1

Estimation of An Event Occurrence for LOPA Studies

Randy Freeman S&PP Consulting Houston, TX 77041 713 408 0357 rafree@yahoo.com

2

Problem

Your LOPA team members tell you that the initiating event of concern has never happened in the history of the process unit. No bad events in 20 years. What do you do?

Ignore the event and move on – It can never happen

What else?

3

Available Methods to Handle Problem

Assume event has happened once, M1 = 1/N

Assume event has almost happened M2 = 1/2N

Bayesian Results M3 = 1/3N M4 = 1/4N

4

Methods (cont)

Poisson Arrivals of Failures At 90% limit

M5 = 0.105/N = 1/10N

At 10% limit M6 = 2.303/N

5

Methods (cont.)

Chi Square Confidence Limit (95%)

M7 = λ = χα;2 / (2 n) = 5.991/(2 n)

Chi Square Confidence Limit (50%)

M8 = λ = χα;2 / (2 n) = 1.3863/(2 n)

6

Methods (cont.)

Binomial Distribution

M9 = 1 – [0.9] 1/n

7

Methods (cont.)

Uniform Distribution Bayes Estimator

M10 = 1/(N+2)

8

Methods (cont.)

Hypothesis Test – Normal distribution with 95% confidence

M11 =

Zα = 1.6445

)( 2

2

α

α

znz+

9

Methods (cont.)

Explosive Initiation Test

M12 = 1 – [0.5]1/N

10

1.00E-03

1.00E-02

1.00E-01

1.00E+00

0 10 20 30 40 50 60 70 80 90 100

Nunber of Trials, N

Failu

re R

ate,

fail/

yr

. M1

M2M3M4M8M9M10

Legend

M3

Best Guess Methods

11

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

0 10 20 30 40 50 60 70 80 90 100

Number of Trials, N

Failu

re R

ate,

fail/

Yr

.

M5M6M7M11M12

Legend

M12

M5

M7

M6

M11

Confidence Limit Methods

12

13

Recommendations for Basic LOPA

Determine if the event of concern is physically possible. If not physically possible, delete from LOPA analysis

Make sure you have a minimum of 10 years of data. If not use values from LOPA book

Use M1 = 1/N for events found to be physically possible

14

Recommendations for Beyond Basic LOPA Reviews

Use estimators M3, M8 or M12.

M3 (Rule of 1/3N) is easier to remember and calculate.

15

Example – Case 1

Data No occurrences in three years What frequency should be assigned? Answer Since the history is less than 10

years, use the frequency presented in LOPA

book.

16

Example – Case 2

Data One occurrence in ten years What frequency should be assigned? Answer Methods presented in this paper do not apply when an event has occurred. Start with a frequency of 1/10 and review value in LOPA book.

17

Example – Case 3

Data No occurrences in ten years What frequency should be assigned? Answer Determine if history is “valid” Start with a frequency of 1/10 If LOPA at greater than order of

magnitude significance, use 1/30

18

Example – Case 4

Data No occurrences in 30 years What frequency should be assigned? Answer Determine if history is “valid” Start with a frequency of 1/10 If LOPA at greater than order of

magnitude significance, use 1/90

19

Example – Case 5

Data No occurrences in 20 years What frequency should be assigned? Answer Determine if history is “valid” No history of pump overpressure of PRV

PRV set P = 150 psig Pump Deadhead P = 100 psig

Not credible scenario – Delete from LOPA Study

Can it really happen?

We pressurize a vessel to 130 psig. The MAWP is 100 psig.

What happens?????

Does the vessel blow up????

20

21

More Information

Vessel in good condition per API 579 – Fitness for Service

Test Pressure = 1.5 * MAWP Test Pressure = 150 psig Piping is 2 inch schedule 40 with a

catastrophic burst pressure of 7000 psig

ANSI Class 150 Flanges with a MAOP of 285 psig at 100 F

22

ANSWER – NOTHING HAPPENS!

No rupture No weld tear No flange failure No release Nothing happens!

Maybe an ASME code violation

requiring an inspection for fitness for service

23

Lessons Learned

Before starting detailed LOPA analysis verify that the scenario of interest can actually happen.

Physics and Chemistry are powerful tools to sort out imaginary from real safety issues.

24

25

Conclusions

There is no single “correct answer” Use an estimator that is consistent

with the other assumptions in your LOPA study

26

Does the Audience Know of Another

Estimator??

More Details

“What to Do When Nothing Has Happened?”, pp 204- 211,Process Safety Progress, Vol. 30, No. 2, September 2011

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/prs.10463, 2011

27

28

QUESTIONS

????

Have a Merry Christmas!

29