups allowing for the validation of the latest developments in numerical modelling. Figure 1 in the next section illustrates this methodology we are building to improve UT reliability. In this paper, we describe the progression of ideas for a phenomenological approach for describing the mechanical parameters of a welded material. The analysis of the advances in material modelling for ultrasonic testing of welds begins in Section 1 with the description of the initial requirements of material modelling for anisotropic and heterogeneous welds, as the numerical modelling of ultrasonic testing requires wave propagation modelling. The material issue is presented with a literature survey. In Section 2, the phenomenological model, MINA, is explained.