Welding fault detection in the industry of hot water tanks remains typically conducted visually or with the assistance of None Destructive Examination, such as X-ray, ultrasound, and penetrant testing. However, this leads to high consumption of time and resources. We propose in this paper a two-level method for automatic welding defect detection and localization. The method is based on the classification of the probability density distributions of the voltage signals underlying the generated stochastic process from the welding operation. In the main phase, we apply a passband filter to the raw signals and use the Kernel Density Estimation to measure the distribution of the filtered signal. The probability density distributions are processed as functional data and classified employing a functional non-parametric kernel classifier. In the second phase, the signal of nonconforming welding is split into segments and their probability density distributions are classified in order to extract the precise location of the defect in the whole signal. The proposed method allows to detect and localize welding defects with high accuracy.