## Multilevel Monte Carlo for Failure Probability Estimation

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Master thesis,
Bachelor thesis
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### Description

Deviations in the manufacturing process of electronic components may lead to rejections due to malfunctioning. Uncertain design parameters (i.e. geometrical and material parameters) can be modeled as random variables. Then, the failure probability of a realization can be estimated. A standard approach for estimating failure probabilities is a Monte Carlo analysis. In a Monte Carlo analysis a large number of sample points is generated according to a given probability distribution. The percentage of sample points not fulfilling some predefined performance feature specifications denotes the failure probability. In order to obtain a reliable estimation, a large number of sample points is required. This leads to high computing costs, since for each sample point a PDE must be solved, e.g. with the finite element method (FEM). Current research deals with the reduction of computational effort. Multilevel Monte Carlo approaches achieve this by evaluating most sample points with low accuracy and therefore low cost, and only a few sample points with high accuracy and therefore high cost [1].

### Work plan

- Familiarization with the topics of failure probability estimation and Monte Carlo analysis
- Literature study on existing Multilevel Monte Carlo approaches
- Efficient implementation of a Multilevel Monte Carlo algorithm in Python
- Evaluation and comparison with existing methods

### Prerequisites

Basic knowledge of electromagnetism, stochastics and FEM, some experience with programming in Python, interest in electromagnetic field simulations.

### References

[1] M. B. Giles, Multilevel Monte Carlo methods, Acta. Num., 24:259–328, 2015