​This book presents a critical overview of statistical fiber bundle models, including existing models and potential new ones. The authors focus on both the physical and statistical aspects of a specific load-sharing example: the breakdown for circuits of capacitors and related dielectrics. In addition, they investigate some areas of open research.This book is designed for graduate students and researchers in statistics, materials science, engineering, physics, and related fields, as well as practitioners and technicians in materials science and mechanical engineering.

The book shows how risk, defined as the statistical expectation of loss, can be formally decomposed as the product of two terms: hazard probability and system vulnerability. This requires a specific definition of vulnerability that replaces the many fuzzy definitions abounding in the literature. The approach is expanded to more complex risk analysis with three components rather than two, and with various definitions of hazard. Equations are derived to quantify the uncertainty of each risk component and show how the approach relates to Bayesian decision theory. Intended for statisticians,...

This book discusses the payout phase of the old-age pension saving scheme, the so-called effective premium, and offers detailed actuarial models and analyses of five old-age pension saving products used in practice. These include the basic permanent monthly annuity, without any benefits for survivors, as well as products which, in addition, also include benefits for survivors or authorized persons in the event of the pensioner’s death. The purpose of the book is to point out the method of determining future old-age pensions from old-age pension savings, and to present the advantages and...