system safety - m10 combinatorial failure probability ... · introduction 1 introduction 2 overview...

System SafetyM10 Combinatorial Failure Probability Analysis V1.0

Matthew Squair

UNSW@Canberra

15 October 2015

1 Matthew Squair M10 Combinatorial Failure Probability Analysis V1.0

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1 Introduction

2 Overview

3 Methodology

4 Limitations, advantages and disadvantages

5 Conclusions

6 Further reading


Introduction

1 Introduction

2 Overview

3 Methodology


5 Conclusions

6 Further reading


Introduction

Learning outcomes

Understand the need for a combinatorial probability method for qualitativeprobability estimates

Be able to describe and illustrate the rules for construction

Understand the strengths and weaknesses of the method


Overview

1 Introduction

2 Overview

3 Methodology


5 Conclusions

6 Further reading


Overview

Overview

“To avoid paralysis resulting from waiting for definitive data, weassume we have greater knowledge than scientists actually possessand make decisions based on those assumptions.”

— William Ruckleshaus


Overview

Origins

Developed for the System Effectiveness and Safety Technical Committeeof the American Institute of Aeronautics and Astronautics

Where we only have subjective estimates of probability measured on anordinal scale, how can we deal with combined probabilities of contributingevents?

Often we have more confidence in our estimates of contributors than ofthe top event alone

This technique was developed to address this problem


Overview

Key definitions

Ordinal scale. The ordinal scale allows for rank ordering of data which inturn allows it to be sorted. The scale does not allow for relative differencesbetween the data values. Mathematical operations cannot be carried outon ordinal values. Subjective probability (likelihood) is an ordinal scaledvalue

Ratio scale. A ratio scale possesses a meaningful (unique andnon-arbitrary) zero value which allows us to express ratio (A is twice aslikely as B) and all mathematical operations are allowed. Quantitativeprobability is a ratio scaled value


Overview

Combinatorial analysis and the system lifecycle


Methodology

1 Introduction

2 Overview

3 Methodology


5 Conclusions

6 Further reading


Methodology

Methodology

1 Arbitrary probability (likelihood) values (dimensionless numbers) havebeen assigned to the probability steps of MIL-STD-882 to convert theordinal scale into a synthetic ratio scale

2 Subjective probabilities (likelihood) of contributor events/conditionsare estimated as usual, using the MIL-STD-882 scale as a guide

3 Probability values corresponding to the estimates are usedcombinatorially, as in the classical numerical methods

4 The probability value for the combined result is then re-translatedinto the subjective scale of MIL-STD-882


Methodology Probability values

Establishing likelihood for union under OR gates

The values selected are dimensionless with NO quantitative significance

Selected to provide a consistent decadal increment between adjacentvalues and thresholds

As a result for the Union set of ei events UOR(e)

∆PUOR(e)=

{0 if | UOR(e) 6 2,

1 if | UOR(e) |> 2(1)


Methodology Probability values

Establishing probability for union under AND gates

And for the Union set of events ei, UAND(e) at the highest level of the scalethe schema ensures that:

∆PUAND(e)=

{0 if | UAND(e) |6 2,

−1 if | UAND(e) |> 2(2)

Common exposure durations

A duration of exposure must still be defined for these combinatorialcalculations, and the exposures durations must be consistent acrossinitiating events


Methodology Probability values scale definition

AIAA/SESTC defined value scale

Figure: AIAA/SESTC combinatorial value scale [Clements 1993]


Methodology Example

Confined space example [Clements 1993]

Example

Problem. A confined space is equipped with forced ventilation and contains an inert gassystem. No history of inert gas leaks but many connections and threaded fittings

The confined space is regularly entered. An O2 detector and alarm system ispermanently installed, has battery backup and is regularly maintained and tested. Thesystem has been found inoperable several times over a 10 year period, but recentrefurbishments are thought to have fixed it

Using engineering judgement assign probability values to each factor an evaluate the

probability of an unannunciated life threatening atmosphere exposure for the coming

year


Methodology Example

Confined space example (cont’d)


Methodology Example

Confined space example (cont’d)

Given the three events must occur these probabilities are combined underan AND gate

Pc = P1 × P2 × P3

= (3× 10−1)× (3× 10−2)× (3× 10−3)

= (2.7× 10−5)

The combined probability (2.7× 10−5) corresponds to a qualitative level ofE or ”Improbable”. The overall probability may be judged to be at thatlevel with the same confidence that we assigned the lower level probabilities


Methodology Example

Subjective fault trees

The combinatorial probability method can be applied to fault trees forwhich we have subjective estimates of the leaf node probabilities.Methodology:

1 Develop fault tree

2 Evaluate and derive the minimum cut sets

3 Assign subjective probabilities to leaf nodes

4 Translate subjective probabilities to probability values

5 Calculate likelihood of TLE as per standard probability theory

6 Transform P(TLE) back into subjective probability


Limitations, advantages and disadvantages

1 Introduction

2 Overview

3 Methodology


5 Conclusions

6 Further reading



Limitations of the method

A set of subjective estimates generates a subjective result, if a quantitativeanalysis is required it needs to use quantitative data

Combinatorial probability is not magic

This method cannot confer less uncertainty upon the final result than isthe uncertainty of judgment for the ingoing contributor likelihoods



Advantages of the method

Advantages of the method are

We can apply this technique without quantitative data

We can apply this during the early concept definition phases

Allows us to utilise component estimates of failure

A good adjunct technique for the PHA

Allows us to construct ’qualitative/subjective’ fault trees

Useful for risk based concept design



Disadvantages of the method

Disadvantages of the method are

This remains a subjective estimate

The numerical ordinal scale can be mis-interpreted


Conclusions

1 Introduction

2 Overview

3 Methodology


5 Conclusions

6 Further reading


Conclusions

Conclusions

Combinatorial failure probability analysis is a useful adjunct techniqueduring the early concept definition phases of the project, but if you havereal quantitative data use it


Further reading

Bibliography

[Clements 1993] Clements, P., (1993) Combinatorial Failure Probability Analysis usingMIL-STD-882C, 5th Ed., Oct 1993, Sverdrup.

[MIL-STD-882C 1993] Standard Practice for System Safety (1993) US Dept of DefenseStandard MIL- STD-882C, 19 January 1993.


system safety - m10 combinatorial failure probability ... · introduction 1 introduction 2 overview...

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