Page 462 - Marine Structural Design

43 8 Part IV Structural Reiiabiliiy

24.4 Selection of Distribution Functions
The probability distribution function for a random variable is most conveniently given in terms
of a standard distribution type with some distribution parameters. Regressions of available
observations of a quantity will not always given enough information to allow for interpretation
of the distribution type for the uncertain quantity and a choice of the distribution type has to be
made. The results of a reliability analysis may be vary sensitive to the tail of the probability
distribution, so a proper choice of the distribution type will often be crucial. Mean and
standard deviations are normally obtained from recognized data sources.
Normal or lognormal distributions are normally used when no detailed information is available.
The lognormal distribution is used to describe load variables, whereas the normal distribution
is used to describe resistance variables. However, a variable that is known never to take on
negative values is normally assigned a log-normal distribution rather than a normal
distribution. The following procedure may be applied for determination of the distribution type
and estimation of the associated distribution parameters:
1. Based on experience from similar types of problems, physical knowledge or analytical
results, choose a set of possible distribution.
2. Estimate the parameters in these distributions by statistical analysis of available
observations of the uncertainty quantities. Regressions may be based on
6 Moment estimators
Least square fit methods
Maximum likelihood methods
Visual inspections of data plotted on probability paper
3. If there are several possible choices, the following technique can be used for acceptance or
rejection of the selection of distribution functions.
Visual identification by plot of data on probability paper or by comparison of moments
Statistical tests e.g. Chi-square
Asymptotic behavior for extreme value distributions
4. If two types of distributions given equally good fits, it is recommended, particularly for
load variables, to choose the distribution that fits possible data observations in the tail
better than the other.
When distributions are chosen using the above methods, it is important that such choices,
including the step leading to the choices, are satisfactorily documented.

24.5 Uncertainty in Ship Structural Design

24.5.1 General
The design of any structure by rational means involves consideration of the uncertainties that
arise in regard to the external actions imposed on the structure as well as the strength and
response properties of the structural elements. These different uncertainties can be taken into
account by introducing probability concepts into the structural design procedure.