Vessel Performance Index

a University of the Aegean, Department of Shipping Trade and Transport, 8 Korai Str. Chios 82100,Chios, Tel: +302271035272 Email: [email protected] b National Technical University of Athens

Vessel Performance Index – CO2 Index Baseline

Alexandros Glykasa*, George Papaioannoub

Summary The Marine Environment Protection Committee MEPC 57, 2008 of the International Maritime Organization, IMO, agreed to take an austere approach towards the emissions created by the marine fleet. In order to reduce the global levels of CO2 emissions it was necessary to introduce a baseline and use this as a benchmark for all vessels of same type. On a basis of theoretical data, IMO introduced a reference benchmark to offer a rational level to compare the performance and emissions created from each vessel. Contrary to IMO analysis the reported work in this manuscript processed actual data from 57 cargo vessels (Tankers and Bulk Carriers) operating worldwide and the results are compared to the theoretical ones from IMO. It is concluded that any presented benchmark requires being representative and available for all the vessels so that operators can measure an index associated to the fuel efficiency of each ship individually. The introduced benchmark pollution level is one of the building blocks for a mandatory design CO2 index.

Approach MEPC 57, 2008 was tasked the first intercessional Meeting of the Working Group on Greenhouse Gas Emissions from Ships (GHG‐WG1) in order to create a mandatory design CO2 index. The GHG‐WG1 developed a concept for a mandatory design CO2 index for new ships, based on submissions from Denmark and Japan. This index is called EEDI (Energy Efficiency Design Index) and it is formed as shown below on Equation (1):

∏ · · ·· · ·

· ·

· (1)

Factors associated with above equation 1 are explained in Table 1. Table 1: EEDI parameters Symbol Explanation Units

CFMEi a non‐dimensional conversion factor for the main engines between fuel consumption measured in grams and CO2 emission also measured in grams, based on carbon content

CFAEi a non‐dimensional conversion factor for the auxiliary engines between fuel consumption measured in grams and CO2 emission also measured in grams, based on carbon content

PMei installed power of the main engines kW PAE installed power of the auxiliary engines kW

SFCMei Specific Fuel Consumption of the main engines g/kWh

a University of the Aegean, Department of Shipping Trade and Transport, 8 Korai Str. Chios 82100,Chios, Tel: +302271035272 Email: [email protected] b National Technical University of Athens

SFCAEi Specific Fuel Consumption of the auxiliary engines g/kWh PPTIi is 75% of the rated power consumption of the shaft motorsPWHR is the rated electrical power generation of waste heat recovery system at PMei

feff is the availability factor of any innovative energy efficient technologyPeff is the main engine power reduction due to innovative energy efficient technology SFCeff is the specific fuel consumption of the main engines at PeffCfeff is the CO2 conversion factor of the fuel used in the main engine

Vref

is the ship speed, measured in nautical miles per hour (knots), on deep water in the maximum design load condition (Capacity) at the output of the engine(s) on Pme and assuming the weather is calm with no wind and no waves. The maximum design load condition shall be defined by the deepest draught with its associated trim, at which the ship is allowed to operate. This condition is obtained from the stability booklet approved by the administration

knots

Capacity DWT for Dry Bulk, Tankers, Container ships, General cargo ships, Tank volume for Gas carriers GT for Ro Ro cargo ships and passenger ships

tonnes m3

Gross ton fj are the corrections to account for ship specific‐design elements

fi is the capacity factor for any technical/regulatory limitation on capacity, and can be assumed one (1,0) if no necessity of the factor is granted

fw

is a non‐dimensional coefficient indicating the decrease of speed in representative sea conditions of wave height, wave frequency and wind speed. fw can be determend by conducting the ship‐specific simulation of its performance at representative sea conditions, or in case that the simulation is not conducted, fw value should be taken from the standard fw table curve. fw should be taken as 1.0 until the guidelines for the ship‐specific simulation or fw table/curve becomes available

The CFMEi and CFAEi for different fuel types are given in table 2. Table 2: Carbon content in each fuel type

Fuel Type g CO2 /g of Fuel

Diesel – Gasoil 3.206Light Fuel Oil (LFO) 3.151Heavy Fuel Oil (HFO) 3.114 Liquid Petrol Gas (LPG) 2.967 Natural Gas 2.931

Methodology The developed work in this study aims to introduce an effective way to categorize the vessels according to their real fuel performance and through analysis of accumulated data on a daily basis for a approximate period of about 5 years and propose a baseline for each ship. This baseline will serve as a benchmark for each specific vessel category. Furthermore, the reported work seeks to analyze and compare the theoretical EEDI values which are proposed in the IMO report. The IMO report is based on the assumption that the specific fuel consumption for all ship types is 190 g/kWh whilst the analysis presented herewith corresponds to real daily consumption data. This analysis also presents the degree upon the theoretical and real values are correlated.

IMO Analysis IMO report on EEDI was based on a large sample of ships given by Lloyds Register Fairplay (LRFP). The criteria set for retrieving the dataset were the following:

• New buildings in the period 01 January 1995 to 31 December 2004; • Minimum of 30 ships in a selection, preferably more than 100 ships; and • All the ships must have their main parameters given to be taken into account in the benchmarking (i.e. speed,

capacity measurement and engine data). Speed is received as the service speed of the vessel at MCR condition (Maximum Continuous Rating of the engines). Capacity is the maximum summer deadweight of the vessel in tones and power is the installed power of main and auxiliary engines measured in kW.

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The vessel types considered for determination were:

• Dry bulk carriers; • Tankers; • Gas carriers; • Containerships; • General cargo ships; • Ro‐ro cargo ships; and • Passenger ships, including ro‐ro passenger ships, but excluding high‐speed craft.

IMO processed the data further using the following assumptions:

• The carbon emission factor is constant for all engines, i.e. CF,ME = CF,AE = CF =3.114 g CO2/g Fuel;3 • The specific fuel consumption for all ship types is constant for all main engines, i.e. SFCME = 190g/kWh; • The specific fuel consumption for all ship types is constant for all auxiliary engines, i.e. SFCAE = 210g/kWh; • The load on main and auxiliary engines are set to 75% of MCR • All correction factors fj, fk and fw are set to 1.

Table 3 concentrates all the results coming from the IMO analysis.

Table 3: Concentrated table with exponential regression lines from all vessel types.

Graph 1 below shows the calculated baseline according to IMO for Dry Bulks.

Graph 1: IMO benchmark for Dry Bulks.

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Vessel Daily Data Acquisition Records for 57 vessels were provided by 4 Major Hellenic Management Companies. The company made available daily noon report data for both bulk carriers and tankers amongst their fleet. The delivered information included the following:

• RPM of the main engines, • Travelling distance [Nm] • Steaming time. [hours] • Average daily speed [Knots] • The fuel consumed [Mt] • Local Weather conditions

The acquired daily noon reports were obtained in raw text format and had to be categorized in a shorted tabular format in order to proceed with the statistical analysis. From the raw data the calculated indexes for each vessel are the following:

• Fuel Economy, measured in tn/mile and tn/hour • Brake Specific Fuel Consumption (BSFC), measured in g/kWh • Energy Efficiency Design Index (EEDI), measured in gCO2/tn Nm

Interpretation of table 2

Fuel Economy The Fuel Economy index was calculated simply by dividing daily oil consumptions with the distance traveled or with the time the main engine was operating.

Break Specific Fuel Consumption BSFC is the rate of fuel consumption divided by the power produced. BSFC allows the fuel efficiency of different reciprocating engines to be directly compared. The BSFC index was calculated as follows:

· , ,·

(2)

Where:

FCME (tn): is the Fuel Consumption of the main engine measured in tn MEKW: is the main engine power measured in kW

Energy Efficiency Design Index Equation (1) includes the correction factors fj, fi, fw as well as the Innovative energy efficient technology factor. However those factors have not been accounted as shown in the MEPC 57, 2008 and was simplified as follows:

• The carbon emission factor is constant for all engines, i.e. CFME = CFAE = CF =3.114 g CO2/g Fuel, • The Specific Fuel Consumption (SPF) for all auxiliary engines is considered constant, i.e SFCAE=210g/kWh, • The load on main and auxiliary engines are set to 75% of MCR • Correction factors fj, fi, fw are considered 1 • Innovative energy efficient technology is not included

So equation (1) becomes:

3.114 · 75% · ·∑ ∑·

(3)

Equation (3) was applied to the number daily values received from the supporting companies for all 57 vessels. Furthermore, using the data from the sea trial specifications for each vessel, a benchmark EEDI was calculated for each ship. This benchmark was used and compared with the EEDI resulting from the daily data and the EEDI from the IMO report.

Data Interpretation The data acquired from the Management Companies, were processed and analyzed. For a more precise analysis, extreme EEDI values were excluded in order to eliminate the effect of insignificant values on the final result. To effectively customize the data

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and ignore irrelevant values, Crystal Ball software was used. This software calculated the 90% ‐ 10% boundaries. Values outside of these boundaries are considered trivial and contribute to a larger standard deviation. Additionally, Crystal Ball calculated the best curve that could fit the data allocation. The distribution compatibility with the data was ranked based on Anderson – Darling goodness‐of‐fit test (O. Thas, 2003). The A‐D test is a one‐sided test1 and the hypothesis that the distribution is of a specific form is rejected if the test statistic, A, is greater than the critical value. Crystal Ball output is shown at the appendix.

Graph 2 and 3 depict the EEDI results for tankers and Bulk Carriers, which are based on the sea trial specifications2. The trend lines (dark and light blue) represent the EEDI for the vessels in a full speed and loaded condition and in an economic speed and ballast condition. Those two lines can be furthermore compared to the global Dry Bulk Benchmark and Tanker Benchmark given by the IMO study.

Graph 2: Comparison sea trials chart for Tankers with the IMO benchmark

Graph 3: Comparison sea trials chart for Bulk Carriers with the IMO benchmark

1 A one-sided test is a statistical hypothesis test in which the values for which we can reject the null hypothesis, H0 are located entirely in one tail of the probability distribution. In other words, the critical region for a one-sided test is the set of values less than the critical value of the test, or the set of values greater than the critical value of the test. A one-sided test is also referred to as a one-tailed test of significance.

2 Sea trial tests refer to the ship performance data of her Main Engine and auxiliary machinery upon satisfactory completion of vessels construction from the ship yard. The trial data are recorded as optimal data for the ship and are unique for each vessel.

y = 640.72x‐0.444 y = 2401.1x‐0.54 y = 829.16x‐0.496

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EEDI (gCO

2/t N

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Full ‐ Loaded condition IMO Benchmark Economic ‐ Ballast condition

y = 14795x‐0.734 y = 3174.7x‐0.612 y = 2503.1x‐0.56

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EEDI (gCO2/t Nm)

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Graph 2 and 3 reveals that the IMO benchmark for Tankers and Bulk Carriers lays above all the sea trial specifications, both for economic speed and ballast condition, and full speed and loaded condition. Thus the proposed EEDI by IMO overestimates the CO2 emissions from vessels.

However, it is obvious that the sea trial specifications deviate in most of the occasions from the real daily consumption data because of numerous parameters associated with the operation of the vessel such as the Maintenance Scheme and procedures followed by each operator, hull biological corrosion, fuel quality ect . The performance level of the vessel and her engine is becoming inferior compared to the data when the vessel was originally delivered from the shipyard. Furthermore, there are other parameters which affect the consumption performance that cannot be preliminary determined such as sea and current conditions. For that purpose, it became essential for this work to come up with some EEDI levels that correspond to the real daily consumption data and compare them with the IMO proposed levels. In this study the SFC of auxiliary engines was also received as 210 g/kWh due to lack of data.

As mentioned previously, the data acquired from the supporting companies were analyzed excluding values which were outside the 90% ‐ 10% confidence level. It was essential to keep the 80% of the data which were mostly concentrated around the mean and exclude data that were more aberrant. This procedure helps for a more precise result. From the remaining data, minimum and maximum values were used as upper and lower limit and correspond to the different performance of each vessel amongst the period of accumulated data. This upper and lower limit defines the boundaries were the 80% of the data lay with high probability. Graph 4 depicts the results for the tankers.

Graph 4: Tankers comparison chart of min and max values with IMO benchmark

The minimum and maximum values of the vessels are shown with the green and red dots respectively. The discontinuous green and red lines result from the power based trend lines and show respectively the lower and upper limits. The IMO benchmark for tankers (purple line) is approaching the upper limit of most of the vessels.

A similar analysis is followed for the Bulk Carriers. Graph 5 shows that the IMO Benchmark for Bulk Carriers (black line) lies between the lower and upper EEDI limit for DWT’s above 50,000. More specifically, IMO benchmark is approaching closer the EEDI for deadweights around the area of 40,000 – 80,000. Below the 40,000 area the benchmark is declining and is placed below all the minimum and maximum EEDI values, as derived from the acquired data. Furthermore, in the region above 80,000 the IMO benchmark although it is between the two limits, it has major divergence from most of the bullets3 shown in that area.

3 Each bullet represents the maximum (red) and minimum (green) EEDI values for a vessel.

y = 7196.x‐0.67 y = 8023.x‐0.64 y = 2401.x‐0.54

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min max IMO Benchmark

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Graph 5: Bulk Carriers comparison chart of min and max values with IMO benchmark

From both graphs (4 and 5) it is shown that by accepting the IMO EEDI levels as a benchmark could in several occasions act favorably for some vessels and in many other will act against them. For instance, some ships have both minimum and maximum EEDI values above the proposed IMO EEDI level. These vessels will always face a pollution penalty, even if the ship is properly maintained.

Energy Efficiency Design Index Analysis The EEDI seems to be a sufficient way to measure conventional ship performance4. This index successfully combines aspects such as vessel speed, deadweight capacity, main and auxiliary engine installed power. All those parameters seem to have a very important impact on CO2 emission levels. For instance the larger the speed the shorter the travel time will be for the same distance. Also higher capacity will enable larger cargo to be transferred and consequently less CO2 emissions per unit of cargo. Furthermore, larger main and auxiliary engine installed power means higher emission volumes.

However, it becomes essential to determine how much influence each of the above parameters has on the EEDI. The way to examine this issue is by applying a Monte Carlo simulation5 and perform a sensitivity analysis. For the sensitivity analysis all the independent variables were formed based on some distribution assumptions, which are mentioned on the appendix. The output of the simulation is presented in graphs 6, 7 and 8.

4 The EEDI doesn’t appear to apply in vessels with complex and sophisticated machinery installations. It is more suitable for application to “conventional” powered and propelled ships which comprise the majority of the world fleet. 5 Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results.

y = 14056x‐0.93 y = 12269x‐0.89 y = 2503.1x‐0.56

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min max IMO Benchmark

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Graph 6: Distribution of EEDI

Graph 7: Sensitivity analysis for the EEDI

Graph 8: EEDI and Deadweight correlation chart

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Graph 6 shows the distribution of the EEDI after 1,000,000 trials. The mean EEDI value is 7.49 gCO2/tn Nm with a standard deviation of 4.26 gCO2/tn. Moreover, the sensitivity analysis in Graph 7 presents the factors that mostly affect the EEDI. As shown from Graph 7 the Deadweight of Vessels has a major contribution in the EEDI. Capacity is negative correlated to the EEDI and influences this index by a factor of 91.8%. Other less influencing parameters are the main engine power (kW) and the specific fuel consumption (g/kWh) with 2.9%, and finally the vessel speed which also negatively affecting the EEDI by a factor of 1.4%. The highly negative correlated capacity and EEDI are also presented in Graph 8 after the 1,000,000 trials. The correlation between EEDI and Capacity is ‐0.9521, which is considered a relatively high.

Environmental Impact Defining a benchmark for each vessel in the global fleet will eventually create higher performance standards and will reduce carbon dioxide emissions. This benchmark could be defined by the initial manufacturing specifications and impose the ship to restrict lifetime emissions accordingly.

The issue that may be raised is whether the potential fuel efficiency gains will be higher from replacing existing vessels with larger one’s rather than with the same size. As it was shown in the sensitivity analysis above the deadweight has a considerable impact on the EEDI. Thus, it might be much more energy efficient to promote the larger capacity vessels. However on the Trade point of view this would not be efficient.

Conclusions The Conclusions drawn from the current analysis are summarized as follows:

1. In many occasions where the deadweight tonnage of the bulk carriers is relatively low the MEPC 57 estimation is deviating from the real data.

2. The EED index (defined by the MEPC 57) is often overestimating the CO2 emission level. 3. All vessels have a minimum and a maximum average consumption, which depends on:

a. The main engine condition b. Fuel purity c. Weather conditions d. The time passed since the last dry docking

4. The electric propulsion systems are facing a disadvantage in the existing formula, because the definition of installed power is not unambiguous. Thus the configurations do not contain the specific amount of energy which is wasted just for propulsion. Consequently vessels with diesel propulsion engines cannot realistically introduce an EEDI benchmark.

5. The negative correlation of DWT and EEDI is very high. This means that DWT affects greatly the level of the EED index. 6. The IMO assumptions regarding the SFC of main and auxiliary engines (190 g/kWh and 210 g/kWh) are

overgeneralizations and do not necessarily stand for the majority of engines. In this study the SFC of auxiliary engines was also received as 210 g/kWh due to lack of data.

Recommendations There are numerous parameters which should be taken into consideration under a legitimate scheme for implying maximum CO2 emissions. It is the view of the writers that such future legislation should be addressed and assessed for each individual vessel by the flag administration.

The CO2 emission level for each boat should not be determined by a general benchmark level defined by the EEDI. Each vessel should be examined separately from the flag administration and receive a relevant certificate for the Allowable Ship Emissions level. Hence, performance data from the sea trials of each vessel during the construction should be taken carefully into consideration and based on those data the Flag Administration should define the EEDI of the vessel for a range of operations.

The EEDI of each ship should not constitute the upper limit of pollution allowance. This would be the case in ideal conditions, where the ship performance is always going to be similar with the sea trials. However this is not the case. The analysis showed that there is a deviation in the daily consumption of 2‐15% from the sea trials during the 2 year data. Ideally the vessel performance would be the same with the sea trial specifications when:

1. The hull is maintained clean

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2. The combustion chamber is performing based on the specifications 3. The fuel purity is according to the specifications

The engine performance and the fuel purity can be directly or indirectly controlled by the ship owner or ship operator. However, the hull cleaningless condition is primarily depended on the freight market or the period intervals during which dry docking (or under sea cleaning) takes place. For instance, if a vessel stays without freight for a period of time, the hull will be exposed to biological corrosion which will consequently affect fuel consumption. Thus the ship will exceed its specified EEDI. In that case there should be an allowance for a specific period (from dry docking to dry docking).

The 75% operational level of the auxiliary and main engine needs further investigation.

EEDI benchmark should be based on full capacity conditions. Otherwise traders would avoid loading the vessel at the maximum capacity.

Correction factors fi, fj, fw need to be taken more seriously into consideration and receive values different than 1. Factor fw (weather conditions) has a great contribution to the vessel performance and needs to be determined based on a standard fw table curve.

Acknowledgements The reported work owns much to the personnel cooperation and data release from the fleet of Eastern Mediterranean Shipping, Evalent Navigation and Chartworld Shipping.

References 1. David Anink, Marnix Krikke, January 2009. The IMO Energy Efficiency Design Index. A Netherlands Trend Study. Centre for

Maritime Technology and Innovation, report Nr. 3064. 2. Directive 2005/33/EC Of The European Parliament And Of The Council of 6 July 2005 amending Directive 1999/32/EC,

2007, Official Journal of the European Union, 22.7.2005

3. Entec UK Limited, August 2005. Service Contract on Ship Emissions: Assignment, Abatement and Market‐based Instruments, European Commission Directorate General Environment.

4. International meeting of the greenhouse gas working group, February 2009. Consideration of the energy efficiency design index for new ships. Application of EEDI to ship’s other than those operating with conventional machinery and power distribution arrangements. IMO report.

5. James J. Corbett, Horst W Koehler, October 2003. Updated emissions from ocean shipping, Journal of Geophysical research.

6. IMO (2008a), "Future IMO regulation regarding green house gas emissions from international shipping," Submitted by Denmark, Marshall Islands, BIMCO, ICS, INTERCARGO, INTERTANKO and OCIMF, MEPC 57/4/2.

7. IMO (2008b), "A mandatory CO2 Design Index for new ships," Submitted by Denmark, Marshall Islands, BIMCO, ICS, INTERCARGO, INTERTANKO and OCIMF, MEPC 57/4/3.

8. IMO (2008c), "Development of an index for CO2 emissions per unit shipping capacity in actual operational conditions," Submitted by Japan, MEPC 57/4/11.

9. IMO (2008d), "A mandatory CO2 Design Index for new ships," Submitted by Denmark, MEPC 57/W.12. 10. Ship emissions study. National Technical University of Athens Laboratory for Maritime Transport, May 2008. 11. Neil Kelso, Beryl Cuthbertson, 1994. Fuel efficiency of ships and aircraft, Bureau of Transport and Communications

Economics, working paper 4, ISBN 0 642 18585 9. 12. O. Thas, J.P. Ottoy , Some generalizations of the Anderson–Darling statistic, Statistics & Probability Letters Volume 64,

pages 255–261, 2003 13. Prediction of air emissions from different ship types by Hans Otto Kristensen, 2000, Danish Ministry of Transport, TEMA

2000, Document from BIMCO.

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Appendix

Vessel Performance Data Table 1 below shows the performance of the dry bulkers and tankers, which is based on the daily noon reports. All the data were processed and displayed in a graph. There were three graphs for each category (tn/mile, tn/hour and g/kWh). The linear trend line of these data was calculated in order to present the general tendency of the vessel performance during the period of study. The content of table 1, is the percentage difference from the first and last point of the linear trend line. The positive sign shows an increasing trend, whereas the negative a decreasing trend.

Table 1: Vessel performance during the period of study.

DRY BULK Fuel Economy

tn/mile Fuel Economy

tn/hour

Break Specific fuel consumption

g/kWh

Vessel 1 3.26% 1.74% 1.58% Vessel 2 ‐5.25% ‐5.89% ‐5.75% Vessel 3 ‐6.00% ‐4.81% ‐2.10% Vessel 4 ‐3.75% ‐1.73% 11.99% Vessel 5 ‐4.17% ‐0.15% 5.43% Vessel 6 2.08% 8.52% 3.44% Vessel 7 8.56% 8.26% 7.97% Vessel 8 ‐0.56% 2.13% 3.33% Vessel 9 8.89% ‐0.21% 3.89% Vessel 10 5.01% ‐0.37% 0.00% Vessel 11 7.84% 5.71% 6.89% Vessel 12 5.05% 0.13% 1.72% Vessel 13 9.89% 5.40% 5.12% Vessel 14 ‐6.04% ‐1.19% ‐1.22% Vessel 15 13.58% 3.67% ‐4.23% Vessel 16 ‐2.46% ‐2.73% ‐2.87% Vessel 17 ‐4.41% ‐1.41% ‐1.31% Vessel 18 108.80% 88.70% 93.71% Vessel 19 4.65% 10.31% 0.26% Vessel 20 2.63% 2.38% 2.44% Vessel 21 59.23% 44.84% 48.13% Vessel 22 ‐3.08% ‐0.15% ‐0.16% Vessel 23 4.59% 6.10% 5.93% Vessel 24 8.32% 4.67% 4.73% Vessel 25 7.93% 6.04% 5.76% Vessel 26 19.26% 27.99% 27.25% Vessel 27 4.52% 1.56% 1.47% Vessel 28 7.44% ‐3.79% ‐3.53% Vessel 29 23.06% 1.82% 2.41% Vessel 30 ‐22.60% ‐8.70% ‐8.94% Vessel 31 8.02% 1.53% 1.45% Vessel 32 26.57% 7.83% 7.68% Vessel 33 3.22% 7.77% 7.91% Vessel 34 15.62% 7.26% 7.20% Vessel 35 8.10% ‐7.22% ‐7.35% Vessel 36 3.36% ‐0.73% ‐0.64% Vessel 37 4.37% 5.62% 5.41% Vessel 38 15.18% 6.44% 6.56% Vessel 39 14.47% 10.04% 9.56%

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Tankers Fuel Economy

tn/mile Fuel Economy

tn/hour

Break Specific fuel consumption

g/kWh

Vessel 1 14.63% ‐4.95% ‐6.17% Vessel 2 0.60% ‐9.15% ‐8.01% Vessel 3 ‐0.27% ‐4.67% ‐2.00% Vessel 4 ‐14.74% ‐15.24% ‐14.76% Vessel 5 ‐1.66% ‐10.00% ‐7.03% Vessel 6 3.37% ‐5.25% ‐1.66% Vessel 7 ‐8.25% ‐0.61% ‐9.13% Vessel 8 ‐9.88% ‐0.69% ‐10.72% Vessel 9 9.87% 0.17% 4.70% Vessel 10 5.15% ‐0.37% ‐4.11% Vessel 11 17.84% ‐0.37% ‐3.06% Vessel 12 12.95% 3.76% 4.63% Vessel 13 ‐3.12% ‐2.01% ‐2.03% Vessel 14 ‐0.15% 1.14% 1.17% Vessel 15 ‐5.29% 1.54% 1.59% Vessel 16 ‐1.75% 1.27% 1.36% Vessel 17 2.59% ‐14.90% ‐15.70% Vessel 18 7.06% 4.89% 4.89%

Monte Carlo Simulation and Sensitivity Analysis Table 2 and 3 below show the statistics from graph 6.

Table 2: Crystal Ball software output for the EEDI index

Statistics: Forecast values

Trials 1,000,000 Mean 7.47 Median 6.13 Mode ‐‐‐ Standard Deviation 4.26

Variance 18.18 Skewness 1.50 Kurtosis 5.20

Coeff. of Variability 0.5706 Minimum 1.56 Maximum 34.41

Range Width 32.85 Mean Std. Error 0.00

Table 3: Crystal Ball software output for the EEDI index in percentiles

Percentiles: Forecast values

100% 1.56 90% 3.49 80% 4.11 70% 4.71 60% 5.37

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50% 6.13 40% 7.09 30% 8.38 20% 10.30 10% 13.65 0% 34.41

Sensitivity Analysis Assumptions Assumption: Auxiliary Engine [kW] Normal distribution with parameters:

Mean 2,500.00 Std. Dev. 360.00

Selected range is from 800.00 to 4,000.00

Assumption: Capacity (DWT) Normal distribution with parameters:

Mean 120,000 Std. Dev. 95,797

Selected range is from 20,000 to 300,000

Assumption: conversion factor Uniform distribution with parameters:

Constant 3.114

Assumption: Main Engine [kW]

Normal distribution with parameters: Mean 27,161Std. Dev. 2,716

Selected range is from 7,000 to 40,000

Assumption: Load of the main and auxiliary engines Normal distribution with parameters:

Mean 85% Std. Dev. 10%

Selected range is from 75% to 90%

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Assumption: Specific Fuel Consumption of the Auxiliary Engine (g/kWh) Normal distribution with parameters:

Mean 190.00 Std. Dev. 21.00

Selected range is from 150.00 to 220.00

Assumption: Specific Fuel Consumption Main Engine (g/kWh) Normal distribution with parameters:

Mean 149.00 Std. Dev. 14.90


Assumption: Velocity reference Normal distribution with parameters:

Mean 13.50 Std. Dev. 1.55


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Vessel Performance Index