OMAE COST EFFECTIVENESS OF HULL GIRDER SAFETY

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1 Proceedings of OMAE 00: Offshore Mechanics and Arctic Engineering Oslo, Norway, 3-8 June, 00 OMAE COST EFFECTIVENESS OF HULL GIRDER SAFETY Rolf Skjong Elzbieta M. Bitner-Gregersen Det Norske Veritas AS NO-3 Høvik, Norway ABSTRACT The paper presents a cost effectiveness assessment of the safety in a design code for oil tankers. The marginal cost to safety improvements is based on code calibration studies for different target reliabilities. This allows basing the actual target reliability indices on risk acceptance criteria derived from cost effectiveness of the marginal change in scantling requirements. This approach is in agreement with the criteria defined in IMO submissions and used in the ongoing IMO coordinated Formal Safety Assessment studies on bulk carriers. The documentation that cost effectiveness criteria may be applied has previously been submitted to IMO. It is concluded that the method works quite well in the examples that are presented, and that the current codes are in close agreement with decision criteria used for other risk control options. As probabilities calculated by structural reliability methods are notional, it is also advantageous to use marginal costs to safety improvement instead of absolute numbers of probabilities as acceptance criterion. It is indicated that a cost effectiveness criterion may replace the current practice of basing target reliabilities on calibration against previous best practices. Although the basic safety philosophy is changed radically, the study does not indicate that the change in criteria would result in much change in design. The advantage of using the suggested approach is the consistency with ongoing FSA development at IMO. INTRODUCTION At present there is a need for development of a methodology, which can be used in the future processes for establishing design rules for ships that are consistent with the current development of Formal Safety Assessment (FSA) at IMO. FSA represent a method for developing a rational and transparent decision-process leading to implementation of Risk Control Options (RCO) in the regulations. The following steps can be identified in an FSA, IMO (997, 00), Mathiesen and Skjong (996): Steps of Formal Safety Assessment Steps In layman terminology Professional language What might go wrong? Hazard Identification a How often or how likely? Frequencies or probabilities b How bad? Consequences c Risk = Probability Consequence 3 Can matters be improved? Identify risk management options 4 What would it cost and how Cost Benefit much better would it be? Evaluation 5 What actions are worthwhile to Recommendation take? IMO What action to take? Decision A Cost Effectiveness Assessment (CEA) is an essential part of Step 4 of an FSA. The CEA is applied in an FSA to assess the marginal return of an additional RCO by comparing the cost of implementation and the benefit of the RCO in terms of the risk that would be averted. A CEA is a useful input for a decision process. It may be noted that the FSA Guidelines (IMO, 997, 00) is assuming that RCOs represent discrete changes in the ship design or operation, whilst in structural design the variables are continuos. The main purpose of any set of design rules, which are applied to a family of structures, is to provide a safety level, which is acceptable by society in general and all stakeholders. For ship Copyright 00 by ASME

2 structures in particular, the targeted reliability level is to a large extent ensured by complying with rule requirements developed and set forth by classification societies. Together with the rules of the classification societies the regulations by IMO constitute the main elements of the safety regime for international shipping. The present paper demonstrates how results from a calibration study can be utilized in a CEA, and how an acceptance criterion based on Net Costs of Averting a Fatality (NCAF) may be used to decide the target reliability, Skjong (00), Skjong and Ronold (998, 00), Norway (000), IMO (00). This paper is based primarily on the results of the reliability-based calibration of the DNV Steel Ship Rules for buckling of ship decks in an extreme sagging condition (Bitner-Gregersen et al., 997; Bitner-Gregersen and Skjong, 997). The reliability level inherent in the current rules, which may be referred to as past practice, has also been assessed in the present study. In this paper, the consequences of adopting different target reliability levels for a ship deck weight and cost are estimated and discussed. CALIBRATION STUDY This chapter essentially sums up some of the basics for the calibration study. Further details are described in Bitner- Gregersen et al. (997,00). Figure : Hull girder collapse, extreme sagging conditions. In general, safety is a wide concept, which embraces safety against several types of failure scenarios including fire, collision, grounding, flooding, capsizing, propulsion and steering failure, and loss of hull integrity, under normal as well as under extreme conditions. In general, there may be an interaction between these general accident scenarios. Such interaction is not treated in any detail in this study. The results presented are limited to the structural collapse of ships (due to buckling of ship decks) operating under extreme sagging conditions, see Figure, with the potential consequence of total loss of ship and crew. For a single skin tanker considered here, the assumption of total loss seems to be rather close to reality as the contributions to the moment capacity from longitudinal bulkheads, ship sides, and bottom are all minimal. Buckling Criteria and Limit State The rule requirements for buckling of plates and stiffeners, DNV (994), involve the control against four different buckling modes classified as; plate, lateral stiffener, torsional stiffener, and web stiffener buckling, respectively. The criteria are rewritten to the present ULS Format as: c 0 Acceptable DNV Rule ( i =,,3,4 ) () i ci i ci a () i The ci s are the critical buckling stresses in the different buckling modes to be checked. The i s are the corresponding acceptable usage factors and the i s are safety factors; i = is used in the present rules. The a is the longitudinal bending stress with contribution from the characteristic still water moment M s and the characteristic dynamic wave moment M w. The criteria written in terms of hull girder moments M S and M w are: Plate buckling c c ( M s M W ) (3).0WD0 Lateral Stiffener buckling (Euler mode) c c ( M s M W ) (4) 0.85WD0 Torsional stiffener buckling c3 3 c3 ( M s M W ) (5) 0.80WD0 Web stiffener buckling c4 4 c4 ( M s M W ) (6) 0.80WD0 where W D0 is the section modulus of the hull girder in the position where the buckling control is to be carried out. The buckling criteria described above represent the International Association of Classification Societies Unified Requirements (IACS/URs). According to modern reliability theory (DNV, 99; Skjong et al., 996), the ULS failure criterion should be expressed in terms of a limit state function, g, which may have any form in general and is a function of N random or fixed variables X=(X,X,...X N ) T that describe the failure set, the failure surface, and the safe set, i.e. Copyright 00 by ASME

3 g g( X, X,..., X N ) (7) such that g( X) 0 constitute the failure domain. The probability of failure is P F P( g( X) 0) (8) The corresponding reliability index defined as P F ( ) (9) denotes the standardized cumulative normal distribution function. For hull girder collapse, the limit state function takes the form g M M M ( M M w ) (0) u a u s M u is the ultimate moment capacity of the hull girder and M a is the total applied moment resulting as the sum of the still water moment M s and the wave moment M W. In this context, M u and M a = M s +M W are stochastic variables, each of which has a probability distribution according to the uncertainties in the applied models. The North Atlantic environment is applied in the analysis. Calibration Method A tailor-made code calibration module integrated with PROBAN, Hauge et al. (990, 99), Ronold and Skjong (00) has been applied for the calibration of the DNV Ship Rules for buckling. The partial safety factors are actually subject to optimization, minimizing the deviation from the target reliability, weighted with a penalty function. Further, it should also be emphasized that rule criteria c i > 0, i=,...4, given by equations 3-6, are all weighted equally and they are hence implicitly assumed to be of equal importance to the safety of the ship. The same fixed target reliability level T has therefore been used for all four criteria in the present calibration analysis. The calibration procedure requires the specification of a target reliability level. The annual probabilities of failure and corresponding reliability indices given in Table have been considered. Table : Annual probabilities and corresponding reliability indices, used as targets Probabilities Reliability indices DNV Classification Note 30.6, DNV (99), proposes a target failure probability of 0 4 for a non-redundant structure with serious consequence of failure, whereas 0 3 is suggested for a redundant structure with less consequence of failure. Use of the calibration module leads to determination of the safety factors that are needed in the code checks, and this is achieved by solution of a non-linear optimization, Hauge et al. (990, 99). Calibration Results The calibration procedure requires several examples, i.e. design cases, to be included in order to obtain trustworthy results. The examples have been chosen as a set of ship designs. The basis for the present analysis has been a single ship in a fully loaded condition. However, in order to create the required amount of examples, the local design of plate and stiffeners is varied under the assumption that the same weight of the total deck field is retained. Thus the loads are the same for all examples, although when the dimensions are changed, the weight and draft will also change slightly, and thus the loads will change, too. Originally the following three commonly used stiffener profiles were considered: i) Flat bar profiles, ii) L-profiles, iii) T- profiles. Only L-profiles and flat bar profiles are included in this paper. For each stiffener profile category, possible local designs are considered. The ship taken as a basis is a VLCC tanker with principal data as follows: Length=50m, Ship width = 39.6m, Ship Depth =3.m, Draft = 5.3m, Block coefficient =0.837, Displacement =30,000 ton. The flat bar profile corresponds to the present original ship design. All other examples are constructed on the basis of this original design. The stiffened deck is modelled with 40 equal stiffeners with associated plate. The cross-sectional data of the hull girder is calculated to be: Section modulus in deck = mm 3, distance from neutral axis to deck line =0mm, total hull girder cross sectional area = mm, total deck area, plates + stiffeners = mm, N stiff = 40. More details may be found in Steen et al. (995). These data are valid for the initial design examples, as the deck area is kept constant equal to its nominal value, and thus the weight is constant, too. The calibration study of the rules has been carried out when two design parameters, the plate thickness t i and the web thickness t wi, are allowed to vary. The plate thickness and the web thickness before and after calibration are listed in Table and Table 3 for flat bar profiles and for L-profiles, respectively. The mean value of before calibration (past practice) is equal to.4 for flat bar profiles and to 3.4 for L-profiles. A CEA in FSA is usually applied to assess the marginal return of additional safety measures comparing: The cost of implementing the RCO The benefit of the RCO (in terms of the risk that is averted, e.g. life saved) 3 Copyright 00 by ASME

4 Table :Plate and web thickness before and after rule calibration, flat bar stiffener profiles Before Calibration Calibrated: T =.5 Calibrated: T =3.09 Calibrated: T =3.5 Calibrated: T =3.7 t t w t t w t t w t t w t Ex. mm mm mm mm mm mm mm mm mm t w mm Table 3: Plate and web thickness before and after rule calibration, L-stiffener profiles Before Calibration Calibrated: T =.5 Calibrated: T =3.09 Calibrated: T =3.5 Calibrated: T =3.7 t t w t t w t t w t t w t Ex. mm mm mm mm mm mm mm mm mm t w mm Thus a CEA shows whether the benefits of a measure outweighs its costs, i.e. it demonstrates cost effectiveness of the safety measure. A ratio called The Gross Cost of Averting a Fatality (GCAF) is defined as follows Cost of RCO GCAF = () Reduction in PLL where PLL is the Potential Loss of Life (Expected Loss). Further, the Net Cost of Averting a Fatality (NCAF) is defined by subtracting eventual economic risk reduction from the cost of the RCO. Cost of RCO - Reduced Economic Loss NCAF = () Reduction in PLL The NCAF is a factor used for comparison of different RCOs. of a Ship Deck Before and After Rule Calibration In order to indicate cost associated with different safety levels adopted, the weights of the ship decks have been calculated before and after the rule calibration. The plate thickness t i and the web thickness t w are the only design parameters, which are allowed vary in the analysis. As a first step the cross-section areas of the ship decks have been calculated before and after calibration, further the numbers obtained have been multiplied 3 by the steel specific gravity equal to 7.85 t/ m. The results are given in Table 4 and Table 5. The numbers listed in the tables are given per meter length and per stiffener (L=50m, N stiff.=40) of a ship deck. 4 Copyright 00 by ASME

5 Table 4: Cross section area and weight of ship decks per meter length and per stiffer before and after rule calibration, flat bar profiles. Before Calibration Calibrated: T =.5 Calibrated: T =3.09 Calibrated: T =3.5 Calibrated: T =3.7 Ex. =3.09 Mean Value Ex. Mean Value Table 5: Cross section area and weight of ship decks per meter length and per stiffer before and after rule calibration, L-profiles. Before Calibration Calibrated: T =.5 Calibrated: T =3.09 Calibrated: T =3.5 Calibrated: T =3.7 = Costs Related to Increase of The cost of the steel for a ship deck including labor varies between USD 000 and USD 3000 per tonne. As an average USD 000 per tonne is used in the following for the ship deck designed with flat bar profiles. The ship design with the L- profiles is estimated to be 4% more expensive per tonne (% more expensive stiffeners representing /3 of the deck weight). Table 6 presents the total average weight of the ship deck and cost before and after rule calibration. The associated total average cost of the ship deck is also given. The increase of the cost of the ship deck related to an adopted new target reliability index is given in Table 7 and Table 8 for flat-bar-profiles and L-profiles, respectively. The increase is calculated for two different safety levels: () =.5 and () the past practice, i.e. the value before calibration. As quoted above, this is =.4 for flat-bar-profiles and =3.4 for L- profiles. As expected, Table 7 and Table 8 demonstrate that an increase of the target reliability level leads to increase of the weight and cost of a ship deck. In the case of the flat-bar-profiles, the increase is almost linear with respect to, while for the L- profiles it has a parabolic form with respect to. Table 6: Total weight and cost for the average ship deck before and after Calibration, Flat bar and L- stiffener profiles. Stiffener profile Before Calibration After =.50 After. =3.09 After =3.50 After =3.7 Flatbar (T),89,03,4,373,440 Flatbar Cost (US$) 3,658,000 4,06,000 4,48,000 4,746,000 4,880,000 L-profile (T),833,67,738,9,07 L-profile Cost (US$) 3,8,640 3,475,680 3,65,040 3,997,760 4,309,760 5 Copyright 00 by ASME

6 Table 7:Increase of the ship deck cost for different target beta, Flat bar stiffener profiles. Cost increase relative =.50 =3.09 =3.50 =3.7 to = % 6.8% 0.% Past practice* =.40 * before calibration.0%.5% 9.7% 33.4% Table 8: Increase of the ship deck cost for different target beta, L-stiffener profiles. Cost increase relative to =.50 =3.09 =3.50 =3.7 = % 5.0% 4.0% Past practice* =3.40 * before calibration -8.5% -5.5% 4.9% 3.0% The reliability indices correspond to the annual probabilities of failure in Table. Thus, based on the results presented in Table 6, in conjunction with Table the Cost of Averting a Fatality (CAF) can be estimated. In order to calculate the GCAF, it is assumed that a loss of an oil tanker with 50% of the entire crew occurs in case of the hull girder collapse. The number of crew on a tanker of this size is expected to be 0. The 50% loss of crew is corresponding to the success rate in evacuations from bulk carriers in similar conditions (Skjong and Wentworth, 00). Further, it is assumed that a ship life cycle is 0 years. As an example, the GCAF for increase of the reliability index from =3.50 to =3.7 for L-profiles then becomes 4,309, ,844, NCAF $7. 3million Table 9 presents both GCAF and NCAF values for different annual probabilities of failure for the flat bar stiffener and L- stiffener profiles, respectively. To arrive at NCAF values the loss of the ship is expected to occur after 5 years of operation with a ship value of $ million. The value of the cargo is estimated at $ million. A high age is assumed both because the diminution to the rule minimum occurs at high ship age and because the historic losses occur at high ship age. Earlier in the ship life the reliability is higher and the value of the ship is also higher. Risk acceptance criteria in the ALARP region may be specified in terms of acceptable NCAF values, see Skjong and Ronold (998,00), Norway (000). In Norway (000) it is documented that tankers safety are in the ALARP region, and the criterion therefore may be applied. The results presented in Table 9 can be used in conjunction with acceptable NCAF values to back-calculate what the target reliability index should be. Table 9: GCAF/NCAF in US$ million for increases of the reliability index Flat Bar L-Profile / / / / /.4 0.3/7.3 The negative NCAF values result from an economic risk reduction outweighing the cost of the RCO. For reliability indices below 3.5 the table indicates a net economic benefit from implementing the measure. The NCAF value used in the various bulk carrier studies (IACS, 00; Japan, 00; Skjong and Wentworth, 00) as an acceptance criteria is in the range $.5 to $3 million as recommended by Norway (000). This corresponds relatively closely to the 0-4 annual probability recommended in DNV (99). Further investigations are required in order to provide accurate estimates of frequency and number of fatalities. For example, a study may be done in order to extract this information from the accident data available in e.g. the LMIS Data Base. The total loss of oil tankers due to foundering (not necessary the hull girder collapse) was (data from 99-97). CONCLUSIONS The present study demonstrates how results from a reliabilitybased rule calibration study can be used as an input to a cost effectiveness evaluation, and how target may be derived by 6 Copyright 00 by ASME

7 CBA. The study is based primarily on the reliability-based calibration of the DNV Steel Ship Rules, considering buckling of ship decks in an extreme sagging condition. The code calibrations have been performed for oil tankers for four annual target reliability levels identified by their corresponding four reliability indices of.50, 3.09, 3.50, and 3.7, respectively. As expected it is demonstrated that an increase of the target reliability leads to increase of weight and cost of a ship deck. Further, it is shown that the rate of increase depends on the stiffener profile type. The results indicate that it is more beneficial to use L-stiffener profiles than flat-bar-profiles for a ship deck as the L stiffener profiles give higher safety level of the tanker (higher reliability index) at the same cost of the ship deck. Furthermore, the paper (based on Bitner-Gregersen and Skjong, 997) represents the first attempt to quantify the Net and Gross Cost of Averting a Fatality (NCAF/GCAF) for current codes as well as the consequence of using NCAF instead of target reliabilities. For a target reliability index of about , the calculated NCAFs are comparable to the values indicated as acceptance criteria by Ronold and Skjong (998, 00) and use in the ongoing FSA studies. It is not suggested at this stage to change the practice (DNV; 99) which is to base decisions regarding choice of the target reliability on calibrations against past practice. To our knowledge this paper represents the first attempt to base such decisions on cost effectiveness assessments in conjunction with acceptance criteria on NCAF. This method is consistent with FSA, IMO (997, 00). A further advantage with this method is that it is quite general. The method may be used also for making decisions regarding second line of defense or robustness, Mathiesen (997). There are many assumptions in this paper that future and more detailed studies may show to be slightly biased, e.g. assumptions regarding frequencies and number of fatalities associated with loss of oil tankers and parameters leading to probability estimates. However, to some extent as a surprise to the authors, the estimated NCAFs are of the order of magnitude consistent with proposed acceptance criterion. It also seems quite practical to use a cost effectiveness criterion. Furthermore, the Rules do not seem to have any unbalance giving preference to first line of defense, which is dealt with in this paper, rather than to last line of defense which is life saving. In the study by Skjong and Wentworth (00) the NCAF of the current lifeboats are estimated to about $ million ( 60, ,000). The structural reliability analysis is based on Bayesian probabilities as some epistemic uncertainties are included in the model. Probabilities are thus properties of our knowledge of the structure and the loads it is subjected to. To use acceptance criteria that are based on a frequency interpretation of probabilities is therefore discomforting. It is actually more satisfactory to use the NCAF criterion, because only information relating to relative changes in the probabilities as a function of design parameters is used in the decision process (Skjong, 00). ACKNOWLEDGEMENT The work reported in this paper has been carried out under the DNV strategic research programmes. The opinions expressed are those of the authors and should not be construed to represent the views of DNV. REFERENCES Bitner-Gregersen, EM, KO Ronold and L Hauge (997) "Reliability based Rules for Longitudinal Strength for Multiple Target Reliability Levels" DNV Research Report No Bitner-Gregersen, EM and R Skjong (997) Cost Benefit Evaluation for Midship Bending criteria, DNV Research Report Bitner-Gregersen, EM; L Hovem and R Skjong (00) Implicit Reliability of Ship Structures OMAE 00. DNV (99) Classification Note 30.6 "Structural Reliability Analysis of Marine Structures" July 99. DNV (994) "Rules for Classification of Ships" Part 3, Chap., January 994. Hauge, L, R Løseth and R Skjong (99) "Optimal Code Calibration and Probabilistic Design" Proceedings, OMAE- 9, Calgary, Canada. Hauge, L, R Løseth and R Skjong (990) "PROBAN - Version 4, Code Optimization" DNV Research Report No IACS (00) Bulk Carrier Safety, FSA Fore end watertight integrity, IMO Marine Safety Committee 74/5/4. IMO (997) "Interim Guidelines for the Application of Formal Safety Assessment (FSA) to the IMO Rule Making Process" Maritime Safety Committee, 68 th session, June 997; and Marine Environment Protection Committee, 40 th session, September 997. IMO (00) "Guidelines for Formal Safety Assessment for the IMO Rule Making Process" IMO/Marine Safety Committee 74/WP.9 Japan (00) Bulk Carrier Safety Report on FSA study on bulk carrier safety IMO Marine Safety Committee 74/5/3 Mathiesen, TC (997) "Cost Benefit Analysis of Existing Bulk Carriers" DNV Paper Series No. 97-P008. Mathiesen, TC and R Skjong (996) "Towards a Rational Approach to maritime Safety and Environment Protection Regulations" Presented at Market Mechanisms for Safer Shipping and Cleaner Oceans, Erasmus University, Rotterdam, The Netherlands, October th - th, Copyright 00 by ASME

8 Norway (000) "Decision criteria including risk acceptance criteria" IMO Marine Safety Committee 7/6, Submitter by Norway. PROBAN (993) Version 4, Theory Manual, DNV Research Report , 993. Ronold, K and R Skjong (00) "The probabilistic code calibration module PROCODE", Joint committee on structural safety, workshop on reliability based code calibration, Zurich, Switzerland, March 00. Available at and Skjong, R (00) "Setting target reliabilities by marginal safety returns", Joint committee on structural safety, workshop on reliability based code calibration, Zurich, Switzerland, March 00. Available at and Skjong, R, EM Bitner-Gregersen, E Cramer, A Croker, Ø Hagen, G Korneliussen, S Lacasse, I Lotsberg, F Nadim and KO Ronold (995) Guidelines for Offshore Structural Reliability Analysis General DNV Report No Skjong, R and KO Ronold (998) Societal Indicators and Risk Acceptance, Offshore Mechanics and Arctic Engineering Conference, OMAE 998 Skjong, R and KO Ronold (00) So much for Safety, Offshore Mechanics and Arctic Engineering Conference, OMAE 00 Skjong, R and BH Wentworth (00) Formal Safety Assessment of Life Saving Appliances for Bulk Carriers, Submitted by Norway and ICFTU to IMO, MSC 74/5/5. Steen. E, L Hauge and R Løseth (995) "Reliability Based Ship Rules for Longitudinal Strength", Det Norske Veritas Research Report No Copyright 00 by ASME