Simulating System Reliability using Monte Carlo Simulation - - PowerPoint PPT Presentation

Presented by:

Justin Willette

Simulating System Reliability using Monte Carlo Simulation

15 October 2013

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Table of Contents

• System Reliability
• Reliability Block Diagrams
• Structure Function
• Calculating System Reliability
• Simulating System Reliability
• Simulation Demonstration

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• Systems are comprised of multiple components specifically arranged for a

design.

• If component reliabilities are known, or reasonably estimated, the

reliability of the system can be estimated with certain confidence.

• This estimate is based on the component configuration, laws of

probability, and key assumptions.

System Reliability

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• The first step in estimating the system reliability is to create a Reliability

Block Diagram (RBD)

• A RBD is a graphical representation of the components of a system and

how they are related to each other in the system

Reliability Block Diagrams

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• Each complete RBD is unique to its design
• RBD’s can be in several different arrangements
• Series
• Parallel
• Complex

B A D C

Reliability Block Diagrams

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• Reduce the RBD into:

– a parallel arrangement of series subsystems OR – a series arrangement of parallel subsystems

RBD

1 3 4 2 2 5 4 1 2 1 3 5 4 2 4 5

Simplifying RBD’s

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• Assumptions:

– A component can only exist in 2 states – Functioning or Failed – Component failures are statistically independent

• Definition:

– The state of component i, denoted by xi, is: 0 if component i has failed 1 if component i is functioning for i = 1, 2, … n

• The structure function, φ(x), relates the state of the system to the states of its

individual components 0 if the system has failed when the state vector is x 1 if the system is functioning when the state vector is x



i

x

  ) (

i

x

Structure Function

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Minimal Path Set: Where s is the number of minimal path sets

) 1 ( 1 ) (

1

 

 

   

s j P i i i

j

x x

RBD

Minimal Cut Set: Where k is the number of minimal cut sets

 

 

           

k j C i i i

j

x x

1

) 1 ( 1 ) ( ) 1 )( 1 )( 1 ( 1 ) (

5 2 4 3 2 4 1

x x x x x x x xi       ) 1 )( 1 )( 1 )( 1 ( ) (

4 2 5 3 1 5 4 2 1

x x x x x x x x x xi      

Calculating the structure function

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• Using the structure function:

Cut Method ≤ Actual Reliability ≤ Path Method ≤ R(S) ≤

• Calculating the actual reliability

– Decomposition also known as the Keystone Method = +

 

 

         

k j C i i

j

p

1

) 1 ( 1

) 1 ( 1

1

 

 

 

s j P i i

j

p

1 2 3 4 1 2 3 4 1 2 3 4

Calculating the System Reliability

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• Software

– Standard Microsoft Excel – VBA programming within Excel – Reliasoft – Raptor

Simulating System Reliability

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• Benefits of using VBA code

– Reuse – More precise calculations – Less likelihood of errors – Simple interface with user – Ability to run a set number of iterations – Ability to lock cells from the user – Faster simulations – Can run on any computer with Microsoft Office

Simulating System Reliability

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• Information needed for simulation using VBA programming

– Reliability Block Diagram – Failure rate of each component (λ) – Operating time of the system (t) – Number of iterations to run

Reliability =

t

e 



Simulating System Reliability

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Simulation demonstration in Excel

Simulating System Reliability

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• VBA Programming reference

Helpful Reference

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• Simulating reliability of a system is preferred to demonstrating reliability

by testing

• Reliability Block Diagrams are specific to each system and must be

considered in order to produce accurate reliability simulations

• Reliability estimates are based on the component configuration, laws of

probability, and key assumptions

• Monte Carlo simulation in Excel is one way to predict a reasonable

estimate of the system reliability

• Using VBA Code is an effective way to run simulations in Excel

Conclusion

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Back-up Slides

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Simulating System Reliability

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Start button

Simulating System Reliability

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Simulating System Reliability

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Simulating System Reliability

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Simulating System Reliability

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Simulating System Reliability

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VBA Code

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