ETL 1110-2-560
30 Jun 01
t β
R(t) = exp -
(8)
α
where
α = the scale parameter or characteristic life
β = the shape parameter
For 0 < β < 1, the Weibull distribution characterizes wear-in or early failures. For β = 1, the Weibull
distribution reduces to the exponential distribution. For 1 < β < ∞, the Weibull distribution characterizes
the wear-out characteristics of a component (increasing hazard rate). The Weibull hazard function is
β -1
β t
h(t) =
(9)
α α
Plots of the reliability and hazard functions for the Weibull distribution are shown in Figures 4 and 5,
respectively.
c. General data required. Reliability analysis provides the best estimate of the reliability antici-
pated from a given design within the data limitations and to the extent of item definitions. The required
data are dependent on the availability and depth of analysis required. Mechanical and electrical com-
ponents are typically complex and made up of many different parts, each with several modes of failure.
These failure modes are associated with many ambiguous variables such as operating environment, lubri-
cation, corrosion, and wear. Historic data for lock and dam equipment have not usually been available.
Lock and dam equipment for which data are not available requires the analysis to be completed using data
from larger systematic samples of similar equipment such as the published failure rate data in Reliability
Analysis Center (1995). Failure rate data can also be obtained by multivariate methods developed in
Naval Surface Warfare Center (1992). Prior to any reliability determination, investigations should be
conducted to gain a thorough knowledge of the mechanical and electrical requirements and layouts, to
identify equipment deficiencies, and learn the project history and future demands.
d. Internet Web site. An Internet Web site (Appendix B) has been established as a means to collect
both historical and recent failure data for lock and dam mechanical and electrical equipment. It is
intended that the data will be continually collected and compiled so that accurate failure rate tables can be
developed. The data will better represent lock and dam equipment. The most important benefit is that the
most current failure data for Corps mechanical and electrical equipment will be available to engineers
doing the reliability work for future projects. In addition, it will provide a central reference source for
operations and engineering personnel to check when failures occur to see if there are common problems
with installed equipment. The most current data has been included in Appendix C. Engineering and
operations personnel are encouraged to input available failure data. The Web site should be checked for
the latest failure rate data when a reliability analysis is being developed.
7. Engineering Reliability Analysis
Assessment of the reliability of a system from its basic elements is one of the most important aspects of
reliability analysis. As defined, a system consists of a collection of items (components, units, etc.) whose
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