ETL 1110-2-560
30 Jun 01
9. Component Reliability
The failure distribution appropriate to the specific electronic, electrical, electromechanical, and
mechanical items should be used in computing the component reliability. In most cases, the failure
distribution will not be known and the exponential or the Weibull may be assumed. The α and β
parameters of the Weibull equation are normally empirically determined from controlled test data or field
failure data. This ETL presents a procedure for estimating these values. If the β value in the Weibull
function is unknown, a value of 1.0 should be assumed. The flat failure region of mechanical and
electrical components is often much longer than the other two regions, allowing this assumption to be
adequate. Once the component reliability values are determined, the RBD method is used to evaluate
their relationship within the system to determine the total system reliability. Appendices D and E contain
more information on determining component reliability. In Appendix F, the mechanical and electrical
subsystem reliability data from Appendixes D and E are applied to the overall system to determine an
overall lock and dam system mechanical and electrical reliability value.
10. System Risk Analysis Using Block Diagrams
The necessity for determining the reliability of a system requires that the reliability be considered from
two perspectives, basic reliability and mission reliability. Both are separate but companion products that
are essential to quantify the reliability of a system adequately. The incorporation of redundancies and
alternate modes of operation to improve mission reliability invariably decreases basic reliability. A
decrease in basic reliability increases the demand for maintenance and support. Basic reliability is
normally applied to evaluate competing design alternatives.
a. Basic reliability - Series System Model. A basic reliability prediction is a simplified model that is
intended to measure overall system reliability. It is used to measure the maintenance and logistic support
burden required by the system. A basic reliability model is an all-series model. Accordingly, all elements
providing redundancy or parallel modes of operation are modeled in series. In a series system, the
components are connected in such a manner that if any one of the components fails, the entire system
fails. Care should be taken when developing this type of model since the final value of the basic
reliability of the system is inversely proportional to the number of components included in the evaluation;
i.e., the more components there are, the lower the reliability. Such a system can be schematically
represented by an RBD as shown in Figure 6.
A
B
C
Figure 6. Series system
For a system with N mutually independent components, the system reliability for time t is
RS(t) = RA(t)*RB(t)*RC(t)*...* RN(t)
(10)
It can also be shown that if hs(t) represents the hazard rate of the system, then
n
∑
hs(t) =
hi(t)
(11)
i=1
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