# Factor of safety and probability of failure

Introduction

How does one assess the acceptability of an engineering design? Relying on judgement alone can lead to one of the two extremes illustrated in Figure 1. The first case is economically unacceptable while the example illustrated in the drawing on the right violates all normal safety standards.

Sensitivity studies

The classical approach used in designing engineering structures is to consider the relationship between the capacity C (strength or resisting force) of the element and the demand D (stress or disturbing force). The Factor of Safety of the structure is defined as F = C/D and failure is assumed to occur when F is less than unity. Factor of safety and probability of failure

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Rather than base an engineering design decision on a single calculated factor of safety, an approach which is frequently used to give a more rational assessment of the risks associated with a particular design is to carry out a sensitivity study. This involves a series of calculations in which each significant parameter is varied systematically over its maximum credible range in order to determine its influence upon the factor of safety. This approach was used in the analysis of the Sau Mau Ping slope in Hong Kong, described in detail in another chapter of these notes. It provided a useful means of exploring a range of possibilities and reaching practical decisions on some difficult problems. On the following pages this idea of sensitivity studies will be extended to the use of probability theory and it will be shown that, even with very limited field data, practical, useful information can be obtained from an analysis of probability of failure. An introduction to probability theory

A complete discussion on probability theory exceeds the scope of these notes and the techniques discussed on the following pages are intended to introduce the reader to the subject and to give an indication of the power of these techniques in...

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