Page 93 - Reliability and Maintainability of In service Pipelines

82 Reliability and Maintainability of In-Service Pipelines

service life, i.e., it is required that it does not collapse or become unsafe and that
it fulfils certain functional requirements.
In order to estimate the reliability by using probabilistic concepts it is neces-
sary to introduce stochastic variables and/or stochastic processes/fields and to
introduce failure and nonfailure behavior of the pipeline under consideration.
Generally the main steps in a reliability analysis for service life prediction are:

1. Identify the significant failure modes of the pipeline.
2. Decompose the failure modes in series systems or parallel systems of single
components (only needed if the failure modes consist of more than one
component).
3. Formulate failure functions (limit state functions) corresponding to each com-
ponent in the failure modes.
4. Identify the stochastic variables and the deterministic parameters in the failure
functions. Further specify the distribution types and statistical parameters for
the stochastic variables and the dependencies between them.
5. Estimate the reliability of each failure mode (illustration of how reliability, or
inversely the probability of failure, changes with time).
6. Evaluate the reliability result by performing sensitivity analyses.

Typical failure modes to be considered in a structural reliability analysis of
pipeline are yielding, corrosion, buckling (local and global), fatigue, and exces-
sive deformations.
The failure modes (limit states) are generally divided into:
Ultimate limit states correspond to the maximum load-carrying capacity which
can be related to, e.g., formation of a mechanism in the pipeline, excessive
plasticity, rupture due to corrosion, and instability.
Conditional limit states correspond to the load-carrying capacity if a local part
of the pipeline has failed. A local failure can be caused by an accidental action
or by fire. The conditional limit states can be related to, e.g., formation of a
mechanism in the pipeline, exceedance of the material strength, or instability
(buckling).
Serviceability limit states are related to normal use of the pipeline, e.g., exces-
sive deflections, local damage, and excessive vibrations.
The fundamental quantities that characterize the behavior of a pipeline are
called the basic variables and can be denoted X 5 (X1, .. ., Xn) where n is the
number of basic stochastic variables. Typical examples of basic variables are
loads, strengths, dimensions, and material properties. The basic variables can be
dependent or independent. A stochastic process can be defined as a random func-
tion of time in which for any given point in time the value of the stochastic
process is a random variable.