TU Delft Repository

The Weibull distribution is one of the most widely used distributions in reliability analysis. The ability to accurately estimate the parameters of Weibull distributed data can be very useful, and particularly important when dealing with small data sets and high degrees of censoring. This project aims to compare the performance of the maximum likelihood (ML) method and a generalised least squares (GLS) method in estimating the parameters of small, censored Weibull distributed data. The study involves a simulation of type II censored Weibull data to estimate the log-Weibull parameters and predict the quantiles of the next failure. Simulations were performed across a broad range of sample sizes and number of observed failures. We evaluated the efficiency and accuracy of both estimation methods. The simulation results demonstrated that the unbiased versions of the ML estimators consistently outperform the GLS estimators in terms of efficiency. The root mean squared error (RMSE) of the ML estimator were lower, indicating a higher accuracy in parameter estimation.

This thesis aims to improve the current risk classification for (company) car insurance at Achmea, focusing on WAM and ARD coverages. By using cluster analysis, specifically K-prototypes and spectral clustering, policyholders are grouped based on zip codes and license plates to enhance the current claim frequency models (and thus premium pricing models). The application of spectral clustering (with U-SPEC as the observation reduction technique) led to significant improvement of the current claim frequency GLM for the ARD coverage. This thesis highlights the potential of cluster analysis in actuarial science, offering new methods for mixed data types and high-dimensional clustering, thus providing a foundation for more accurate claim frequency models. The time stabilities and stabilities with respect to the number of observations of the clusters are also investigated.

This thesis aims to improve the current risk classification for (company) car insurance at Achmea, focusing on WAM and ARD coverages. By using cluster analysis, specifically K-prototypes and spectral clustering, policyholders are grouped based on zip codes and license plates to enhance the current claim frequency models (and thus premium pricing models). The application of spectral clustering (with U-SPEC as the observation reduction technique) led to significant improvement of the current claim frequency GLM for the ARD coverage. This thesis highlights the potential of cluster analysis in actuarial science, offering new methods for mixed data types and high-dimensional clustering, thus providing a foundation for more accurate claim frequency models. The time stabilities and stabilities with respect to the number of observations of the clusters are also investigated.

Background: Real-time adaptive radiotherapy workflows require fast spatial dose calculations with clinical accuracy. Modern physics-based dose calculation algorithms often compromise between speed and accuracy. In contrast, deep learning methods have shown to be effective at predicting spatial dose distributions with high accuracy in sub-second times. Very High Energy Electrons (VHEE) have shown potential as a treatment modality in recent years due to their penetrative ability and conformality. Creating a need for fast and accurate VHEE spatial dose calculations. Purpose: This study presents a deep learning-based algorithm that utilizes convolutional layers and the self-attention mechanism to predict VHEE beam spatial dose distributions in sub-second times. Methods: The presented Electron-Dose Transformer Algorithm (E-DoTA) maps the 3D patient geometry and beam characteristics (using a vector representing the beam energy and a 3D Gaussian with a specific Gaussian positional spread representing the beam shape) to a 3D dose distribution. E-DoTA uses a series of 3D convolutional layers to extract features from the patient geometries and beam shape, followed by a transformer to route information between the extracted features and the added energy vector, which are then upsampled to the 3D dose distribution. E-DoTA is trained on 60,000 combinations of patient geometries and beam characteristics, derived from 15,000 independent patient geometries based on 12 distinct patient CT scans from the abdomen region. The model’s accuracy and prediction speed are assessed using 8,000 previously unseen patient geometries and beam characteristics. Results: E-DoTA predicts dose distributions of VHEE beams with high accuracy, achieving a gamma pass rate of 97.05% ± 3% (3mm, 1%) and an average relative dose error of 0.254% ± 0.096% in approximately 131 ms. Conclusions: The fast and high-accuracy dose predictions allow the speed-up of VHEE spatial dose distribution calculations, which is currently only provided by slow Monte Carlo algorithms. Further optimizations to E-DoTA could allow for more accurate and faster dose calculations, thereby potentially accelerating VHEE radiotherapy workflows.

Background: Real-time adaptive radiotherapy workflows require fast spatial dose calculations with clinical accuracy. Modern physics-based dose calculation algorithms often compromise between speed and accuracy. In contrast, deep learning methods have shown to be effective at predicting spatial dose distributions with high accuracy in sub-second times. Very High Energy Electrons (VHEE) have shown potential as a treatment modality in recent years due to their penetrative ability and conformality. Creating a need for fast and accurate VHEE spatial dose calculations. Purpose: This study presents a deep learning-based algorithm that utilizes convolutional layers and the self-attention mechanism to predict VHEE beam spatial dose distributions in sub-second times. Methods: The presented Electron-Dose Transformer Algorithm (E-DoTA) maps the 3D patient geometry and beam characteristics (using a vector representing the beam energy and a 3D Gaussian with a specific Gaussian positional spread representing the beam shape) to a 3D dose distribution. E-DoTA uses a series of 3D convolutional layers to extract features from the patient geometries and beam shape, followed by a transformer to route information between the extracted features and the added energy vector, which are then upsampled to the 3D dose distribution. E-DoTA is trained on 60,000 combinations of patient geometries and beam characteristics, derived from 15,000 independent patient geometries based on 12 distinct patient CT scans from the abdomen region. The model’s accuracy and prediction speed are assessed using 8,000 previously unseen patient geometries and beam characteristics. Results: E-DoTA predicts dose distributions of VHEE beams with high accuracy, achieving a gamma pass rate of 97.05% ± 3% (3mm, 1%) and an average relative dose error of 0.254% ± 0.096% in approximately 131 ms. Conclusions: The fast and high-accuracy dose predictions allow the speed-up of VHEE spatial dose distribution calculations, which is currently only provided by slow Monte Carlo algorithms. Further optimizations to E-DoTA could allow for more accurate and faster dose calculations, thereby potentially accelerating VHEE radiotherapy workflows.