Structural Reliability - Some Contributions to Offshore Technology
Authors: Cornell C. Allin 
Published: October 2008

ABSTRACT
A robust, explicit expression for the failure probability of an offshore structure under extreme, global loads is used to demonstrate many lessons that structural reliability has brought to safety assessment and design criteria development. These include demonstration of the sensitivity to the environment and the structure and insensitivity to statistical characterization of the capacity. There follows a set of recommended simplifications for reliability analysis, design criteria construction and risk management of offshore structural systems.

INTRODUCTION
Structural reliability analysis has been applied to the offshore field for three decades. Elements have been used both to develop industry design and reassessment guidelines and to assist the design and requalification of individual structures. The objective here, while backward-looking and broad-based, is not to review these many individual advances nor to present a general theoretical framework into which they might all fit. Rather, the paper tries to draw some broad conclusions for offshore design and reassessment from experience derived from many past reliability studies and from a few simple, explicit (probably unfamiliar) equations that ollow from elementary reliability theory. An implication of this objective and its bases is that there will be few specific attributions and references, and often very little apparent formal support for and very few explicit qualifications about the limits of applicability of many of the generalizations; the reader must beware and the slighted authors must accept apologies.
After the introduction of a robust equation for the probability of failure of an offshore structure, its interpretations and implications will be discussed. This includes both member and system-level issues. These include the role of site, load type, structural type, and hydrodynamic factors on the effectiveness of load factor values and post-linear capacity. The importance of an ultimate strength-level safety check will become evident. There follows a discussion of several topics important to the consistent development, application and interpretation of modern probability-based structural criteria, including which uncertainties should be included and how. Finally, topics which might best be called risk management are addressed including the role of cost benefit analysis and the level of the target failure probability and what it should depend on. The emphasis here is on the reliability of fixed structures with respect to extreme, global loading events such as storms, earthquakes, ice, and large ship impacts.

A DIRECT RELIABILITY EQUATION
A simple expression for the probability of failure is helpful in assessing the importance of various issues in safety assessment and code creation. It reads:
(Available In Full Paper)
in which and H is the complementary cumulative distribution function (CCDF) of the load, S; h is the probability density function of the capacity or resistance; fJ R is the coefficient of variation of the capacity; and R is the mean capacity.
The simple form results from any of several assumptions, making it quite robust. For example, assume, as we shall subsequently in this paper, that H has the following form l (at least in the region of importance to the integral, namely over 1 to 2 capacity standard deviations below R, Le., from about 0.7 to 1.0R)