Soft Methods in Safety and Reliability Engineering
It is beyond controversy that probability is an established measure in safety and reliability engineering; and it is not intended to question its successful application. However, the application of probabilities is no plain sailing.
Since David Hilbert's demand for an axiomatic framework in 1900 it has been known that probabilities cannot be defined. In 1933 Andrey N. Kolmogorov inaugurated such a framework. Other axiomatic frameworks followed later on, but Kolmogorov's was the only one that found its way into engineering. Another critical issue is the concept of probability — the interpretation of what a probability actually is. Starting with Cardano (mid 16th century) and currently ending with Karl Popper (20th century) the approaches to interpretation all led to discussions on epistemological and mathematical dilemmas. Despite the aspects described above, scientific inquisitiveness is another attractive motive to consider further measures and their applicability to safety and reliability engineering.
Two (actually three) non-probabilistic measures already appeared on the safety and reliability engineering horizon: In 1965 Lotfi A. Zadeh introduced fuzzy membership grades, which found their way to the reliability community in the early 1990s. In the late 1990s Dempster-Shafer's belief and plausibility measures were discussed (e.g. at ESREL 1998). Following Jonathan Lawry [Preface to Soft Methods for Integrated Uncertainty Modelling. Springer, 2006], soft methods are understood as those uncertain formalisms not part of mainstream statistics and probability theory. A small, but steadily growing number of approaches in safety and reliability modelling utilise concepts, tools, and techniques based on theories such as