A brief CV
Born: August 1. 1946
Nationality: Norwegian
Present position: Professor in mathematical statistics, with special responsibility for reliability, at the Section of Statistics and Insurance Mathematics, University of Oslo since 1986.
Academic degrees: Cand.real., University of Oslo 1970, Department of
Statistics and Insurance Mathematics. Ph.D., University of Sheffield 1976,
Department of Probability and Statistics. Thesis: A contribution to the theory of
birthanddeath queueing models.
Work experience: Associate professor, with special responsibility for reliability, at the Section of Statistics and Insurance Mathematics, University of Oslo 19811986. Adjunct appointment, Norwegian Computing Centre, 19982011.
Fields of interest and present research activities: Reliability theory, risk analysis, Bayesian methods, model evaluation, earthquake predictions, effects and side effects of medical drugs, risk and society.
Membership in academic and professional committees, scientific review work including peerreview, outreach activities, and other professional merits:
Memberships
Society of Reliability Engineers (VicePresident Scandinavian Chapter 1983–87).
Norwegian Statistical Association (President 1989–90).
Norwegian Actuarial Society.
Bernoulli Society.
International Statistical Institute (Elected member 1997).
Participant Pugwash Conferences on Science and World Affairs (Nobel peace
prize laureate 1995) 1988, 1990, 1994, 1996, 1997, 1999, 2011, 2015
(Chairman Norwegian Pugwash Committee since 1996).
Associate editor Methodology and Computing in Applied Probability since 1999.
Refereeing in altogether 33 international journals.
Held 45 invited lectures in 15 countries. For instance:
Invited organizer of and speaker at the reliability theory session at the 18 th
European Meeting of Statisticians, Berlin, DDR, August 1988.
Invited organizer of and speaker at the reliability theory session at the 48 th
Session, International Statistical Institute, Kairo, Egypt, September 1991.
Invited organizer of and speaker at the reliability theory session at the 16 th
Nordic Meeting of Statisticians, Lund, Sweden, August 1994.
International guests: 17 altogether.
Book: Multistate Systems Reliability Theory with Applications.
John Wiley & Sons (ISBN 9780470697504) 231 pages.
Papers: 65 published papers in international peer reviewed journals
out of which 39 papers were published in journals ranked as being in the best
class. 25 papers were in book chapters. The topics were mainly reliability theory,
queueing theory, Bayesian methods, biostatistics and, reliability and society.
Three invited contributions on queueing theory and reliability theory in the
Encyclopedia of Statistical Sciences.
Stays abroad:
Leverhulme European Visiting Fellow, University of Sheffield, October 1973–
July 1975.
Visiting Fellow, Operations Research Center, University of California, Berkeley, August 1980–March 1981.
Visiting professor, Department of Statistics, University of Warwick, Great Britain,
September 1994–February 1995.
Visiting professor, Statistical and Applied Mathematical Sciences Institute, North
Carolina, January–April 2003.
Some academic administrative positions:
Head Department of Statistics and Insurance Mathematics, 1987–1988, 20052008.
Dean, Faculty of Mathematics and Natural Sciences, 1990–1993.
Some administrative positions outside academia:
Board Member, Centre for Industrial Research, 1992.
Board Member, Norwegian Computing Centre, 1993–1996.
Observer, Norwegian Delegation to the UN General Assembly, 1998, 2001.
Chairman, The National Committee for Research Ethics in Science and
Technology, 2000–2005.
Board of congregations, Oslo,19821990.
Norwegian Church Parliament 1995, 1997.
Doctoral students presently under supervision:
Kristina Skutlaberg (Aalvik Eide). Discrete event simulation applied to the
analysis of multistate systems in reliability.
Long distance running:
Winner Norwegian championship in marathon 1970 and 25 km road race 1974,
30 km road race international against Sweden 1971, over 40 London marathon 1987.
Altogether 16 medals in Norwegian championships and 13 internationals
in long distance running. Participant European championship in marathon 1971.
Personal best marathon 2.17.02 London Marathon 1985.
Emneord:
Statistikk,
Stokastisk analyse/Finans  forsikring og risiko
Publikasjoner

Aarnes, Ole Johan; Reistad, Magnar; Breivik, Øyvind; BitnerGregersen, Elzbieta M.; Eide, Lars Ingolf; Gramstad, Odin; Magnusson, Anne Karin; Natvig, Bent & Vanem, Erik (2017). Projected changes in significant wave height toward the end of the 21st century: Northeast Atlantic. Journal of Geophysical Research  Oceans.
ISSN 21699275.
122(4), s 3394 3403 . doi:
10.1002/2016JC012521

Gåsemyr, Jørund Inge & Natvig, Bent (2017). Improved availability bounds for binary and multistate monotone systems with independent component processes. Journal of Applied Probability.
ISSN 00219002.
54(3), s 750 762 . doi:
10.1017/jpr.2017.32

Gåsemyr, Jørund Inge & Natvig, Bent (2017). NodeLevel Conflict Measures in Bayesian Hierarchical Models Based on Directed Acyclic Graphs, In Javier Prieto Tejedor (ed.),
Bayesian Inference.
INTECH.
ISBN 9789535135777.
Kapittel 2.
s 23
 37

Skutlaberg, Kristina & Natvig, Bent (2016). Minimization of the Expected Total Net Loss in a Stationary Multistate Flow Network System. Applied Mathematics.
ISSN 21527385.
7(8), s 793 817 . doi:
10.4236/am.2016.78071
Fulltekst i vitenarkiv.

Eisinger, Siegfried; Oliveira, Luiz F.; Tveit, Kristine & Natvig, Bent (2015). Safety instrumented systems operated in the intermediate demand mode, In Luca Podofillini; Bruno Sudret; Bozidar Stojadinovic; Enrico Zio & Wolfgang Kröder (ed.),
Safety and Reliability of Complex Engineered Systems.
CRC Press.
ISBN 9781138028791.
Artikkel.
s 4053
 4062

Huseby, Arne; Vanem, Erik & Natvig, Bent (2015). A new Monte Carlo method for environmental contour estimation, In Tomasz Nowakowski; Marek Mlynczak; Anna JodejkoPietruczuk & Sylwia WerbinskaWojciechowska (ed.),
Safety and Reliability : Methodology and Applications: Proceedings of the European safety and reliability Conference, ESREL 2014, Poland, 1418 september 2014.
Taylor & Francis.
ISBN 9781138026810.
Chapter 270.
s 2091
 2098
Vis sammendrag
Environmental contour estimation is an efficient and widely used method for identifying extreme conditions as a basis for e.g., ship design. Monte Carlo simulation is a flexible method for estimating such contours. A main challenge with this approach, however, is that extreme conditions typically correspond to events with low probabilities. Thus, in order to obtain satisfactory estimates, large numbers of simulations are needed. While these simulations can be carried out very fast, the analysis of the resulting data can be very timeconsuming. In the present paper we propose a new Monte Carlo method where only the extreme simulation results are stored and analyzed. This method utilizes the fact that an unbiased estimate of an environmental contour does not depend on the exact values of the nonextreme results. It is sufficient to know the number of such results. Probabilistic structural reliability analysis is performed to ensure that mechanical structures can withstand certain design loads. Obtaining precise environmental contours has become an important part of this analysis. The proposed method improves precision and speeds up calculations.

Huseby, Arne; Vanem, Erik & Natvig, Bent (2015). Alternative environmental contours for structural reliability analysis. Structural Safety.
ISSN 01674730.
54, s 32 45 . doi:
10.1016/j.strusafe.2014.12.003
Vis sammendrag
This paper presents alternative methods for constructing environmental contours for probabilistic struc tural reliability analysis of structures exposed to environmental forces such as wind and waves. For such structures, it is important to determine the environmental loads to apply in structural reliability calcula tions and structural design. The environmental contour concept is an effective, riskbased approach in establishing such design conditions. Traditionally, such contours are established by way of a Rosenblatt transformation from the environmental parameter space to a standard normal space, which introduces uncertainties and may lead to biased results. The proposed alternative approach, however, eliminates the need for such transformations and established environmental contours based on direct Monte Carlo sampling from the joint distribution of the relevant environmental parameters. In this paper, three alter native implementations of the proposed generic approach will be outlined.

Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Marianne, Røine & Klemp, Marianne (2015). Comparing Effects of Biologic Agents in Treating Patients with Rheumatoid Arthritis: A Multiple Treatment Comparison Regression Analysis. PLoS ONE.
ISSN 19326203.
10(9) . doi:
10.1371/journal.pone.0137258
Vis sammendrag
Rheumatoid arthritis patients have been treated with disease modifying antirheumatic drugs (DMARDs) and the newer biologic drugs. We sought to compare and rank the biologics with respect to efficacy. We performed a literature search identifying 54 publications encompassing 9 biologics. We conducted a multiple treatment comparison regression analysis letting the number experiencing a 50% improvement on the ACR score be dependent upon dose level and disease duration for assessing the comparable relative effect between biologics and placebo or DMARD. The analysis embraced all treatment and comparator arms over all publications. Hence, all measured effects of any biologic agent contributed to the comparison of all biologic agents relative to each other either given alone or combined with DMARD. We found the drug effect to be dependent on dose level, but not on disease duration, and the impact of a high versus low dose level was the same for all drugs (higher doses indicated a higher frequency of ACR50 scores). The ranking of the drugs when given without DMARD was certolizumab (ranked highest), etanercept, tocilizumab/ abatacept and adalimumab. The ranking of the drugs when given with DMARD was certolizumab (ranked highest), tocilizumab, anakinra, rituximab, golimumab/ infliximab/ abatacept, adalimumab/ etanercept. Still, all drugs were effective. All biologic agents were effective compared to placebo, with certolizumab the most effective and adalimumab (without DMARD treatment) and adalimumab/ etanercept (combined with DMARD treatment) the least effective. The drugs were in general more effective, except for etanercept, when given together with DMARDs.

Gåsemyr, Jørund Inge; Natvig, Bent & Tvete, Ingunn Fride (2014). Estimating Response Ratios from Continuous Outcome Data. Methodology and Computing in Applied Probability.
ISSN 13875841.
. doi:
10.1007/s1100901494085
Vis sammendrag
Several methods for imputing the number of responders from summary continuous outcome data in randomized controlled trials exist. A method by Furukawa and others was used in the quite common case that only such summary continuous outcome measures, but not the actual numbers of responders, are reported in order to estimate response rates (probabilities) for different treatments and response ratios between treatments in such trials. The authors give some empirical justification, but encourage search for theoretical support and further empirical exploration. In particular, a problem that needs to be addressed is that randomness in baseline score is not taken into consideration. This will be done in the present paper. Assuming a binormal model for the data, we compare theoretically the true response rate for a single treatment arm to the theoretical response rate underlying two versions of the suggested imputation method. We also assess the performance of the method numerically for some choices of model parameters. We show that the method works satisfactorily in some cases, but can be seriously biased in others. Moreover, assessing the uncertainty of the estimates is problematic. We suggest an alternative Bayesian estimation procedure, based directly on the normal model, which avoids these problems and provides more precise estimates when applied to simulated data sets.

Kristiansen, Monica; Natvig, Bent & Winther, Rune (2014). Assessing software reliability of multistate systems, In Raphaël Steenbergen; P.H.A.J.M. van Gelder; S. Miraglia & A.C.W.M. Vrouwenvelder (ed.),
Safety, reliability and risk analysis : beyond the horizon : proceedings of the European Safety and Reliability Conference, ESREL 2013, Amsterdam, the Netherlands, 29 September2 October 2013.
CRC Press.
ISBN 9781138001237.
KAPITTEL.

Natvig, Bent (2014). On the deterioration of nonrepairable multistage strongly coherent systems. Journal of Applied Probability.
ISSN 00219002.
51(1), s 69 81 . doi:
10.1239/jap/1395771414

Vanem, Erik; Huseby, Arne & Natvig, Bent (2014). Bayesian hierarchical spatiotemporal modelling of trends and future projections in the ocean wave climate with a CO2 regression component. Environmental and Ecological Statistics.
ISSN 13528505.
21(2), s 189 220 . doi:
10.1007/s1065101302516

Aursnes, Ivar; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent & Klemp, Marianne (2013). Are Both Antidepressant Drug Effects and Test Scores Unspecific?. Journal of Pharmacological & Biomedical Analysis.
ISSN 23274638.
1(1) . doi:
10.4172/23274638.1000102

Huseby, Arne & Natvig, Bent (2013). Discrete event simulation methods applied to advanced importance measures of repairable components in multistate network flow systems. Reliability Engineering & System Safety.
ISSN 09518320.
119, s 186 198 . doi:
10.1016/j.ress.2013.05.025
Vis sammendrag
Discrete event models are frequently used in simulation studies to model and analyze pure jump processes. A discrete event model can be viewed as a system consisting of a collection of stochastic processes, where the states of the individual processes change as results of various kinds of events occurring at random points of time. We always assume that each event only affects one of the processes. Between these events the states of the processes are considered to be constant. In the present paper we use discrete event simulation in order to analyze a multistate network flow system of repairable components. In order to study how the different components contribute to the system, it is necessary to describe the often complicated interaction between component processes and processes at the system level. While analytical considerations may throw some light on this, a simulation study often allows the analyst to explore more details. By producing stable curve estimates for the development of the various processes, one gets a much better insight in how such systems develop over time. These methods are particulary useful in the study of advanced importance measures of repairable components. Such measures can be very complicated, and thus impossible to calculate analytically. By using discrete event simulations, however, this can be done in a very natural and intuitive way. In particular significant differences between the BarlowProschan measure and the Natvig measure in multistate network flow systems can be explored.

Huseby, Arne; Vanem, Erik & Natvig, Bent (2013). A New Method for Environmental Contours in Marine Structural Design, In conference ASME (ed.),
Proceedings of ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2013). Volume 2A: Structures, Safety and Reliability.
ASME Press.
ISBN 9780791855324.
Paper No. OMAE201310053.

Huseby, Arne; Vanem, Erik & Natvig, Bent (2013). A new approach to environmental contours for ocean engineering applications based on direct Monte Carlo simulations. Ocean Engineering.
ISSN 00298018.
60, s 124 135 . doi:
10.1016/j.oceaneng.2012.12.034

Vanem, Erik; Natvig, Bent; Huseby, Arne & BitnerGregersen, E. M. (2013). An Illustration of the Effect of Climate Change on the Ocean Wave Climate  A Stochastic Model, In Bharat Raj Singh (ed.),
Climate Change  Realities, Impacts Over Ice Cap, Sea Level and Risks.
INTECH.
ISBN 9789535109341.
Chapter 20.
s 481
 508

Kristiansen, Monica Lind; Natvig, Bent & Winther, Rune (2012). A componentbased approach for assessing reliability of compound software, In . PSAM&ESREL (ed.),
11th International Probabilistic Safety Assessment and Management Conference and the Annual European Safety and Reliability Conference 2012, 2529 June 2012, Helsinki, Finland.
Curran Associates, Inc..
ISBN 9781622764365.
KAPITTEL.
s 1823
 1832

Kristiansen, Monica Lind; Winther, Rune & Natvig, Bent (2012). Establishing prior probability distributions for probabilities that pairs of software components fail simultaneously, In Christophe Bérenguer; Antoine Grall & Carlos Guedes Soares (ed.),
Advances in Safety, Reliability and Risk Management  proceedings of the European Safety and Reliability Conference, ESREL 2011.
CRC Press.
ISBN 9780415683791.
Kapittel.
s 96
 104

Natvig, Bent; Gåsemyr, Jørund Inge & Reitan, Trond (2012). Bayesian Assessment of Availabilities and Unavailabilities of Multistate Monotone Systems. Methodology and Computing in Applied Probability.
ISSN 13875841.
14(4), s 1075 1095 . doi:
10.1007/s1100901192213

Vanem, Erik; Huseby, Arne & Natvig, Bent (2012). A Bayesian hierarchical spatiotemporal model for significant wave height in the North Atlantic. Stochastic environmental research and risk assessment (Print).
ISSN 14363240.
26(5), s 609 632 . doi:
10.1007/s0047701105224

Vanem, Erik; Huseby, Arne & Natvig, Bent (2012). A Stochastic Model in Space and Time for Monthly Maximum significant Wave Height, In
Geostatistics Oslo 2012.
Springer.
ISBN 9789400741522.
41.
s 505
 517

Vanem, Erik; Huseby, Arne & Natvig, Bent (2012). Modelling ocean wave climate with a Bayesian hierarchical spacetime model and a logtransform of the data. Ocean Dynamics.
ISSN 16167341.
62(3), s 355 375 . doi:
10.1007/s1023601105055

Vanem, Erik; Natvig, Bent & Huseby, Arne (2012). Modelling the Effect of Climate Change on the Ocean Wave Climate Around the World, In
The Proceedings of the Tenth (2012) ISOPE Pacific/Asia Offshore Mechanics Symposium PACOMS2012.
International Society of Offshore & Polar Engineers.
ISBN 9781880653937.
paper.
s 145
 152

Vanem, Erik; Natvig, Bent & Huseby, Arne (2012). Modelling the effect of climate change on the wave climate of the world’s oceans. Ocean Science Journal.
ISSN 17385261.
47(2), s 123 145 . doi:
10.1007/s1260101200137

Klemp, Marianne; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent & Aursnes, Ivar (2011). MetaRegression Analysis of Paroxetine Clinical Trial Data. Does Reporting Scale Matter?. Journal of Clinical Psychopharmacology.
ISSN 02710749.
31(2), s 201 206 . doi:
10.1097/JCP.0b013e318210bac1

Klemp, Marianne; Tvete, Ingunn Fride; Skomedal, Tor; Gåsemyr, Jørund Inge; Natvig, Bent & Aursnes, Ivar (2011). A Review and Bayesian MetaAnalysis of Clinical Efficacy and Adverse Effects of 4 Atypical Neuroleptic Drugs Compared With Haloperidol and Placebo. Journal of Clinical Psychopharmacology.
ISSN 02710749.
31(6), s 698 704 . doi:
10.1097/JCP.0b013e31823657d9

Kristiansen, Monica Lind; Winther, Rune & Natvig, Bent (2011). A Bayesian hypothesis testing approach for finding upper bounds for probabilities that pairs of software components fail simultaneously. International Journal of Reliability, Quality and Safety Engineering (IJRQSE).
ISSN 02185393.
18(3), s 209 236 . doi:
10.1142/S021853931100410X

Natvig, Bent (2011). Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems. Methodology and Computing in Applied Probability.
ISSN 13875841.
13(3), s 523 547 . doi:
10.1007/s1100901091702
Vis sammendrag
In Natvig and Gåsemyr (Methodol Comput Appl Probab 11:603–620, 2009) dynamic and stationary measures of importance of a component in a binary system were considered. To arrive at explicit results the performance processes of the components were assumed to be independent and the system to be coherent. Especially the Barlow–Proschan and the Natvig measures were treated in detail and a series of new results and approaches were given. For the case of components not undergoing repair it was shown that both measures are sensible. Reasonable measures of component importance for repairable systems represent a challenge. A basic idea here is also to take a socalled dual term into account. For a binary coherent system, according to the extended Barlow–Proschan measure a component is important if there are high probabilities both that its failure is the cause of system failure and that its repair is the cause of system repair. Even with this extension results for the stationary Barlow–Proschan measure are not satisfactory. For a binary coherent system, according to the extended Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. With this extension the results for the stationary Natvig measure seem very sensible. In the present paper most of these results are generalized to multistate strongly coherent systems. For such systems little has been published until now on measures of component importance even in the nonrepairable case.

Natvig, Bent; Huseby, Arne & Reistadbakk, Mads (2011). Measures of component importance in repairable multistate systemsa numerical study. Reliability Engineering & System Safety.
ISSN 09518320.
96(12), s 1680 1690 . doi:
10.1016/j.ress.2011.07.006

Vanem, Erik; Huseby, Arne & Natvig, Bent (2011). A BayesianHierarchical SpaceTime Model for Significant Wave Height Data, In
30th International Conference on Ocean, Offshore and Arctic Engineering (OMAE2011)  Vol. II.
ASME Press.
ISBN 9780791844342.
Paper no. OMAE201149716.
s 517
 530

Huseby, Arne & Natvig, Bent (2010). Advanced discrete simulation methods applied to repairable multistate systems, In Radim Bris; Sebastián Martorell & C. Guedes Soares (ed.),
Reliability, Risk and Safety. Theory and Applications.
CRC Press.
ISBN 9780415555098.
Volume I.
s 659
 666

Huseby, Arne; Natvig, Bent; Gåsemyr, Jørund Inge; Skutlaberg, Kristina & Isaksen, Stefan (2010). Advanced discrete event simulation methods with application to importance measure estimation in reliability, In Aitor Goti (ed.),
Discrete Event Simulation.
INTECH.
ISBN 9789533071152.
Kapittel 11.
s 205
 222
Vis sammendrag
In the present chapter we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary component availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. Such measures can often be expressed as weighted integrals of the timedependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained. Combined with the appropriate weight function the importance measures of interest can be estimated.

Kristiansen, Monica Lind; Winther, Rune & Natvig, Bent (2010). On component dependencies in compound software. International Journal of Reliability, Quality and Safety Engineering (IJRQSE).
ISSN 02185393.
17(5), s 465 493 . doi:
10.1142/S0218539310003895
Vis sammendrag
On Component Dependencies in Compound Software

Kristiansen, Monica; Winther, Rune & Natvig, Bent (2010). Identifying possible rules for selecting the most important component dependencies in compound software, In Ben Ale; Ioannis Papazoglou & Enrico Zio (ed.),
Reliability, risk and safety : back to the future.
CRC Press.
ISBN 9780415604277.
Artikkel.
s 1561
 1568

Natvig, Bent; Huseby, Arne & Reistadbakk, Mads (2010). Measures of component importance in repairable multistate systemsa numerical study, In Ben Ale; Ioannis Papazoglou & Enrico Zio (ed.),
Reliability, risk and safety : back to the future.
CRC Press.
ISBN 9780415604277.
Artikkel.
s 677
 685

Gåsemyr, Jørund Inge & Natvig, Bent (2009). Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models. Scandinavian Journal of Statistics.
ISSN 03036898.
36(4), s 822 838 . doi:
10.1111/j.14679469.2009.00659.x

Huseby, Arne; Eide, Kristina A.; Isaksen, Stefan; Natvig, Bent & Gåsemyr, Jørund Inge (2009). Advanced discrete event simulation methods with application to importance measure estimation, In Sebastián Martorell; C. Guedes Soares & Julie Barnett (ed.),
Safety, Reliability and Risk Analysis: Theory, Methods and Applications.
CRC Press.
ISBN 9780415485166.
volume 3.
s 1747
 1753
Vis sammendrag
In the present paper we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. As explained in (Natvig and Gåsemyr 2008) such measures can often be expressed as weighted integrals of the timedependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained and combined with the appropriate weight function, and thus producing the importance measure of interest.

Natvig, Bent; Eide, Kristina A.; Gåsemyr, Jørund Inge; Huseby, Arne & Isaksen, Stefan (2009). Simulation based analysis and an application to an offshore oil and gas production system of the Natvig measures of component importance in repairable systems. Reliability Engineering & System Safety.
ISSN 09518320.
94(10), s 1629 1638 . doi:
10.1016/j.ress.2009.04.002

Natvig, Bent; Eide, Kristina A.; Gåsemyr, Jørund Inge; Huseby, Arne & Isaksen, Stefan (2009). The Natvig measures of component importance in repairable systems applied to an offshore oil and gas production system, In Sebastián Martorell; C. Guedes Soares & Julie Barnett (ed.),
Safety, Reliability and Risk Analysis: Theory, Methods and Applications.
CRC Press.
ISBN 9780415485166.
volume 3.
s 2029
 2035
Vis sammendrag
In the present paper the Natvig measures of component importance for repairable systems, and its extended version are applied to an offshore oil and gas production system. According to the extended version of the Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. The results include a study of how different distributions affect the ranking of the components. All numerical results are computed using discrete event simulation. In a companion paper (Huseby, Eide, Isaksen, Natvig, and Gåsemyr 2008) the advanced simulation methods needed in these calculations are decribed

Natvig, Bent & Gåsemyr, Jørund Inge (2009). New Results on the BarlowProschan and Natvig Measures of Component Importance in Nonrepairable and Repairable Systems. Methodology and Computing in Applied Probability.
ISSN 13875841.
11(4), s 603 620 . doi:
10.1007/s1100900890791
Se alle arbeider i Cristin

Natvig, Bent (2011). Multistate Systems Reliability Theory with Applications.
John Wiley & Sons.
ISBN 9780470697504.
231 s.
Se alle arbeider i Cristin

Øverland, Lars Kristian & Natvig, Bent (2018, 04. januar). Risikovurderinger knyttet til store teknologiske systemer som kjernekraftverk og atomvåpen.. [Radio].
Matematisk institutt, UiO..

Gåsemyr, Jørund Inge & Natvig, Bent (2017). Improved availability bounds for binary and multistate monotone systems with independent component processes.

Natvig, Bent & Osen, Kirsten K. (2017). Rakettforsvar og sannsynligheter. Klassekampen.
ISSN 08053839.
49(14), s 23 23
Vis sammendrag
Hva hjelper det å kunne registrere alle innkommende raketter hvis en ikke greier å skyte alle ned?

Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Klemp, Marianne & Binde, Caroline Ditlev (2017). Behandling av Parkinson pasienter: sammenligning av monoamin oxidase typeB inhibitor medikamenter.

Kristiansen, Ingrid; Natvig, Bent; Kaggestad, Johan; Bjørholt, Per Gunnar & Dahl, Øyvind (2016). Nekrolog Stener Speilberg. Aftenposten (morgenutg. : trykt utg.).
ISSN 08043116.
157(267), s 36 36

Lodgaard, Sverre & Natvig, Bent (2016). Ståle Eskeland til minne. Klassekampen.
ISSN 08053839.
5, s 27 27

Natvig, Bent (2016). Mål for betydningen av ulike komponenter i reparerbare multinære systemer. En simuleringsbasert analyse av et olje og gass produksjonssystem.

Natvig, Bent (2016). Om forfallet av ikke reparerbare multinære systemer.

Natvig, Bent & Dalin, Astrid (2016). Trening for Pakinsonister. Hva sier erfaring og forskning om effekter av trening?. Parkinsonbrevet.
(4), s 7 9

Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils Christian; Røine, Marianne & Klemp, Marianne (2016). Correction: Comparing Effects of Biologic Agents in Treating Patients with Rheumatoid Arthritis: A Multiple Treatment Comparison Regression Analysis. PLoS ONE.
ISSN 19326203.
. doi:
10.1371/journal.pone.0146633

Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne & Klemp, Marianne (2016). Comparing Effects of Biologic Agents in Treating Patients with Rheumatoid Arthritis.

Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne & Klemp, Marianne (2016). En sammenligning av biologiske legemidler for behandlingen av leddgiktpasienter. Revmatologi BestPractice.
(26)

Natvig, Bent (2015). En skaptrønder fra Oslo vest ser tilbake..

Osen, Kirsten K. & Natvig, Bent (2015). Folkereisning for å avskaffe atomvåpen. Vårt land.
ISSN 08055424.
71(182), s 19 19

Osen, Kirsten K. & Natvig, Bent (2015). Nedrustningen svikter. Vårt land.
ISSN 08055424.
71(100), s 11 11

Osen, Kirsten K. & Natvig, Bent (2015). Samfunnssikkerheten. Atomvåpen. Klassekampen.
ISSN 08053839.
s 23 23

Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne & Klemp, Marianne (2015). Rangering av biologiske legemidlers effekt i revmatoid artrittbehandling – ett tillegg til SAMBAnotat 22/2014. NRnotat. SAMBA/13/2015.

Kristiansen, Monica; Holone, Harald & Natvig, Bent (2014). A Componentbased Approach for Assessing Reliability of Compound Software.

Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent; Meland, Nils; Marianne, Roine; Skomedal, Tor & Klemp, Marianne (2014). A Mixed Treatment Comparison analysis of drugs for treating patients with Rheumatoid arthritis.

Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne; Skomedal, Tor & Klemp, Marianne (2014). Treating patients with Rheumatoid arthritis: a Mixed Treatment Comparison analysis of antiTNF drug effects.

Huseby, Arne Bang; Natvig, Bent & Vanem, Erik (2013). Alternative environmental contours for structural reliability analysis.

Kristiansen, Monica; Natvig, Bent & Winther, Rune (2013). Assessing software reliability of multistate systems.

Osen, Kirsten K. & Natvig, Bent (2013). Tiden inne for et atomvåpenforbud. Klassekampen.
ISSN 08053839.
s 22 22

Tvete, Ingunn Fride; Klemp, Marianne; Natvig, Bent; Gåsemyr, Jørund Inge; Skomedal, Tor; Roine, Marianne & Meland, Nils (2013). Multiple treatment comparison analysis.

Kristiansen, Monica Lind; Natvig, Bent & Winther, Rune (2012). A componentbased approach for assessing reliability of compound software.

Natvig, Bent (2012). On the reduction in remaining system time above a specific state due to a jump downwards of a component in nonrepairable multistate strongly coherent systems. Statistical research report (Universitetet i Oslo. Matematisk institut. 1. Fulltekst i vitenarkiv.

Sunnannå, Lars Magne & Natvig, Bent (2012, 10. november). 34åringen som vant presidentvalget.
Aftenposten.

Christensen, Arnfinn; Grunt, Hilde; Jødahl, Roar; Storvik, Geir Olve & Natvig, Bent (2011, 24. august). Tilfeldig! Neppe? En statistiker klarte å knekke vinnerkoden i et stort kanadisk skrapelotteri. Hvor tilfeldig er vinnertallene?. [Internett].
forskning.no.

Kristiansen, Monica Lind; Winther, Rune & Natvig, Bent (2011). A Bayesian hypothesis testing approach for finding upper bounds for probabilities that pairs of software components fail simultaneuosly. Statistical research report (Universitetet i Oslo. Matematisk institut. 1.
Vis sammendrag
Predicting the reliability of software systems based on a componentbased approach is inherently difficult, in particular due to failure dependencies between software components. One possible way to assess and include dependency aspects in software reliability models is to find upper bounds for probabilities that software components fail simultaneously and then include these into the reliability models. In earlier research, it has been shown that including partial dependency information may give substantial improvements in predicting the reliability of compound software compared to assuming independence between all software components. Furthermore, it has been shown that including dependencies between pairs of dataparallel components may give predictions close to the system's true reliability. In this paper, a Bayesian hypothesis testing approach for finding upper bounds for probabilities that pairs of software components fail simultaneously is described. This approach consists of two main steps: 1) establishing prior probability distributions for probabilities that pairs of software components fail simultaneously and 2) updating these prior probability distributions by performing statistical testing. In this paper, the focus is on the first step in the Bayesian hypothesis testing approach, and two possible procedures for establishing a prior probability distribution for the probability that a pair of software components fails simultaneously are proposed.

Kristiansen, Monica Lind; Winther, Rune & Natvig, Bent (2011). Establishing prior probability distributions for probabilities that pairs of software components fail simultaneously.

Natvig, Bent; Bjune, Gunnar & Klepsvik, Karsten (2011, 01. mars). Vitenskapsfolk som diplomater. [Radio].
NRK P2 Ekko.

Osen, Kirsten K. & Natvig, Bent (2011). Hiroshima og Nagasaki. Klassekampen.
ISSN 08053839.
43(179), s 38 39

Osen, Kirsten K. & Natvig, Bent (2011). Nytt håp om nedrustning. ATOMVÅPEN. Klassekampen.
ISSN 08053839.
43(244), s 19 19

Søndenaa, Thor & Natvig, Bent (2011, 01. september). Professor slakter TØIs sykkelrapport.
Våre veger.

Vanem, Erik; Huseby, Arne & Natvig, Bent (2011). Stochastic Modeling of Wave Climate Using a Bayesian Hierarchical SpaceTime Model with a LogTransform.

Kristiansen, Monica; Winther, Rune & Natvig, Bent (2010). Identifying possible rules for selecting the most important component dependencies in compound software.
Vis sammendrag
Since it is practically impossible to include all component dependencies in a system?s reliability calculation, a more viable approach would be to include only those dependencies that have a significant impact on the assessed reliability. In this paper, the concepts dataserial and dataparalell components are defined. Then a test system, consisting of five components, is investigated to identify possible rules for selecting the most important component dependencies. To do this, two techniques are applied: 1) direct calculation and 2) Principal Component Analysis (PCA). The results from the analyses clearly show that including partial dependency information may give substantial improvements in the reliability predictions, compared to assuming independence between all software components. However, this is only as long as the most important component dependencies are included in the reliability calculations. It is also apparent that dependencies between dataparallel components are far more important than dependencies between dataserial components. Further the analyses indicate that including only dependencies between dataparallel components may give predictions close to the system?s true failure probability. Including only dependencies between dataserial components may however result in predictions even worse than by assuming independence between all software components.

Kristiansen, Monica; Winther, Rune & Natvig, Bent (2010). On component dependencies in compound software. Statistical research report (Universitetet i Oslo. Matematisk institut. 5.
Vis sammendrag
Predicting the reliability of software systems based on a component approach is inherently difficult, in particular due to failure dependencies between the software components. Since it is practically difficult to include all component dependencies in a system's reliability calculation, a more viable approach would be to include only those dependencies that have a significant impact on the assessed system reliability. This paper starts out by defining two new concepts: dataserial and dataparallel components. These concepts are illustrated on a simple compound software, and it is shown how dependencies between dataserial and dataparallel components, as well as combinations of these, can be expressed using conditional probabilities. Secondly, this paper illustrates how the components' marginal reliabilities put direct restrictions on the components' conditional probabilities. It is also shown that the degrees of freedom are much fewer than first anticipated when it comes to conditional probabilities. At last, this paper investigates three test cases, each representing a wellknown software structure, to identify possible rules for selecting the most important component dependencies. To do this, three different techniques are applied: 1) direct calculation, 2) Birnbaum's measure and 3) Principal Component Analysis (PCA). The results from the analyses clearly show that including partial dependency information may give substantial improvements in the reliability predictions, compared to assuming independence between all software components.

Natvig, Bent & Gåsemyr, Jørund Inge (2010). Evaluation of Bayesian hierarchical models. From Bayesian pvalues to conflict measures.

Natvig, Bent; Gåsemyr, Jørund Inge & Reitan, Trond (2010). Bayesian assessment of availabilities and unavailabilities of multistate monotone systems. Statistical research report (Universitetet i Oslo. Matematisk institut. 3.
Vis sammendrag
In the present paper we consider a multistate monotone system of multistate components. Following a Bayesian approach, the ambition is to arrive at the posterior distributions of the system availabilities and unavailabilities to the various levels in a fixed time interval based on both prior information and data on both the components and the system. We argue that a realistic approach is to start out by describing our uncertainty on the component availabilities and unavailabilities to the various levels in a fixed time interval, based on both prior information and data on the components, by the moments up till order m of their marginal distributions. From these moments analytic bounds on the corresponding moments of the system availabilities and unavailabilities to the various levels in a fixed time interval are arrived at. Applying these bounds and prior system information we may then fit prior distributions of the system availabilities and unavailabilities to the various levels in a fixed time interval. These can in turn be updated by relevant data on the system. This generalizes results given in (Natvig and Eide 1987) considering a binary monotone system of binary components at a fixed point of time. Furthermore, considering a simple network system, we show that the analytic bounds can be slightly improved by straightforward simulation techniques.

Natvig, Bent & Huseby, Arne (2010). Measures of component importance in repairable multistate systems a numerical study.

Natvig, Bent; Huseby, Arne & Reistadbakk, Mads (2010). Measures of component importance in repairable multistate systems – a numerical study. Statistical research report (Universitetet i Oslo. Matematisk institut. 4.
Vis sammendrag
In [10] dynamic and stationary measures of importance of a component in a repairable multistate system were introduced. For multistate systems little has been published until now on such measures even in the nonrepairable case. According to the BarlowProschan type measures a component is important if there is a high probability that a change in the component state causes a change in whether or not the system state is above a given state. On the other hand, the Natvig type measures focus on how a change in the component state affects the expected system uptime and downtime relative to the given system state. In the present paper we first review these measures which can be estimated using the simulation methods suggested in [4]. Extending the work in [8] from the binary to the multistate case, a numerical study of these measures is then given for two three component systems, a bridge system and also applied to an offshore oil and gas production system. In the multistate case the importance of a component is calculated separately for each component state. Thus it may happen that a component is very important at one state, and less important, or even irrelevant at another. Unified measures combining the importances for all component states can be obtained by adding up the importance measures for each individual state. According to these unified measures a component can be important relative to a given system state but not to another. It can be seen that if the distributions of the total component times spent in the non complete failure states for the multistate system and the component lifetimes for the binary system are identical, the BarlowProschan measure to the lowest system state simply reduces to the binary version of the measure. The extended Natvig measure, however, does not have this property. This indicates that the latter measure captures more information about the system.

Tvete, Ingunn Fride; Klemp, Marianne; Skomedal, Tor; Gaasemyr, Jørund; Natvig, Bent & Aursnes, Ivar Andreas (2010). Clinical efficacy and adverse effects of several antipsychotics.

Tvete, Ingunn Fride; Klemp, Marianne; Skomedal, Tor; Gaasemyr, Jørund; Natvig, Bent & Aursnes, Ivar Andreas (2010). Clinical efficacy and adverse effects of the partial dopaminergic agonist aripiprazole compared with other antipsychotics.

Grosvold, Anne & Natvig, Bent (2009, 15. mai). Lotto og sannsynlighetsregning. [TV].
Grosvold.

Huseby, Arne & Natvig, Bent (2009). Advanced discrete simulation methods applied to repairable multistate systems.

Klemp, Marianne; Tvete, Ingunn Fride; Skomedal, Tor; Gaasemyr, Jørund; Natvig, Bent & Aursnes, Ivar Andreas (2009). BAYESIAN STATISTICAL APPROACH FOR COMPARING THE CLINICAL EFFICACY OF THE PARTIAL DOPAMINERGIC AGONIST ARIPIPRAZOLE TO OTHER ANTIPSYCHOTICS.

Natvig, Bent (2009). Drømmer om 92 millioner. Vårt land.
ISSN 08055424.
65(114), s 7 7

Natvig, Bent (2009). "Elevundersøkelsen" Råkjør mot elevene for å høyne svarprosenten. Skolemagasinet  Fagavis for læremidler og skoleutvikling.
20(2), s 2 2

Natvig, Bent (2009). Measures of component importance in nonrepairable and repairable multistate strongly coherent systems. Statistical research report (Universitetet i Oslo. Matematisk institut. 2.
Vis sammendrag
In Natvig and Gåsemyr (2009) dynamic and stationary measures of importance of a component in a binary system were considered. To arrive at explicit results the performance processes of the components were assumed to be independent and the system to be coherent. Especially the BarlowProschan and the Natvig measures were treated in detail and a series of new results and approaches were given. For the case of components not undergoing repair it was shown that both measures are sensible. Reasonable measures of component importance for repairable systems represent a challenge. A basic idea here is also to take a socalled dual term into account. For a binary coherent system, according to the extended BarlowProschan measure a component is important if there are high probabilities both that its failure is the cause of system failure and that its repair is the cause of system repair. Even with this extension results for the stationary BarlowProschan measure are not satisfactory. For a binary coherent system, according to the extended Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. With this extension the results for the stationary Natvig measure seem very sensible. In the present paper most of these results are generalized to multistate strongly coherent systems. For such systems little has been published until now on measures of component importance even in the nonrepairable case.

Natvig, Bent (2009). Rett mann i rett tid. Dagsavisen.
ISSN 15032892.
s 5 5
Vis sammendrag
Fredspris til rett mann i rett tid. Det beste argument for at USAs president Barack Obama fortjener Nobels fredspris for 2009 er hans bidrag til atomnedrustning. Det viktigste konkrete bidraget, offentliggjort 17. september, er skrinleggingen av rakettskjoldplanene i Polen og Tsjekkia uten krav om motytelser fra Russland. Her retter han opp tabben fra talen i Praha 5. april der han sa at han ville gå videre med disse planene, uten å innse at dette ville forsure samarbeidet med Russland. Håpet nå er at dype kutt i atomvåpenarsenalene til USA og Russland vil kunne bli offentliggjort før prisutdelingen 10. desember. Det andre konkrete bidraget er tilbakesendingen av Pentagons forslag til gjennomgang av USAs atomvåpenpolitikk. Obama karakteriserte forslaget som ”business as usual” og forlangte en strategi i overensstemmelse med sine egne visjoner. Som fredsprisvinner forventes det av ham at han følger opp med snarlig skrinlegging av alle rakettforsvarsplaner, ratifisering av prøvestansavtalen samt bidrag til total omlegging av NATOs atomvåpenstrategi som slutt på førstebruksopsjonen. Bent Natvig, leder Den norske Pugwashkomité.

Natvig, Bent (2009). Slik kan du sikre deg GIGANTPOTTEN. VG : Verdens gang.
ISSN 08055203.
(134), s 7 7

Natvig, Bent (2009). Updating information on statistical uncertainty from expert evaluationsrelevance for the Nature Index?.

Osen, Kirsten K. & Natvig, Bent (2009). Arbeidsuhell av Espen Barth Eide?. Aftenposten (morgenutg. : trykt utg.).
ISSN 08043116.

Natvig, Bent; Eide, Kristina; Gåsemyr, Jørund Inge; Huseby, Arne & Isaksen, Stefan (2008). The Natvig measures of component importance in repairable systems applied to an offshore oil and gas production system.
Vis sammendrag
In the present paper the Natvig measures of component importance for repairable systems, and its extended version are applied to an offshore oil and gas production system. According to the extended version of the Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. The results include a study of how different distributions affect the ranking of the components. All numerical results are computed using discrete event simulation. In a companion paper (Huseby, Eide, Isaksen, Natvig, and Gåsemyr 2008) the advanced simulation methods needed in these calculations are decribed.

Gåsemyr, Jørund Inge & Natvig, Bent (2008). Extension of a conflict measure of inconsistencies in Bayesian hierarchical models. Statistical research report (Universitetet i Oslo. Matematisk institut. 6.

Hagelund, Helge; Osen, Kirsten K. & Natvig, Bent (2008). Norge og atomnedrustning. Klassekampen.
ISSN 08053839.

Huseby, Arne; Eide, Kristina; Isaksen, Stefan; Natvig, Bent & Gåsemyr, Jørund Inge (2008). Advanced discrete event simulation methods with application to importance measure estimation.
Vis sammendrag
In the present paper we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. As explained in (Natvig and Gåsemyr 2008) such measures can often be expressed as weighted integrals of the timedependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained and combined with the appropriate weight function, and thus producing the importance measure of interest.

Huseby, Arne; Eide, Kristina; Isaksen, Stefan; Natvig, Bent & Gåsemyr, Jørund Inge (2008). Advanced discrete event simulation methods with application to importance measure estimation. Statistical research report (Universitetet i Oslo. Matematisk institut. 11.
Vis sammendrag
In the present paper we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary component availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. As explained in Natvig and Gåsemyr (2009) such measures can often be expressed as weighted integrals of the timedependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained. Combined with the appropriate weight function the importance measures of interest can be estimated.
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Publisert 13. nov. 2010 12:06
 Sist endret 4. feb. 2016 12:24