Anthony King M2.3 System Reliability and Modeling
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Module 2.3: Systems Reliability and Modeling
Anthony King
College of Aeronautics, Embry-Riddle Aeronautical University
SYSE 515: Math Applications in Systems Engineering
Federica Robinson-Bryant Instructor
October 24, 2023
2
Module 2.3: Systems Reliability and Modeling
1.
Interpreting a Fault Tree –
A fault tree analysis is a top-down approach to failure analysis that begins at the system
level (Hoyland & Rausand, 2004). By analyzing Figure 1 it can be determined that an engine can
fail from various channels of specific problems. There are two symbols in this example that are
critical in determining the probability of failure. These are called “and” gates and “or” gates
(Ayyub & McCuen, 2011). The crescent moon shaped symbols under all the events that are
within the rectangular boxes are the “or” gates. These symbols mean that the output event occurs
if any one of the input events occur. For example, the “Fuel problems” failure will occur if either
the exhaustion or contamination failures occur (Richardson & Wortman, 2018). These “or” gates
are computed by the additive law of probability (Ayyub & McCuen, 2011).
The symbol directly under the “Overheated Wire” basic event looks very similar to the
“or” gate but has a straight line at the bottom instead of a curved line. This is the “and” gate,
which follows the multiplicative law of probability (Ayyub & McCuen, 2011). This symbol
means that the output event occurs only if all the input events occur simultaneously (Richardson
& Wortman, 2018).
After reviewing this fault tree analysis, we can conclude that the probabilities of
exhaustion and contamination would be added together, broken valve and broken connecting rod
would be added together, and broken fuel pumps will be added to the product of excessive
current on system wiring and power applied to system for extended time. After all those totals
are added together, then the probability of failure will be revealed.
3
Figure 1
Fault Tree Diagram
Note.
ERAU Module 2.3 Assignment: Systems Reliability and Modeling Activity 1, 2023,
(
https://erau.instructure.com/courses/164517/assignments/3296367?module_item_id=10062929
)
2.
Solve for Overheated Wire and Mechanic Failure –
Figure 2
Calculations for Activity 2
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The probability of an overheated wire is 0.000000000018 or 0.0000000018%. The
probability of having a mechanic failure is 0.000001 or 0.0001%.
3.
Other reliability models -
Another reliability model that can be applied throughout the system lifecycle is a decision
tree. Figure 3 below depicts the beginning of the tree to the left and the end of the tree to the
right. The tree shows decision and chance nodes. Refer to the key on the bottom left of the figure
to locate the different nodes. Based off the different decisions and their corresponding outcomes,
a prediction can be made for the total expected cost or utility value (Ayyub & McCuen, 2011).
Figure 3
Decision Tree Example
Note.
Ayyub, B. & McCuen, R., 2011, (
https://ebookcentral.proquest.com/lib/erau/reader.action?
docID=1631123
)
5
The decision tree can be applied throughout the system lifecycle because it gives the user
a mathematical calculation to decide which decision is most cost effective and reasonable.
6
References
Ayyub, B. & McCuen, R. (2011).
Probability, Statistics, and Reliability for Engineers and
Scientists
. Taylor & Francis Group.
https://ebookcentral.proquest.com/lib/erau/reader.action?docID=1631123
Hoyland, A. & Rausand, M. (2004).
System Reliability Theory Models, Statistical Methods, and
Applications
(2
nd
ed.). Wiley.
https://www.ntnu.edu/documents/624876/1277590549/chapt03-fta.pdf/c2e449ab-3221-
472c-b3d7 3310942ee511#:~:text=%20Fault%20tree%20analysis%20(FTA,the%20ways
%20it%20can%20happen.&text=caused%20by%20individual%20or%20combined
%20lower%20level%20failures%20or%20events
.
Richardson, W. & Wortman, B. (2018).
Certified Reliability Engineer Primer
(5
th
ed.). Quality
Council of Indiana.
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