International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 3

Number 2

June 2009

181

1 INTRODUCTION

1.1 The Universal Learning Curve

We have developed a general accident theory, so in

this paper we emphasize and extract the relevant ap-

plication to marine shipping. For any technological

system with human involvement, like ships and

shipping, the basic and sole assumption that we

make is the “Learning Hypothesis” as a physical

model for human behavior when coupled to a tech-

nology (Duffey & Saull 2002, 2008).

Simply and directly, we postulate that humans

learn from their mistakes (outcomes) as experience

is gained.

Although we make errors all the time, as we

move from being novices to acquiring expertise, we

should expect to reduce our errors, or at least not

make the same ones. Thus, hopefully, we should de-

scend a “Universal Learning Curve” (ULC) like that

shown in Figure 1, where our rate of making mis-

takes decreases as we learn from experience and is

exponential in form.

Figure 1. The Learning Hypothesis – as we learn we descend

the curve.

Universal Learning Curve

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.1 0.2 0. 3 0.4 0.5 0. 6 0.7 0.8 0. 9 1

Increasing Accumulated Experience

Observed Rate of Making Errors

Learning path

Novice or Error prone

Experienced or Safest

High

Low

Less

Managing and Predicting Maritime and Off-

shore Risk

R.B. Duffey

Atomic Energy of Canada Limited, Chalk River, Canada

J.W. Saull

International Federation of Airworthiness, East Grinstead, W. Sussex, United Kingdom

ABSTRACT: We wish to predict when an accident or tragedy will occur, and reduce the probability of its oc-

currence. Maritime accidents, just like all the other crashes and failures, are stochastic in their occurrence.

They can seemingly occur as observed outcomes at any instant, without warning. They are due to a combina-

tion of human and technological system failures, working together in totally unexpected and/or undetected

ways, occurring at some random moment. Massive show the cause is due to an unexpected combination or

sequence of human, management, operational, design and training mistakes. Once we know what happened,

we can fix the engineering or design failures, and try to obviate the human ones. We utilize reliability theory

applied to humans, and show how the events rates and probability in shipping is related to other industries and

events through the human involvement. We examine and apply the learning hypothesis to shipping losses and

other events at sea, including example Case Studies stretching over some 200 years of: (a) merchant and fish-

ing vessels; (b) oil spills and injuries in off-shore facilities; and (c) insurance claims, inspection rules and

premiums. These include major losses and sinkings as well as the more everyday events and injuries. By us-

ing good practices and achieving a true learning environment, we can effectively defer the chance of an acci-

dent, but not indefinitely. Moreover, by watching our experience and monitoring our rate, understand and

predict when we are climbing up the curve. Comparisons of the theory to all available human error data show

a reasonable level of accord with the learning hypothesis. The results clearly demonstrate that the loss (human

error) probability is dynamic, and may be predicted using the learning hypothesis. The future probability es-

timate is derivable from its unchanged prior value, based on learning, and thus the past frequency predicts the

future probability. The implications for maritime activities is discussed and related to the latest work on man-

aging risk, and the analysis of trends and safety indicators.

182

The past rate of learning determines our trajectory

on the learning path and thus:

− how fast we can descend the curve;

− the rate at which errors occur determines where

we are on the curve;

− changes in rate are due to our actions and feed-

back from learning from our mistakes;

− no reduction in error or outcome rate could mean

we have reached the lowest we are able to or that

we have not sustained a learning environment;

and

− an increase in rate signifies forgetting.

In our book that established the existence of the

learning curve (Duffey & Saull 2002), we examined

many case studies.

We highlight in this paper the data and infor-

mation for marine events and their learning trends.

We have also found data for oil spills at sea. Since

spills are just another accident in a homo-

technological system (HTS), namely a ship operated

by people, it was interesting to show if the usual

everyday marine accidents do exhibit learning. Ma-

rine accident outcomes include groundings, colli-

sions, fires and all manner of mishaps. The most re-

cent data we found were on the web in the Annual

Report for 2004 of the UK Marine Accident Investi-

gation Board (MAIB, for short, at

www.maib.gov.uk). The MAIB responsibility is to

examine reported accidents and incidents in detail.

The MAIB broke down the accidents by type of

ship, being the two broad categories of merchant

ships that carry cargo, or fishing vessels that ply

their trade in the treacherous waters off the UK is-

lands,

In both types of ship, the number of accidents

were given as the usual uninformative list of tabula-

tions by year from 1994 to 2004, together with the

total number of ships in that merchant or fishing

vessel category, some 1000 and 10,000 vessels re-

spectively. Instinctively we think of fishing as a

more dangerous occupation, with manual net han-

dling and deck-work sometimes in rough seas and

storms, but surprisingly it turns out not to be the

case.

Figure 2. The learning curve for shipping accidents.

We analyzed these accidents by simply replotting

the data as the accident rate per vessel versus the

thousands of accumulated shipping–years of experi-

ence, kSy. By adopting this measure for experience,

not only can we plot the data for the two types on

the same graph, we also see if we have a clear learn-

ing trend emerging. The result is shown by Figure 2,

where the line or curve drawn shown is our usual

theoretical MERE learning form.

We see immediately that, at least in the UK, the

(outcome) accident rate is higher for merchant ves-

sels than fishing boats, but also that learning is evi-

dent in the data that fit together on this one plot only

if using experience afloat as a basis. The other ob-

servation is that the fishing vessels are at the mini-

mum rate per vessel that the merchant vessels are

just approaching. Perhaps the past few centuries of

fishing experience has lead to that low rate so that,

in fact, fishermen and fisherwomen are highly

skilled at their craft. The lowest attained rate of ~

0.05 accidents per vessel corresponds to an hourly

rate if afloat all day and working all the time, of:

~ 0.05/(365 x 24) ~ 5.10

-6

per hour (1)

That is one accident per vessel every 175,000

hours, which is about the least achieved by any HTS

or industry anywhere in the world, including the

very safe ones like aircraft, nuclear and chemical in-

dustries of 100,000 to 200,000 hours. Even allowing

for a duty factor afloat for the vessel or crew of 50%

or so, or working at sea half the time, it is still of the

same order. That last result is by itself simply amaz-

ing, and reflects the common factor of the human

involvement in HTS. We now examine the learning

hypothesis analysis again, but in some more detail.

2 THE RISK OF LOSING A SHIP

We can use data from shipping, as it is a technologi-

cal system with human involvement that is observed

and includes both outcomes and a measure of expe-

rience. Shipping losses are an historic data source, as

insurers and mariners tracked sinkings; and the hu-

man element is the main cause of ship loss, rather

than structural defects in the ships themselves.

A large dataset exists for ship losses in the USA,

(Berman 1972). We analysed these extraordinary da-

ta files, which cover some 10,000 losses (outcomes)

over an Observation Range of nearly 200 years from

1800 to 1971. We excluded Acts of War so as to

avoid uncontrolled external influences and non–

human errors. It is not known how many ships were

afloat in total, only which ones sank, and thus be-

came recorded outcomes.

A ship is built in a given year, sails for a while

accumulating experience in ship-years afloat, Sy,

Shipping Accidents

UK 1994-2004

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 20 40 60 80 100

Experience afloat, kSy

Rate/vessel, IR

Merchant vessels

Fishing vessels

MERE, IR= 0.05+0.24exp-(acckSy/7.6)

183

and may or may not sink. From some 10,000 ships

that were lost, we took a sample of the data only for

ships over 500 tons, chosen so that we can compare

with modern large commercial losses. In our sample

of the data there were a total (N) of 510 losses of the

ships.

From the entire set, we show one sample Obser-

vation Range in Table 1 for 1850 to 1860, selected

arbitrarily from the entire data set. For these loss

(outcome) data for 1850 to 1860, 17 ships were lost

which had accumulated 265 shipping-years (accSy)

of depth of experience before being lost. The losses,

= 17, are sparsely distributed and apparently ran-

dom, as we might expect. The entire observation set

of 1800 to 1971 can be formed by stacking these in-

cremental observations ranges together for all the

observed range and number of outcomes. But this

again is only one subset of an array that could

stretch over all recorded history, and all human ex-

perience - we just happen to not have all that data.

Table 1. Actual Ship Loss Data matrix: A sample outcome observation interval

Year 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 Sy accSy

#Losses

1 0 0 0

2 1 1 4 4 2

3 1 3 7 1

4 1 4 11 1

5 0 11 0

6 1 1 12 23 2

7 0 23 0

8 0 23 0

9 0 23 0

10 1 10 33 1

11 0 33 0

12 0 33 0

13 1 13 46 1

14 0 46 0

15 0 46 0

16 0 46 0

17 0 46 0

18 0 46 0

19 1 2 57 103 3

20 1 1 40 143 2

21 0 143 0

22 0 143 0

23 0 143 0

24 0 143 0

25 0 143 0

26 0 143 0

27 1 27 170 1

28 0 170 0

29 0 170 0

30 1 30 200 1

31 1 31 231 1

32 0 231 0

33 0 231 0

34 1 34 265 1

35 0 265 0

36 0 265 0

37 0 265 0

38 0 265 0

39 0 265 0

40 0 265 0

Totals 1 2 2 3 2 2 0 1 3 1 0 265 265 17

184

The usual time history is given by the sum of the

losses for any given year. Thus, for any year, y,

there is a loss rate given by summing over all the

experience range of losses for that particular obser-

vation, j

range year:

= ∑

(ε) (2)

Meanwhile, for a given experience, ε, the total

number of losses, N, is given by summing all the

losses over the range at a particular experience, as:

= ∑

(ε) (3)

The sum of the number of Sy at any experience

interval is simply given by adding up outcomes:

Sy (ε) = ∑

(Sy n

(ε)) (4)

Hence, the accumulated experience in accSy’s is

as shown from adding the Sy’s for all losses:

accSy = ∑

(Sy n

(ε)) (5)

Now we can calculate the outcomes for all the en-

tire Observation Range for 1800-1971. We find the

total losses of >500 tonnes are now of course as

summed as all outcomes:

= ∑

(ε) = 510 (6)

and the accumulated experience is summed over the

depth of experience:

accE = ε = ∑

(ε) Sy) = 11,706 accSy (7)

So we have confirmed the postulate that we may

represent outcomes by a distribution of errors as a

function of experience, and where all outcomes are

equally likely.

On average, therefore, ships spent an average of

11,706/510 = 23 years afloat before sinking.

3 SHIPPING LOSS DISTRIBUTION

FUNCTIONS

If the losses were truly random in time, then on av-

erage the chance is equal that a ship would be lost

either side of the middle of the Observation Range,

or centered on the date:

1800 + (1971 - 1800)/2 = 1885, (8)

and the loss rate distribution should follow a bino-

mial (normal) distribution. The actual distribution of

the loss rate data does just that, and data for the en-

tire Observation Range is shown in Figure 3, includ-

ing the 95% confidence bounds.

Figure 3. Loss rate fitted with a normal distribution.

The fitted loss rate distribution actually centers on

1900, and is given by:

IR(per kSy)=0.0095+0.86 exp 0.5((Y–1900)/19)

(9)

where 1 kSy = 1000 Sy.

Since the data have a normal distribution, the out-

comes are indeed randomly distributed throughout

the entire 1800-1971 Range. The standard deviation

of 19 Sy and the 95% confidence limits do actually

encompass the predicted date of 1885, within the er-

rors of the data sampling and fitting. The most prob-

able loss (outcome) rate is ~ 0.86 per 1000 Sy,

which is close to that observed today (~1per kSy) by

major loss insurers. The most probable rate has not

changed for over 200 years, and the range at 95%

confidence is 0.7 – 1 per kSy.

As to the systematic effects of ship-age, it has

been characteristic practice to have higher insurance

for older ships, implying there risk of loss is greater,

and that the outcomes (vessel sinkings, groundings,

collisions, etc.) are not random. Older vessels are

then classified as higher or greater risk. The actual

data are shown in Figure 4 for losses in excess of

500 tonnes for two outcome sets spread over two

centuries. Clearly, there is little difference between

them; and the outcomes are almost normally distrib-

uted over the life of the ships with about 40-50 years

maximum. The maximum loss fraction peak is at

about 15-20 years of ship-life.

Figure 4. Comparison of shop losses as a function of age.

USA Shipwreck History 1800-1971 (extract): Normal Distribution centered on 1900

Loss Rate (per 1000) = 0.0095 + 0.86exp(-0.5(x-1900)/19)^2)

r^2=0.43192861

1800

1850

1900

1950

Year of Loss

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

Loss Rate (IR per 1000 )

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

Loss Rate (IR per 1000 )

Comparative Age Distribution of Shipping Losses

0 5 10 15 20 25 30 35 40 45 50 55

Age Range (years)

Percent of Losses (%)

UK P&I Club Profile1997

US Berman Data 1850-1971

185

Now in terms of the influence of accumulated ex-

perience, we may plot the loss rate per ship-year

versus the accumulated experience in accSy as

shown in Figure 5.

Figure 5. The learning curve for shipping.

The loss rate as a function of the accumulated ex-

perience in accSy is then given by a best-fit line of

the exponential form derived for the distribution of

the total number of microstates:

A ≈ A

+ A

–ε/k

(10)

A (losses per Sy) = 0.08+0.84 exp–(accSy/213) (11)

This result implies an initial loss rate many times

higher than the equilibrium value, and a minimum

rate of ~ 0.08 per Sy for those that sank. This is of

course telling us that on average the ships that sank

lasted for a depth of experience afloat of about

(1/0.08) or ~13 Sy, starting off lasting some 10 times

less (~1 Sy). It does not tell us how long the average

ship lasted, including those that were not lost, and

indeed this is irrelevant for the moment. We just

want to predict the relation between sinking rates

and ship lifetimes. On an accumulated rate basis the

predicted loss rate is now ~1 per 1000 Sy, illustrat-

ing the importance of the data sample size Observa-

tion Range for apparently random events.

Thus we have confirmed the postulates that:

− a systematic learning curve exists superimposed

on the apparently random losses which we ob-

serve as outcomes;

− a relevant measure for accumulated experience

and depth of experience can be found (in this case

years-afloat); and

− a minimum asymptotic rate does exist, and is de-

rivable from the learning curve.

4 OIL SPILLS AT SEA: TRACKING LEARNING

TRENDS

We have provided an initial analysis of importance

to the safety and environmental impact of the oil

storage and transportation industry, using publically

available USA data on oil spills, shipping losses and

pipeline accidents, not having access to the oil and

gas industry’s privately held spill database (Duffey

et al 2004).

Spills and accidents can arise in many ways e.g.:

− while filling;

− in storage;

− during transport;

− at process and transfer facilities; plus

− failure of vessels and pipelines.

We would expect significant human involvement

in the design, management and operation of all these

technological activities, in the piping, pumping,

tanks, valves and operations. For handling and stor-

age of (petro) chemicals, the risk of a spill or a loss

is also dependent on the human error rate in the

transport or storage mode and the accumulated expe-

rience with the transport or storage system.

Figure 6. The oil spill learning curve

The US Coast Guard database for oil spills was

the most comprehensive we found, but is given in

the usual annual format of tables. For shipping

spills, in the oil spill database for the observation in-

terval from 1973 to 2000, we found information for

231,000 spill events for the USA, while transporting

a total of oil of nearly 68 Btoe, of which 8,700

events were spills of more than 1000 gallons. As-

suming there is pressure from the EPA, industry,

owners and others to reduce spills rates, then there is

a nominally large HTS learning opportunity. We can

easily extract the number of spills from such tables

and transform it to an experience basis (Duffey &

Saull 2008), replacing the list of numbers of out-

comes on a purely calendar year reporting basis. The

measure for the accumulated experience we took

was the total amount of oil being shipped in and out

of the USA, which is not given in or by the USGS

raw datatables. The US DOE track the oil consump-

tion information and where it comes from for purely

USA Ship Loss Data 1800-1971 (extract)

Loss rate, IR(i) (per Sy)=0.08+0.84exp-(accSy/213)

r^2=0.9026953

3000 6000 9000 12000 15000

Accumulated Experience, ship-years (accSy)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Loss Rate, (IR( i ) per Sy )

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Loss Rate, (IR( i ) per Sy )

US Oil Spills 1972-2000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000

Accumulated Oil Shipped, Imports+Exports, accMtoe

Spill Rate ( per Mtoe)

Tanker Spills (S/Mtoe)

Spills>1000gals (S/Mtoe)

MERE, IR (S/Mtoe)=0.018+0.4 exp-(accMtoe/21600)

Data sources:

US Coast Guard Polluting IncidentCompendium,2003;

US DOE EIA, US Trade Overview,2003

186

energy analysis purposes. The datatables for crude

oil and petroleum products were given in the DOE

Petroleum Overview, for 1949-2001, and the details

of the calculations we have given elsewhere (Duffey

& Saull 2008 in Chapter 8).

The summary result is shown in Figure 6, and fol-

low a clear learning curve, which is also shown fit-

ted to the data.

5 INSURING MODERN LOSSES: THE MOST

PROBABLE AND MINIMUM ERROR RATE

Now having established the learning curves and loss

rates from historical data, we have also confirmed

the results by testing the analysis against other data

for modern fleets, where losses for all ships over 500

tonnes were tracked. These include data for modern

vessels (Institute of London Underwriters 1988) for

losses greater than 500 tonnes for 1972-1998, and

for the latest (UK Protection and Indemnity Mutual

Insurance Club 2000) Major Claims data from 1976-

1999.

In these modern datasets, we also know how

many ships were afloat, but the years afloat for each

ship were not known (the converse to the Berman

dataset). The Observation Ranges were smaller (~ 25

years), but covered the world-wide total losses

which are comparable in number.

The data is shown in Figure 7, where we have the

loss rate for the ILU dataset for 1972-1998 world-

wide is given by, for some 30,000 ships afloat in any

Sy, accumulating nearly a million Sy in total, and

some 3,000 outcomes (losses) over the 26 year

Range:

A ≈ A

+ A

–ε/k

(12)

or,

A (losses per kSy) = 0.95 + 7 exp -(acckSy/600) (13)

Figure 7. Modern Ship Losses

This result shows an asymptotic or minimum loss

rate of ~ 0.95 per kS/y for losses > 500 tonnes in

1972-1998 (despite observing nearly 2 /kSy now).

We have a similar estimate for the Major Loss data,

that is greatest in terms of financial cost, which

shows a loss rate of ~1 /kSy (Pomeroy 2001), which

is a value consistent with the above analyses.

This lowest predicted minimum rate of ~ 0.95

/kSy is consistent with the most probable rate inde-

pendently derived from the data for losses only (i.e.,

0.86 ± 0.1 per kSy) for 1800-1971. Since the two da-

tasets do not overlap, meeting in 1970, and one is for

losses only in the USA and one is for all ships afloat

world-wide, we have shown that:

− the minimum error rate predicted for modern

ships is close or equivalent to the most probable

loss rate for the last 200 years, which if correct

also confirms the postulate of the most probable

distribution used in deriving the microstates dis-

tribution formula;

− the distribution of microstates (manifested as an

outcome rate) is apparently independent of tech-

nology or date, and is due to the dominant contri-

bution of the human element; and

− the learning curve approach is consistent with the

statistical distribution of error states.

6 LEARNING RATES AND EXPERIENCE

INTERVALS: THE UNIVERSAL LEARNING

CURVE

The two datasets we have studied are at first sight

quite distinct, even though both are observed and

recorded only for losses greater than 500 tonnes. The

observational intervals, the accumulated experience

and the number of outcomes are drastically different.

One set (set A) is from 1800 to 1971, and gives a

distribution of microstates for only losses for the

USA with an experience base of about 10 kSy. The

other (set B) extends that set A from 1971 to 1996,

but is for the distribution of microstates for losses of

all ships world-wide with an experience base of

nearly 1000 kSy. Therefore, the depth of experience

is quite different. The accumulated experience, Σn

, is then quite different for each set, by the same

factor of 100. Above, we have shown the learning

curve rate constants are also different, being

~ 200 Sy for set A, and ~ 600 kSy for set B, which is

a factor of ~ 3000.

So, for these Ranges, the predicted “learning rate

ratio” between experience intervals for the losses on-

ly in the USA and for the whole world fleet afloat is:

/β

~ 30 (14)

Recall again that dataset A was for all ships afloat

world-wide, while dataset B was just for those that

ILU Data 1972-1997

0 200 400 600 800 1000 1200 1400

Accumulated Experience ( acckSy)

Loss Rate ( L/kSy)

ILU Loss Data 1971-1996(>500t)

MERE, IR= 0.95+ 7exp(-acckSy/600)

187

sank in the USA. The ratio above suggests that the

experience interval ratio of the USA losses to the

world fleet afloat is (ε

/ε

) ~ 1/30 (i.e., 3%), particu-

larly if β

~ β

To test that ratio prediction, recall also that for

the ILU data in ~ 25 years we had 3000 losses of

~ 30,000 ships afloat at any time. That is a loss rate

percentage for the whole fleet of order (3000/25) X

(100/30000) = 0.4% world-wide. But only a fraction

of the world fleet actually sailed and sank near the

USA. To determine that fraction, we sought another

random sample Observation Range of losses and

found an excellent one in the “Atlas of Ship Wrecks

and Treasure” (Pickford 1994). Now the Atlas lists

about 184 ships sunk off the East, West and Carib-

bean coasts of the USA between 1540 and 1956 out

of a listed sample world-wide of 1400 losses. That is

only a fraction of (184/1400) x 100 = 13% of the

world’s ship losses were in the waters off the USA.

We assume that fraction holds for the much later

ILU dataset, which was for all ships > 500 tons.

So if just 13% of the ships world-wide sank off

the coasts of USA, and only 0.4% of the fleet sank in

total around the world, we would have 0.4%/0.13 ~

3% as the experience interval ratio of only the USA

losses to the total world total fleet afloat. Therefore,

we have near perfect agreement versus the predicted

ratio from the theory of 3% (or a factor of 30).

Given the uncertainties in the calculations, and

the vast differences in the datasets, this degree of

agreement with the prediction seems almost seems

fortuitous and better than might be expected. But the

comparison does confirm the general approach and

indicate how to compare datasets that possess very

different experience bases.

Let us try to test another prediction: if the theory,

postulates and analogies are correct the two datasets

should both follow the trend predicted by the ULC.

We can directly compare the two learning rates for

set (A) and set (B) with their very different experi-

ence bases by using the non-dimensional formula-

tion of the ULC for correlating data, i.e.,

E* = exp-KN* (15)

We correct the learning rate constant for the USA

losses only for the ratio of ~ 30 derived above. The

actual learning curves give all the needed estimates

from the data for A

and A

, which is sufficient to

calculate E* for each microstate. We also have the

total experience, ε, necessary to derive the non-

dimensional value of N*. Strictly speaking N*

should be taken as the ratio of experience, ε, to the

experience, ε

, needed or observed to reach the min-

imum error rate, λ

, or at least the maximum experi-

ence already achieved with the system.

The comparisons of the ULCs suggested by the

theory are shown in Figure 8. We have also shown

the best-fit correlation to world data, i.e., with K ~ 3,

E* = exp-3N* (16)

Figure 8. Comparison of trends with the ULC

The value of K ~ 3 was derived from analyzing

vast datasets covering millions of error states that

included amongst other things (Duffey & Saull

2002, see Figure 1.7 in Chapter 1): USA data for

deaths in recreational boating 1960-1998; automo-

bile crashes 1966-1998; railway accidents 1975-

1999; coal mining for 1938-1998; plus South Afri-

can gold and coal mining injuries 1969-1999; UK

cardiac surgeries 1984-1999; US oil spills 1969-

2001; French latent error data 1998-1999; US com-

mercial aircraft near misses 1987-1997; and also

world pulmonary deaths for 1840-1970.

The two other lines, for the US (Berman) losses

only and ILU world shipping datasets, are given by

the MERE predictions calculated from:

E* = exp-KN* = exp - ((1 - A/A

)/(1-A

)) (17)

whence

A = A

+ (A

- A

– ε/k

(18)

and the values for k, A

and A

are derived directly

from those given by the theory and the data. The 213

Sy in the exponent is adjusted for the observational

experience interval ratio and becomes k = 213 x 30

= 6390 Sy = 6.4 kSy.

Hence, the only adjustment we have made or

needed was to correct the learning rate constant for

the differing depths of experience. We justify the

factor of ~ 30 simply to bring the experience interval

for the losses in the US only data consistently into

line with the world experience interval. The remain-

ing differences between the predictions are well

within the overall data scatter.

This method thus allows apparently quite dispar-

ate datasets to be renormalized and intercompared.

The universal learning trends are essentially the

Universal Learning Curves

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

E*= exp-3N*

MERE :US Only Loss Data 1800-1971

MERE: ILU W orld Loss Data 1971-1996

188

same, and we have validated the overall theoretically

predicted trend.

Thus, we have succeeded in not only getting the

two very different datasets on the same plot, but in

obtaining agreement with the world trend derived

from a wide range of totally independent data. Using

the non-dimensional variables derived from theory,

we have shown that the trends are correct. This

agreement is despite the numerical changes being

very large, by a factor of ~ 100 in the learning rate

ratio and a factor of 1000 in the accumulated experi-

ence, as we have discussed above.

7 PRACTICAL APPLICATION: PREDICTING

LOSSES AND MANAGING RISK

Data are essential to measuring performance. Note

that the shipping error/loss rate is not affected by the

massive technology changes in shipping (from sail

to steam, from wood to steel) occurring over the last

two hundred years. Losses are dominated by human

(crew) performance. The overall loss rate (~ one per

thousand ship years afloat) enables the prediction of

loss probability, which affects both insurance costs

and classification. In addition, the learning curve

provides the probability of operational error, which

is a function of the shipping maneuver or course

transient. In principle, the analysis then provides the

likelihood of collision, grounding or near misses.

As for other industries and technologies, it would

be useful and necessary to have further data mari-

time continuously collected on actual events, and to

develop nautical performance indicators, that can be

updated continually for loss and risk assessment

purposes. Such an activity is underway for offshore

oil and gas fields in the North Sea for both mobile

and fixed facilities (Duffey & Skjerve 2008). Such

objective measures and indicators enable the pres-

ence or absence of learning trends to be discerned,

enhancing the management of risk exposure and

prediction of losses, and hence would help guide

improvements in maritime training, safety and loss

control.

8 CONCLUSIONS

We have described a general and consistent theoreti-

cal model, however simplified it may be, which de-

scribes the rate of outcomes (losses) based on the

classic concept of learning from experience. The ap-

proach is quantifiable and testable versus the exist-

ing data and potentially able to make predictions.

We reconcile the apparently random occurrence of

outcomes (accidents and errors) with the observed

systematic trend from having a learning environ-

ment. We can now explain and predict outcomes,

like ship losses, collisions and sinkings, and their

apparently random occurrences because the human

element component is persistent and large.

We infer that risk reduction (learning) is propor-

tional to the rate of errors being made, which is de-

rived from the total number of distributions of er-

rors. We have validated the new theory, and in this

paper summarize the use of marine loss and oil spill

data as a working example. We analyzed shipping

losses over the last two hundred years, which are an

example of one such system and a rich data source

because insurers and mariners tracked sinkings.

Human error is and was the pervasive and main

cause of ship loss, rather than structural defects in

the ships themselves. The validation results support

the basic postulates, and confirm the macroscopic

ULC behavior observed for technological systems.

Our new theory offers the prediction and the

promise of determining and quantifying the influ-

ence of management, regulatory, liability, insurance,

legal and other decisions.

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