ETL 1110-2-560
30 Jun 01
factors to relate the data to other conditions of environment and stress where K is the environmental factor
adjustment coefficient used to represent component stress levels altered by environmental conditions.
Typical K factors are given in Table D-1 where K1 relates to the general environment of operation, K2 to
the specific rating or stress of the component, and K3 to the general effect of temperature. The equipment
on the lock is considered to be exposed to an outdoor marine environment. For this example, a K1 factor
of 2 is used and K2 and K3 are 1.0.
c. Lock equipment reliability. The Weibull distribution was used to perform the reliability analysis
for each component in the block diagram. The values for β were selected from the values given in
Table 7-2 of Bloch and Geitner (1994), and reproduced as Table D-2, by choosing a dominant failure
mode for each component. If β cannot be determined, a value of 1.0 should be used. It should be noted
that most of the β values in Table D-2 are greater than or equal to 1.0, but not greater than 3.0. These
values represent random and wear-out failures as indicated by Regions B and C of the bathtub curve. The
characteristic life parameter α is determined from the failure rate data. Table D-3 contains failure rates
for several common mechanical components found on locks and dams. Appendix C contains a table of
failure rate data for lock and dam equipment. This table was generated from data entered in the Web site
database for Corps equipment. While α is normally determined through experimental methods, it can be
approximated from the ratio of α to Mean Time to Failure (MTTF) as a function of β by using Table D-4.
For example, the dominant failure mechanism for the spur gears is considered to be wear such as fretting,
scoring, or pitting. From Table D-2, the shape parameter β (Weibull Index) is 3.0, and from Table D-4
α/MTTF = 1.10. The life parameter α is calculated as follows:
(1) Table D-3 was used as the source for the failure rate data. These values are taken from a higher
number of sources and have less variability. From the published data of Table D-3, the summary or
combined failure rate λ computed from all individual data sources for spur gears is given as 3.2232
failures per million operating hours. The environmental factors are K1=2, K2=K3=1.
(2) The adjusted failure rate λ′ is
λ′ = λKn
(D-1)
λ′ = 3.2232 * K1* K2* K3 = 6.446 failures per million operating hours
and
MTTF = 1/λ′
(D-2)
6
= 1/6.446 = 0.155 H 10 hr
therefore
α = MTTF * 1.1
(D-3)
= 0.155 H 106 * 1.1 = 0.17 H 106 hr
α = 0.17 H 106/8760 = 19.4 years
(3) The Weibull reliability function from the main text for the components becomes
D-2
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