Leak frequency analysis for hydrogen-based technology using bayesian and frequentist methods

Barua, S., Basyouny, K., Islam, MT., 2014. A full Bayesian multivariate count data model of collision severity

with spatial correlation. Anal Methods Accid Res, 2014; 3-4:28–43.

Bedrick, J., Christensen, R., Johnson, W., 2017. A new perspective on priors for generalized linear models. J. Am.

Stat. Assoc. 1996; 91(436):1450–1460, http://www.jstor.org/stable/2291571/; [accessed September 2017].

Casamirra, M., Castiglia, F., Giardina, M., Lombarado, C., 2009. Safety studies of a hydrogen refueling station:

Determination of the occurrence frequency of the accidental scenarios, International Journal of Hydrogen

Energy, Vol. 34, pp. 5846-5854.

Redbook Dutch Model, 1997. Methods for determining and processing probabilities, Committee for the

Prevention of Disasters (CPR 12E), The Hague, The Netherlands.

Gheriani, M., Khan, F., Chen, D., Abbassi, R., 2017. Major accident modelling using spare data, Process Safety

and

Environmental

Protection,

Volume

14

106,

Pages

52-59,

ISSN

0957-5820,

https://doi.org/10.1016/j.psep.2016.12.004.

International Energy Agency (IEA), Technology Roadmap Hydrogen and Fuel Cells, 2015.

Japan

Hydrogen

Fuel

Cell

Demonstration

Project

(JHFC),

http://www.jari.or.jp/portals/0/jhfc/station/index.html; [accessed September 2017].

Japan Hydrogen and Fuel Cell Demonstration Project (JHFC Phase2), 2011.

http://www.jari.or.jp/Portals/0/jhfc/data/report/pdf/tuuki_phase2_01.pdf

Japan Nuclear Technology Institute (JNTI). Estimation of domestic general equipment failure rate considering

uncertainty

of

failure

counts

(1982~2002,

for

21

years,

49

plants

data),

http://www.genanshin.jp/archive/failure_rate/; March 2009 [accessed September 2017].

Japan Nuclear Technology Institute (JNTI). Estimation of domestic general equipment failure rate considering

uncertainty

of

failure

counts

(1982~2010,

for

29

years,

56

plants

data),

http://www.genanshin.jp/archive/failure_rate/; June 2016 [accessed September 2017].

Jones, N., 1984. A Schematic Design for a HAZOP Study on a Liquid Hydrogen Filling Station.

International

Journal of Hydrogen Energy, Vol. 9, pp. 115-121.

Khalil, Y., 2017. A probabilistic visual-flowcharting-based model for consequence assessment of fire and

explosion events involving leaks of flammable gases. Journal of Loss Prevention in the Process Industries

50 (2017) 190–204.

Kikukawa, S., Mistuhashi, H., Miyake, A., 2009. Risk assessment for liquid hydrogen fueling stations.

International Journal of Hydrogen Energy, Vol. 34, pp. 1135-1141, 2009.

Kodoth, M., Aoyama S., Sakamoto, J., Kasai, N., Shibutani, T., Miyake, A., 2018. Evaluating uncertainty in

accident rate estimation at hydrogen refueling station using time correlation model, International Journal

of

Hydrogen

Energy,

Volume

43,

Issue

52,

2018,

Pages

23409-23417,

ISSN

0360-

3199,https://doi.org/10.1016/j.ijhydene.2018.10.175.

Kodoth, M., Khalil, Y., Shibutani, T., Miyake, A., 2019. Verification of appropriate life parameters in risk and

reliability quantifications of process hazards, Process Safety and Environmental Protection, 2019, ISSN

0957-5820, https://doi.org/10.1016/j.psep.2019.05.021.

Kubo, T., 2012. Introduction to statistical modeling for data analysis (generalized linear model, hierarchical

Bayesian model, Markov chain Monte Carlo method). Tokyo: Iwanami; 2012.

LaChance, J., Houf, W., Middleton, B., Fluer, L., 2009. Analyses to support development of risk-informed

separation distances for hydrogen codes and standards. SAND2009-0874 Sandia National Laboratories;

2009. http://prod.sandia.gov/techlib/access-control.cgi/2009/090874.pdf; [accessed September 2017].

Markowski, A., Siuta, D., 2017. Selection of representative accident scenarios for major industrial accidents,

Process Safety and Environmental Protection, Volume 111, Pages 652-662, ISSN 0957-5820,

https://doi.org/10.1016/j.psep.2017.08.026.

Ministry of Economy, Trade and Industry (METI). 2015. The condition of reviewing regulations corresponding

to

the

demand

of

new

era

(related

to

hydrogen

and

fuel

cell

vehicle),

http://www.meti.go.jp/committee/sankoushin/hoan/koatsu_gas/pdf/007_05_01.pdf; March 2015 [accessed

September 2017].

15

Ministry of Economy, Trade and Industry (METI). 2016. The project for investigating measures of promoting

non-fossil energy introduction (formulating technological regulation of high-pressure gas for safe spread

of

new

energy

technologies),

(3)

Overseas

survey,

http://www.meti.go.jp/meti_lib/report/2016fy/000124.pdf; March 2016 [accessed September 2017].

Nakayama, J., Sakamoto, J., Kasai, N., Shibutani, T., Miyake, A., 2016. Preliminary hazard identification for

qualitative risk assessment on a hybrid gasoline-hydrogen fueling station with an on-site hydrogen

production system using organic chemical hydride. International Journal of Hydrogen Energy, Vol. 41, pp.

7518-7525.

Nelson, W., 2000. Theory and Applications of Hazard Plotting for Censored Failure Data, Technometrics, Vol. 42,

No. 1, pp. 12–25.

NIST/SEMATECH, 2012. E-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/,April

2012.

Ntzoufras, I., 2009. Bayesian Modeling Using WinBUGS. John Wiley & Sons, Inc., Hoboken, NJ, USA, January

2009.

Pasman, H., Rogers, W., 2012. Risk assessment Risk assessment by means of Bayesian networks: A comparative

study of compressed and liquefied H2 transportation and tank station risks. International Journal of

Hydrogen Energy, Vol. 37, pp. 17415-17425, 2012.

Sakamoto, J., Sato, R., Nakayama, J., Kasai N., Tadahiro, S., Miyake, A., 2016. Leakage-type-based analysis of

accidents involving hydrogen fueling stations in Japan and USA. Int. J. Hydrogen Energy, 2016;

41(46):21564–21570.

Sato, R., Nakayama, J., Sakamoto, J., Kasai, N., Shibutani, T., Miyake, A., 2016. Investigation of hydrogen

leakage from joint part in hydrogen stand. The Collection of Presentation Papers at the Mechanical

Engineering Congress 2016 Japan.

The California Energy Commission (CEC), 2004. Technical Consultant Report on Failure Modes and Effects

Analysis for Hydrogen Fueling Options. CEC-600-2005-001, Nov 2004.

The High Pressure Gas Safety Institute of Japan (KHK), 2012. The high-pressure gas incidents database,

https://www.khk.or.jp/english/accident_reports.html; [accessed Feb 2017].

The High Pressure Gas Safety Institute of Japan, 2015. Notes on Accidents related to Hydrogen Refueling Stations,

2015 (in Japanese).

Yamada, T., Kobayashi, H., Akatsuka, H., Hamada, K., 2015. Analysis of high-pressure gas incidents in hydrogen

fueling stations. J High Press Gas Safety Institute Japan, 52 (10) (2015), pp. 23-29 [in Japanese].

Yang, M., Khan, F., Lye, L., 2013. Precursor-based hierarchical Bayesian approach for rare event frequency

estimation: A case of oil spill accidents. Process Safety and Environmental Protection, Volume 91, Issue 5,

Pages 333-342, ISSN 0957-5820, https://doi.org/10.1016/j.psep.2012.07.006.

16

Appendix

Appendix A. Detailed explanation of estimation using a log-normal time function

This appendix gives a detailed explanation of Section 3.2.1. In order to calculate accident rate over time,

each parameter in Eq. (2) is estimated to describe the accident data. In Eq. (2), parameters a, σ, and μ are

considered random variables. Bayesian statistics estimate a parameter’s value by updating its distribution by

some data; thus, each parameter is first given prior distribution. If prior information is available about these

parameters, the prior distribution reflects this information and is usually called “informative prior” (e.g.,

(Bedrick, 1996)). In contrast, when there is no prior information, prior distribution with little information

(e.g., normal distribution with mean zero and variance 104) is used as a “non-informative prior.” In this case,

no prior information is available, and thus, a non-informative prior is used.

The value for each parameter was estimated using the Bayesian statistics supporting software WinBUGS.

To calculate the posterior distribution by updating the prior distribution with the accident data, WinBUGS

uses Markov Chain Monte Carlo simulation, and it needs an initial value for each parameter. An appropriate

initial value was chosen by judgement or automatically selected by software, and it was checked for

calculation errors.

For this estimation, the following Bayesian model is introduced. Note that other methods such as least

squares fitting can also suffice and so there is no special reason to use the Bayesian model. However, using

the Bayesian model often enables complex modeling and utilization of other information in addition to the

observed data. The time-series accident rate is described by following logical relationship:

 ln t j  

j  a

exp 

2 2

2  t j

2 

(A1)

where,

𝜆𝑗 : expected value of accident rate for the jth month

a: coefficient

σ, μ: parameters of the log-normal function

tj: jth operation time

j: index of the operation time

Each month’s accident rate is considered as a random variable following the log-normal distribution below:

λj ~ LN(μ2, j,τ)

(A2)

where,

λj: accident rate of the jth operation time tj

LN(μ2, j,τ): log-normal distribution with mean μ2, j and inverse square of standard deviation τ

µ2, j: expected value of the log-normal distribution of the accident rate for the jth operation month

17

τ: inverse square of the standard deviation of the log-normal distribution

To connect Eq. (A1) and (A2), the relation between parameter µ2, j and the expected value of accident rate

𝜆𝑗 is utilized as follows:

 2, j  ln  j  

2

(A3)

Prior distribution (“non-informative prior”) of each parameter is set as follows:

a ~ Gamma(1,1)

τ ~ Gamma(1,1)

σ ~ Unif (0,10)

μ ~ Unif (0,10)

where,

Gamma(a,b): gamma distribution with shape parameter a and rate parameter b

Unif (a,b): uniform distribution with lower bound a and upper bound b

Using this statistical model and the accident data, the accident rate was estimated as shown in Fig. 4.

Appendix B. Detailed explanation of estimation using a Weibull time function

This appendix gives a detailed explanation of Section 3.2.2. It differs from Appendix A in its description of

the time-series accident rate and each parameter’s prior distribution and initial value, but the flow of

modeling and estimation are virtually the same as in Appendix A. Firstly, the time-series accident rate is

described by following logical relationship:

   t j

 j  a 

   

 1

 t

exp  

 



(B1)

where,

𝜆𝑗 : expected value of the accident rate for the jth month

a: coefficient

α, β: parameters of the Weibull function

tj: jth operation time

j: index of the operation time

Each month’s accident rate is considered as a random variable following the log-normal distribution below:

λj ~ LN(μ2, j,τ)

(B2)

where,

λj: accident rate of operation time tj

LN(μ,τ): log-normal distribution with mean μ and inverse square of standard deviation τ

µ2, j: expected value of the log-normal distribution of accident rate for jth operation month

18

τ: inverse square of the standard deviation of the log-normal distribution

To connect Eq. (B1) and (B2), the relation between parameter µ2, j and the expected value of accident rate

𝜆𝑗 is utilized as follows:

 2, j  ln  j  

2

(B3)

Prior distribution (“non-informative prior”) of each parameter is set as follows:

a ~ Gamma(1,0.00001)

α ~ Gamma(0.1,0.00001)

β ~ Gamma(0.1,0.00001)

τ ~ Gamma(1,0.00001)

where,

Gamma(a,b): gamma distribution with shape parameter a and rate parameter b

Using this statistical model and the accident data, the accident rate was estimated, as shown in Fig. 5.

19

...