# An expert-based approach to production performance analysis of oil and gas facilities considering time-independent Arctic operating conditions

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## Abstract

The availability and throughput of offshore oil and gas plants operating in the Arctic are adversely influenced by the harsh environmental conditions. One of the major challenges in quantifying such effects is lack of adequate life data. The data collected in normal-climate regions cannot effectively reflect the negative effects of harsh Arctic operating conditions on the reliability, availability, and maintainability performance of the facilities. Expert opinions, however, can modify such data. In an analogy with proportional hazard models, this paper develops an expert-based availability model to analyse the performance of the plants operating in the Arctic, while accounting for the uncertainties associated with expert judgements. The presented model takes into account waiting downtimes and those related to extended active repair times, as well as the impacts of operating conditions on components’ reliability. The model is illustrated by analysing the availability and throughput of the power generation unit of an offshore platform operating in the western Barents Sea.

## Keywords

Reliability, availability and maintainability analysis (RAM) Throughput Expert opinions Failure and repair rate Arctic operating conditions Oil and gas## Abbreviations

- CDF
Cumulative distribution function

- DM
Decision maker

- FTTF
First time to failure

- GEN
Generator

- GT
Gas turbine

- MC
Monte Carlo

- MTTF
Mean time to failure

- MTTR
Mean time to repair

- O&G
Oil and gas

- ORDA
Offshore reliability data

Probability density function

- PHM
Proportional hazard model

- RAM
Reliability, availability, and maintainability

- TR
Train

- TTF
Time to failure

- TTR
Time to repair

## List of symbols

*E*Degree of increase in MTTR of a component operating in an Arctic location. In other words, component MTTR increases by a factor of (1 +

*E*). In*E*_{ i }, subscript*i*refers to component*i**E*′Time-independent factor by which component active repair rate is decreased due to the effects of Arctic operating conditions on maintenance crew performance

- \(F_{i,E}^{DM} (\varepsilon )\)
Decision maker’s CDFs of random variables

*E*(i.e., the degree of increase in a component’s MTTR) corresponding to component*i*- \(F_{{i,\Delta }}^{DM} (\delta )\)
Decision maker’s CDF of random variable Δ (i.e., the degree of reduction in a component’s MTTF) corresponding to component

*i*- \(F_{TDT}^{(A)} (t)\)
The CDF of total downtimes, including active repair times and waiting downtimes, corresponding to a component, whose repair is performed under Arctic operating environment

- \(F_{TTF}^{(B)} (t)\)
Failure probability function of a component operating in the base area. In \(F_{TTF}^{(A)} (t)\), superscript

*A*refers to the Arctic- \(F_{TTR}^{(A)} (t)\)
CDF of active TTRs of a component in the Arctic offshore

- \(F_{WDT} (t)\)
CDF of waiting downtimes

- \(F_{\varPhi }^{DM} (\psi )\)
Decision maker’s CDF of unknown random variable

*Φ*- \(F_{\varPhi }^{j} (\psi )\)
Expert

*j*’s CDF of unknown random variable*Φ**m*Mean of the natural logarithm of

*WDT*s**m**Vector of the means of normal distributions fitted to experts’ data

*m*′Mean of the lognormal distribution of

*WDT*s, \(F_{WDT} (t)\)*m*_{j}Mean of the normal distribution fitted to the data given by expert

*j**m*^{DM}Mean of DM’s distribution obtained by Bayesian aggregation of experts’ distributions

*MTTF*_{B}Mean time to failure of a component operating in the base area. In

*MTTF*_{ A }, subscript*A*refers to the Arctic*MTTR*_{B}MTTR of a component operating in the base area. In

*MTTR*_{ A }, subscript*A*refers to the Arctic*N*_{C}Total number of system components

*N*_{e}Total number of experts

*N*_{s}^{1}Number of required samples drawn from DM’s CDFs \(F_{{i,\Delta }}^{DM} (\delta )\) and \(F_{i,E}^{DM} (\varepsilon )\) to effectively represent uncertainties in system availability and throughput results

*N*_{s}^{2}Number of required samples drawn from waiting downtime and active repair distributions to form the distribution of total downtime

*PGS*_{s}Power generation scenario

*s**TDT*Total downtime corresponding to each corrective maintenance task, which includes both waiting downtime and active repair time

*TTR*Active time to repair

*w*_{j}Expert

*j*’s weighting factor*WDT*Waiting downtime corresponding to each corrective maintenance task

*y*_{j}Experience of expert

*j*in years*β*_{B}Shape parameter of a Weibull failure probability function of a component operating in the base area. In

*β*_{ A }, subscript*A*refers to the Arctic*Δ*Degree of reduction in MTTF of a component in an Arctic location. In other words, component MTTF reduces by a factor of (1 −

*Δ*). In*Δ*_{ i }, subscript*i*refers to component*i**Δ*′Time-independent factor by which component failure rate increases due to the effects of operating environment

*ζ*_{1}A random number drawn from uniform distribution over (0, 1)

*ζ*_{2}A random number drawn from uniform distribution over (0, 1)

*η*_{B}Scale parameter of a Weibull failure probability function of a component operating in the base area. In

*η*_{ A }, subscript*A*refers to the Arctic*λ*_{B}(*t*)Weibull failure rate of a component operating in the base area. In

*λ*_{ A }(*t*), subscript*A*refers to the Arctic*μ*_{B}Active repair rate of a component operating in the base area.

*μ*_{ B }refers to the active TTRs and excludes other waiting downtimes. In*μ*_{ A }, subscript*A*refers to the Arctic*ρ*_{jk}Correlation coefficient of the data given by experts

*j*and*k**σ*Standard deviation of the natural logarithm of

*WDT*s*σ*′Standard deviation of the lognormal distribution of

*WDT*s,*F*_{ WDT }(*t*)*σ*_{j}Standard deviation of the normal distribution fitted to the data given by expert

*j**σ*^{DM}Standard deviation of DM’s distribution obtained by Bayesian aggregation of experts’ distributions

**Σ**Covariance matrix representing the correlation among experts

- \(\{ \varDelta_{ji,5\% } ,\varDelta_{ji,50\% } ,\varDelta_{ji,95\% } \}\)
The 5th, 50th, and 95th quantiles of the degree of reduction in MTTF of component

*i*, given by expert*j*- \(\{ E_{ji,5\% } ,E_{ji,50\% } ,E_{ji,95\% } \}\)
The 5th, 50th, and 95th quantiles of the degree of increase in MTTR of component

*i*, given by expert*j*

## Notes

### Acknowledgments

The authors would like to thank the anonymous experts for their participation in this study.

## References

- Ansell JI, Philipps MJ (1997) Practical aspects of modelling of repairable systems data using proportional hazards models. Reliab Eng Syst Saf 58:165–171. doi: 10.1016/S0951-8320(97)00026-4 CrossRefGoogle Scholar
- Artiba A, Riane F, Ghodrati B, Kumar U (2005) Reliability and operating environment-based spare parts estimation approach: a case study in Kiruna Mine. Swed J Qual Maint Eng 11:169–184CrossRefGoogle Scholar
- Barabadi A, Markeset T (2011) Reliability and maintainability performance under Arctic conditions. Int J Syst Assur Eng Manag 2:205–217. doi: 10.1007/s13198-011-0071-8 CrossRefGoogle Scholar
- Barabadi A, Barabady J, Markeset T (2011a) Maintainability analysis considering time-dependent and time-independent covariates. Reliab Eng Syst Saf 96:210–217. doi: 10.1016/j.ress.2010.08.007 CrossRefGoogle Scholar
- Barabadi A, Barabady J, Markeset T (2011b) A methodology for throughput capacity analysis of a production facility considering environment condition. Reliab Eng Syst Saf 96:1637–1646. doi: 10.1016/j.ress.2011.09.001 CrossRefGoogle Scholar
- Barabadi A, Gudmestad OT, Barabady J (2015) RAMS data collection under Arctic conditions. Reliab Eng Syst Saf 135:92–99. doi: 10.1016/j.ress.2014.11.008 CrossRefGoogle Scholar
- Bedford T, Cooke R (2001) Probabilistic risk analysis: foundations and methods. Cambridge University Press, CambridgeCrossRefGoogle Scholar
- Clemen RT, Winkler RL (1999) Combining probability distributions from experts in risk analysis. Risk Anal 19:187–203Google Scholar
- Clemen RT, Winkler RL (2007) Aggregating probability distributions. In: Edwards W, Miles RF Jr, Von Winterfeldt D (eds) Advances in decision analysis: from foundations to applications. Cambridge University Press, Cambridge, pp 154–176CrossRefGoogle Scholar
- Cooke RM (1991) Experts in uncertainty: opinion and subjective probability in science. Oxford University Press, OxfordGoogle Scholar
- Dale CJ (1985) Application of the proportional hazards model in the reliability field. Reliab Eng 10:1–14. doi: 10.1016/0143-8174(85)90038-1 CrossRefGoogle Scholar
- Dubi A (2000) Monte Carlo applications in systems engineering. Wiley, ChichesterGoogle Scholar
- French S (1985) Group consensus probability distributions: a critical survey. In: Bernardo JM, Groot MHD, Lindley DV, Smith AFM (eds) Bayesian statistics. Elsevier, North Holland, pp 183–201Google Scholar
- Gao X, Barabady J, Markeset T (2010) An approach for prediction of petroleum production facility performance considering Arctic influence factors. Reliab Eng Syst Saf 95:837–846. doi: 10.1016/j.ress.2010.03.011 CrossRefGoogle Scholar
- Genest C, McConway KJ (1990) Allocating the weights in the linear opinion pool. J Forecast 9:53–73. doi: 10.1002/for.3980090106 CrossRefGoogle Scholar
- Genest C, Zidek JV (1986) Combining probability distributions: a critique and an annotated bibliography. Stat Sci 1:114–135CrossRefMathSciNetGoogle Scholar
- Gudmestad OT, Karunakaran D (2012) Challenges faced by the marine contractors working in western and southern Barents Sea. Paper presented at the OTC Arctic technology conference, Houston, Texas, USA, 3–5 DecemberGoogle Scholar
- ISO (2001) ISO 12494: atmospheric icing of structures. ISO, GenevaGoogle Scholar
- ISO (2010) ISO 19906: petroleum and natural gas industries—Arctic offshore structures. ISO, GenevaGoogle Scholar
- Jardine A, Anderson P, Mann D (1987) Application of the Weibull proportional hazards model to aircraft and marine engine failure data. Qual Reliab Eng Int 3:77–82CrossRefGoogle Scholar
- Kumar D, Klefsjö B (1994) Proportional hazards model: a review. Reliab Eng Syst Saf 44:177–188. doi: 10.1016/0951-8320(94)90010-8 CrossRefGoogle Scholar
- Labeau PE, Zio E (2002) Procedures of Monte Carlo transport simulation for applications in system engineering. Reliab Eng Syst Saf 77:217–228. doi: 10.1016/S0951-8320(02)00055-8 CrossRefGoogle Scholar
- Løset S, Shkhinek K, Gudmestad OT, Strass P, Michalenko E, Frederking R, Kärnä T (1999) Comparison of the physical environment of some Arctic seas. Cold Reg Sci Technol 29:201–214. doi: 10.1016/S0165-232X(99)00031-2 CrossRefGoogle Scholar
- Mannan S (2014) Lees’ process safety essentials: hazard identification, assessment and control. Butterworth-Heinemann, Oxford. doi: 10.1016/B978-1-85617-776-4.00004-X Google Scholar
- Meyer MA, Booker JM (1991) Eliciting and analyzing expert judgement—a practical guide. Academic Press, London. doi: 10.1137/1.9780898718485 Google Scholar
- Morris PA (1977) Combining expert judgments: a Bayesian approach. Manag Sci 23:679–693CrossRefzbMATHGoogle Scholar
- Mosleh A, Apostolakis G (1986) The assessment of probability distributions from expert opinions with an application to seismic fragility curves. Risk Anal 6:447–461CrossRefGoogle Scholar
- Mosleh A, Bier VM, Apostolakis G (1987) Methods for the elicitation and use of expert opinion in risk assessment: phase 1, a critical evaluation and directions for future research (NUREG/CR-4962). U.S. Nuclear Regulatory Commission, Washington DCGoogle Scholar
- Murthy DNP, Xie M, Jiang R (2004) Weibull models. Wiley, New JerseyzbMATHGoogle Scholar
- Naseri M, Barabady J (2013) Offshore drilling activities in Barents Sea: challenges and considerations. Paper presented at the proceedings of the 22nd international conference on port and ocean engineering under Arctic conditions (POAC), Espoo, Finland, 9–13 JuneGoogle Scholar
- Naseri M, Barabady J (2015) Reliability analysis of Arctic oil and gas production plants: accounting for the effects of harsh weather conditions using expert data. J Offshorr Mech Arct Eng (under review)Google Scholar
- OREDA Participants (2009) Offshore reliability data handbook, 5th edn. OREDA Participants, TrondhimGoogle Scholar
- Pilcher JJ, Nadler E, Busch C (2002) Effects of hot and cold temperature exposure on performance: a meta-analytic review. Ergonomics 45:682–698CrossRefGoogle Scholar
- Podofillini L, Dang VN (2013) A Bayesian approach to treat expert-elicited probabilities in human reliability analysis model construction. Reliab Eng Syst Saf 117:52–64. doi: 10.1016/j.ress.2013.03.015 CrossRefGoogle Scholar
- Pulkkinen U (1993) Methods for combination of expert judgements. Reliab Eng Syst Saf 40:111–118. doi: 10.1016/0951-8320(93)90101-4 CrossRefGoogle Scholar
- Rausand M, Høyland A (2004) System reliability theory: models, statistical methods, and applications, vol 396. Wiley, HobokenGoogle Scholar
- Rufo MJ, Pérez CJ, Martín J (2012) A Bayesian approach to aggregate experts’ initial information. Electron J Stat 6:2362–2382CrossRefMathSciNetzbMATHGoogle Scholar
- Stapelberg RF (2009) Handbook of reliability, availability, maintainability and safety in engineering design. Springer, New YorkzbMATHGoogle Scholar
- Winkler RL (1981) Combining probability distributions from dependent information sources. Manag Sci 27:479–488CrossRefzbMATHGoogle Scholar
- Zio E (2013) The Monte Carlo simulation method for system reliability and risk analysis. Springer, LondonCrossRefGoogle Scholar