ETL 1110-2-550
30 May 97
Appendix F
particular piece of equipment. Hence, the generic
Review of Recent Research in
function needs to be modified by conditioning on a
particular piece of equipment, resulting in a modi-
Hydropower Reliability Analysis
fied hazard function. By conditioning on a particu-
lar piece of equipment, the physical or performance
condition of the equipment is introduced as a factor
F-1. Introduction
for modifying the generic function. The Corps
maintains information on test results of a particular
This appendix presents a summary of recent
piece of equipment that are aggregated to obtain a
research related to hydropower reliability analysis
condition index. The test results and the condition
that may be useful in conducting maintenance and
index are needed to perform this modification.
rehabilitation studies.
c. Once a generic hazard function and a
condition index are obtained for a particular piece
F-2. Reliability Analysis of Hydroelectric
of equipment, they can be combined to obtain the
Power Equipment
modified hazard function using Bayesian tech-
niques. Reliability functions were developed for
a. In this study an assessment method of the
groups of generators that were defined by the date
time-dependent reliability and hazard functions of
of having the plant on line and the power rating of
hydropower equipment is developed (Ayyub et al.
the generators. The resulting reliability functions
1996). Life data of equipment can be classified into
are called herein the group reliability functions.
several types. For hydropower equipment, complete
These reliability functions can be used as prior
data or right censored data are commonly encoun-
information in the Bayesian techniques to obtain
tered. The 1993 inventory of generators as pro-
plant-specific reliability functions by utilizing new
vided by the Corps includes records of failure and
plant information on generator failures or censoring
replacement. A preliminary examination of these
to obtain plant reliability functions as posterior
records revealed that the average age at failure is
reliability functions. Alternately, plant reliability
28 years. Also, the average age of equipment based
functions can be developed using the same methods
on this 1993 inventory is 24 years. Generators were
that were used for the groups to obtain prior plant
grouped by plant-on-line date and power into
reliability functions. Then, new plant information
12 groups. The life data of generators within each
on generator failures or censoring can be utilized to
group were analyzed. Survivorship functions were
obtain updated plant reliability functions as poste-
developed, and models based on nonlinear numeri-
rior reliability functions. These two cases have the
cal curve fitting using an exponential function with
common objective of obtaining plant-specific relia-
a second-order polynomial tail were proposed.
bility functions and updating these functions using
Early-life special models and late-life prediction
new life or censoring data. Then, a method is pre-
(extrapolation) models were also developed. The
sented to obtain a unit (i.e., generator) specific
effect of manufacturer on generator reliability was
reliability function based on a plant (or group)
investigated. It can be concluded that the differ-
reliability function based on obtaining either
ences between the survivorship values of the Gen-
censoring information or the condition index of the
eral Electric Corp. and the Westinghouse Corp.
unit. Examples were used to demonstrate the use of
generators are, in general, statistically insignificant.
these methods.
b. The above-mentioned reliability and hazard
d. The suggested methods in this study were
functions can be viewed as marginal functions that
demonstrated using hydropower generators. Other
do not account for the particular condition of a piece
similar hydropower equipment types can be treated
of equipment, but they provide average or generic
using similar methods.
results for a group or stratum. In the practical use
of hazard functions in investment decision analysis,
a generic function might not be sufficient for a
F-1
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