ETL 1110-2-547
30 Sep 95
c. Parallel series systems.
B-11. Target Reliability Indices
(1) Solutions are available for systems requiring
Reliability indices are a relative measure of the current
r-out-of-n operable components, which may be
condition and provide a qualitative estimate of the
applicable to problems such as dewatering with
expected performance. Embankments with relatively
multiple pumps, where r is defined as the number of
high reliability indices will be expected to perform
reliable units. Subsystems involving independent
their function well. Embankments with low reliability
parallel and series systems can be mathematically
indices will be expected to perform poorly and present
combined by standard techniques.
major rehabilitation problems. If the reliability indices
are very low, the embankment may be classified as a
(2) Upper and lower bounds on system reliability
hazard. The target reliability values shown in
can be determined by considering all components to be
Table B-1 should be used in general.
from subgroups of parallel and series systems, respec-
tively; however, the resulting bounds may be so broad
Table B-1. Target Reliability Indices
as to be impractical. A number of procedures are
found in the references to narrow the bounds.
Expected
Probability of
Performance
Unsatisfactory
Level
Beta
Performance
(3) Engineering systems such as embankments are
complex and have many performance modes. Some of
High
5
0.0000003
these modes may not be independent; for instance,
Good
4
0.00003
several performance modes may be correlated to the
occurrence of a high or low pool level. Rational
Above average
3
0.001
estimation of the overall reliability of an embankment
Below average
2.5
0.006
is a topic that is beyond this ETL.
Poor
2.0
0.023
d. A practical approach.
Unsatisfactory
1.5
0.07
(1) The reliability of a few subsystems or com-
Hazardous
1.0
0.16
ponents may govern the reliability of the entire system.
Note: Probability of unsatisfactory performance is the probability
Thus, developing a means to characterize and compare
that the value of performance function will approach the limit
the reliability of these components as a function of
state, or that an unsatisfactory event will occur. For example, if
the performance function is defined in terms of slope instability,
time is sufficient to make engineering judgments to
and the probability of unsatisfactory performance is 0.023, then
prioritize operations and maintenance expenditures.
23 of every 1,000 instabilities will result in damage which causes
a safety hazard.
(2) For initial use in reliability assessment of
geotechnical systems, the target reliability values
presented below should be used. The objective of the
Major Rehabilitation Program would be to keep the
reliability index for each significant mode above the
target value for the foreseeable future.
B-11
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