Page 115 - Reliability and Maintainability of In service Pipelines

104 Reliability and Maintainability of In-Service Pipelines

4.3.3 Developing Gamma Distributed Degradation Model in Case of
Unavailability of Corrosion Depth Data 112
4.4 Monte Carlo Simulation Method 114
References 116
Further Reading 117

4.1 Background

As it was concluded in the previous chapter, probably the most viable approach
to predict the structure’s reliability or its service life under future performance
conditions is through probability-based techniques involving time-dependent reli-
ability analyses.
By using these techniques a quantitative measure of structural reliability is
provided to integrate information on design requirements, material and structural
degradation, damage accumulation, environmental factors, and nondestructive
evaluation technology. The technique can also investigate the role of in-service
inspection and maintenance strategies in enhancing reliability and extending ser-
vice life. Several nondestructive test methods that detect the presence of a defect
in a pipeline tend to be qualitative in nature in which they indicate the presence
of a defect but may not provide quantitative data about the defect’s size, precise
location, and other characteristics that would be needed to determine its impact
on structural performance. None of these methods can detect a given defect with
certainty. The imperfect nature of these methods can be described in statistical
terms. This randomness affects the calculated reliability of a component.
Structural loads, engineering material properties, and strength-degradation
mechanisms are random. The resistance, R(t), of a structure and the applied loads,
S(t), both are stochastic functions of time. At any time, t, the safety limit state,
GR; S; tÞ,is(Melchers, 1999):
ð
GR; S; tÞ 5 RtðÞ 2 SðtÞ ð4:1Þ
ð
Making the customary assumption that R and S are statistically independent ran-
dom variables, the probability of failure resulting from Eq. (4.1), P f (t), is (Melchers,
1999):
N
ð
P f tðÞ 5 PGðtÞ # 0Š 5 F R ðxÞf s ðxÞdx ð4:2Þ
½
0
in which F R (x) and f S (x) are the probability distribution function of R and density
function of S, respectively. Eq. (4.2) provides quantitative measures of structural
reliability and performance, provided that P f can be estimated and validated.