# Reliability of Marine Structures

Reliability implies estimate of limit state probabilities of the marine structure under adverse environmental loading, while safety is used to indicate reliability.

Safety is related to an existing process. It has direct consequences to failure. It is deterministic approach. On the other hand, reliability is a probability of the realization of safety. It has a converse consequence of failure. Reliability is assessed even before failure is foreseen and therefore reliability methods are based on engineering judgement. Accuracy of the results of a reliability approach essentially depends on the data from which the results are arrived.

As both safety and reliability are circumscribed around failure probability, the definition of failure becomes important. It (failure) generally expressed in probabilistic terms and is assessed by the ability of a system to perform its intended function adequately on demand for a period under specific conditions. Reliability is the probability of a system performing its required function adequately for a specified period under stated conditions. The most important aspect of reliability is accounting for the uncertainties that make marine structures vulnerable to failure for a predefined limit state. Accuracy of reliability analysis depends on how accurately all the uncertainties are accounted for in the analysis.

The period of time, during which the structure is unable to perform, is called downtime or shut down time.

Uncertainties in Marine Structures

In dealing with design of marine structures, uncertainties are unavoidable. Uncertainties are broadly classified into two types:

(i)                  Those associated with normal randomness (aleatory type) and

(ii)                Those associated with erroneous predictions and estimations of reality. (epistemic type)

The aleatory type generally arises from the loads that result from nature (e.g., earthquakes and floods). On the other hand, the epistemic type needs to be reduced using appropriate prediction models and sampling techniques.

DETERMINISTIC AND PROBABILISTIC APPROACHES

Deterministic Approach

An approach based on the premise that an explicit and unique solution is available is a deterministic approach. In this approach, uncertainties are not formally recognized or accounted for; hence, uncertainties are associated with a probability of either 0 or 1. Although safety factors indirectly account for the uncertainties, one is concerned only with the reliability associated with this value. In conventional analysis, however, one is not concerned with the reliability associated with this unique value.

Probabilistic Approach

A probabilistic approach is based on the concept that several or varied outcomes of a situation are possible; hence, there is no unique solution for a given problem. Uncertainties are formally recognized in this approach. Description of the physical system includes randomness of the data and other uncertainties. This approach aims to determine only the probability of the outcome of any event that may occur. It is expressed in percent, indicating the degree of confidence in the estimated values. Probabilistic modeling aims to study a range of outcomes from given input data. Accordingly, the description of a physical situation or system includes randomness of data and other uncertainties. The selected data for a deterministic approach will, in general, not be sufficient for a probabilistic study of the same problem.

Reliability analysis cannot be accurate because it is practically impossible to identify all uncertainties; hence, engineering judgment is applied. Further, the method of modeling and analyzing them is not easy. Therefore, many assumptions are made during the analysis, which is the primary reason for inaccurate results. Most importantly, analytical formulation of the limit state surface and subsequent integration of the probability density function within the domain of interest is a highly complex task that declines the accuracy of the reliability estimates (Naess and Moan, 2013).

FORMULATION OF A RELIABILITY PROBLEM

Formulation of a reliability problem can be broadly divided into two groups:

(i) time-invariant problems and (ii) time-variant problems.

In both cases, limit state function, which could be based on the serviceability requirements or ultimate strength criteria, is defined. The reliability problem seeks to find the probability of the limit state of failure or violation of limit state conditions (Papoulis and Pillai, 1991).