ETL 1110-2-550
30 May 97
e. The CI does provide objective information
were estimated. The statistics of this evaluation
about the current condition of the equipment, but it
showed that there is no significant difference
is difficult to determine a failure rate from a CI. In
between the condition indices for the stator in the
addition to the CI value, there are other meas-
two different conditions. Based on this evaluation,
urements (such as hours of usage, severity of
it is concluded that the CI would not improve the
usage, routine maintenance practices, and
reliability information given by historical data for
manufacturer) that are important in accurately
the 15 units examined. The CI estimations were
determining service life and predicting failure rates.
based on only 4 of the 13 tests needed to fully
determine the CI. Had all tests been performed, the
results may have shown that the CI could be used to
F-4. Reliability of Hydroelectric Power
improve the reliability estimates.
Equipment Study
b. Capacity and Demand Analysis.
A reliability study of hydroelectric power equipment
was conducted by JAYCOR at the request of the
(1) For equipment lacking a statistically
COE (Mlakar 1993). In this study, a Weibull
significant base of data, a capacity and demand
distribution was fitted to survivor data to produce
formulation can be used to estimate reliability. The
failure rate estimates of generator stators. A
reliability of the previous section can be used to
Bayesian analysis with the COE condition indices
estimate the reliability of an item if statistically
was performed. The results suggest that the CIs
significant data exist. For most hydroelectric power
contribute little additional reliability information.
equipment, these data do not exist. In these cases,
For equipment lacking a statistically significant
the reliability can be estimated using probabilistic
base of data, a capacity and demand formulation
techniques to describe deterministic design
was used to estimate reliability.
parameters.
a. Survivor Data Analysis.
(2) In summary, the proximity to a limiting
state of performance is quantified as the factor of
(1) In this study, a survivor curve presents the
safety, F. This measure is defined as the ratio of
percentage of units in a given group which are
capacity to resist, C, to the applied demand, D, and
surviving as a function of the age in service. The
is also a function of a set of variables, Xi describing
survivor curve can be represented by the reliability
the components geometry, material, and boundary
function of probability theory which describes the
conditions. Typically the logarithm of the random
probability of satisfactory performance as a func-
variable (F) is considered, and the reliability index
tion of age. The Weibull distribution was used to
(b) is defined as the ratio of the mean and standard
describe the reliability distribution. The charac-
deviation of ln(F). The reliability index represents
teristic age and shape parameters were found for a
the number of standard deviations from the limiting
data set by performing an algebraic transformation
state to the mean. Generally, the mean and standard
to the data and fitting the transformed data with a
deviation of the ln(F) are not known but information
line. The scale and shape parameters were found
may be known about the means and standard
from the slope and intercept of the line. Once these
deviations of the Xi variables. If so, the mean and
parameters are known, the associated hazard
standard deviation of the ln(F) can be approximated
function can be obtained. This hazard function
using a Taylor Series Finite Difference estimation.
provides the failure probability as a function of age
Finally, the reliability index can be used to estimate
for the component.
the reliability by assuming that ln(F) is normally
distributed in which F(b) is the cumulative normal
(2) To investigate the accuracy of the CI to
distribution function. This formulation can be used
predict whether a component is "sat" or "unsat,"
to estimate the reliability as a function of
CIs for 15 units in a known satisfactory condition
component age, R(t), because as a component ages
and 3 units in a known unsatisfactory condition
the underlying variables Xi change. Having
F-3
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