Failure Probability Bounds of Complex Telecommunication System by Use of LP

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Failure Probability Bounds of Complex
Telecommunication System by Use of LP
American University of Armenia

• Supervisor Dr. Alexan Simonyan
• Referee Sargis Zeytunyan
• Student Yelena Vardanyan

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Outline

• Introduction
• Chapter 1 Reliability and Failure Probability
  Analysis for 9 Stations
• Gamma Distribution
• Weibull Distribution
• Exponential Distribution
• Chapter 2 Theoretical Background
• Failure Probability Bounds of
  the Whole System by the use of LP
• LPs Size and Decomposition Approach
• LP Formulation
• Advantages of LP bounds method
• LP Formulation for Conditional Probability
• Chapter 3 LP formulation of the
  telecommunication system
• LP formulation for sub-component
• LP formulation for Conditional Probability
• General LP for the sub-component
• LP formulation for entire system
• Conclusions and Recommendations for Future Work

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Introduction
The main goal of this research is to give general
picture of the complex telecommunication system
which percent of time the system is available
with its 100 working condition and which percent
of time the system is not available (failure
probability bounds). This work is done, based on
the results of T. Ghazaryans thesis the failure
time distribution of all stations with their
estimated parameters. The mentioned thesis is
done in terms of power supply, one from the
series of problems which can cause outages, based
on the real-life data.

• Reliability is the probability that system will
  not fail under some specified set of
  circumstances.

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Reliability and Failure Probability Analysis for
9 Stations
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Gamma Distribution
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Reliability and Failure Probability Analysis
Gamma Distribution
for t gt 0
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Weibull Distribution
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Reliability and Failure Probability Analysis
Waibull Distribution
for t gt 0
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Exponential Distribution
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Reliability and Failure Probability Analysis
Exponential Distribution
for t gt 0
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Calculated Reliabilities and Failure
Probabilities
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Failure Probability Bounds of the Whole System by
use of LP

• The system failure probability bounds was old
  enough announced in 1965 and first was explored
  by Hailperin. Then Kounias and Marin in 1976 used
  the method to look at the accuracy of some
  theoretical bounds.

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Advantages of LP Bounds Method

• Any type of information can be used
• Marginal component failure probabilities
• Joint component failure probabilities
• The method guarantees the narrowest possible
  bounds
• The method is applicable to general systems
• Easy identification of critical components and
  cut sets within a system

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LPs Size and Decomposition Approach

• The approach is the following
• Decompose the system into a number of subsystems
• Consider each subsystem and perform analyses
  separately
• Consider subsystems as components for the whole
  system

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LP Formulation

• The general formulation of LP is the following

pj
0 , j 1,2,.n
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LP Formulation

• n equality or inequality constraints results from
  knowledge of uni-component probabilities,
• equality or inequality constraints results from
  knowledge of bi-component probabilities,

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Conditional Probability

• P(AB) P(BA)P(A)

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LP Formulation for Conditional Probability
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LP Formulation for Telecommunication System

• The number of unknown variables would be 29512,
• 9 equality constraints result from the knowledge
  of the marginal (uni-) component failure
  probabilities,
• C92 36 equality constraints result from the
  knowledge of the joint (bi-) component failure
  probabilities
• Probability axioms

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LP Formulation for Super-Component
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LP Formulation for Conditional Probability
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Calculated Conditional Probabilities
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LP for the super-component
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Calculated Bounds for Super-Component

• The failure probability of sub-component in terms
  of defined system event
• (AUBUCUDUE) ? (0.3815328 0.4315) interval.

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LP Formulation for Entire System
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Calculated Conditional Probabilities
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LP Formulation for Entire System
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Calculated Bounds for Entire System

• The failure probability of entire
  telecommunication system in terms of defined
  system event
• (A1UB1UC1UD1UE1) ? (0.571007 0.6745) interval.

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Conclusion

• This means in general, the working condition of
  the whole telecommunication system varies from
  100 working condition 57-67 in time
• Or
• The working condition of the whole
  telecommunication system varies from 100 working
  condition 34-40 minutes in one hour.

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RECOMMENDATIONS for FUTURE WORK

• To get failure probability of the entire system
  by use of Simulation
• To do sensitivity analysis and find out the
  weakest component (station) in this system.

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References

• A.D.Kiureghian, Junho Song, Multi-scale
  Reliability Analysis and Updating of Complex
  Systems by Use of Linear Programming 2005
• Arnljot Hoyland, Marvin Rausand, System
  Reliability Theory 1994
• Richard A. Johnson, Miller Freunds Probability
  Statistics for Engineers 1994
• Tigran Ghazaryan, thesis work Availability,
  Reliability and Maintainability of the power
  supply system of the Telecommunication Company ,
  Yerevan, 2006.
• Sheldon M. Ross Introduction to probability and
  statistics for engineers and scientists 1987
• E. E. Lewis Reliability engineering 1996

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Thank You