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

improve the reliability estimates.

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.

(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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