International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 4

Number 2

June 2010

223

1 INTRODUCTION

The safety of the ship system could be considered

as a series of barriers or against the potential for

failure. These barriers may include hardware, soft-

ware, and the human element and the presence of

one or more of the barriers will prevent accidents

from happening. But it happens that the safety barri-

ers are penetrated and an accident occurs.

Figure 22. Ships accident statistic, American Bureau of Ship-

ping, 2004

Very often when an incident has occurred, once

tends to interpret the past, prior to the event, only in

terms of its bearing on that event which means that

the total contemporaneous context is missing. So

once concentrate only on “significant” event’s

chains.

2 THE SYSTEM

2.1 The ship system

The ship safety model should cover the ship geo-

graphically and all the installed systems including

propulsion and electric power production, energy

production, emergency power, bridge systems, safe-

ty systems, human factor and passenger related sys-

tems.

The necessary methodology consists of following

stages, (Soares, Teixeira, 2001):

1 Generic Ship Model

2 Topographical Safety Block Diagram

3 Ship Safety Model

Generic Ship Model describes how all the ship

functions, subsystems and systems, influence the

ship safety. Importance of each component should

be clearly defined. Generic Ship Model could be fur-

ther utilized as a basis for comprehensive Ship Safe-

ty model.

Specific criteria should be developed to enable ef-

ficient estimation of the crew influence on the ship

safe factor.

Serie1;

Human

Factor;

44,00%;

44%

Serie1;

Device

Failure;

40,00%;

40%

Serie1;

Hydromet

eorologica

conditio…

Serie1;

Others;

1,00%; 1%

Human Factor

Device Failure

Hydrometeorolo

gical conditions

Others

Finite Discrete Markov Model of Ship Safety

L. Smolarek

Gdynia Maritime University, Gdynia, Poland

ABSTRACT: The ship safety modeling is the process used to convert information from many sources about

the ship as an antropotechnical system into a form so that it can be analyzed effectively. The first step is to fix

the system (ship, human, environment) boundaries to clearly identify the scope of the analysis. The ship can

be generally defined by conceptual sketches, schematics drawings or flow diagrams to establish the element

hierarchy which evolves from the physical and functional relationships. The man could be generally defined

by the operational procedures. The environment could be generally defined by the mission place and time of

the year. The information is needed considering that the accidents are caused by factors associated with ship

(failure, design defect), man (human error, workload), and environment. Safety is a system property that we

intuitively relate to a system’s design, accident rates and risk. This work proposes finite discrete Markov

model as an example of systematic approach to the analysis of ship safety.

224

Figure 23. Generic model of some ship’s subsystems and sys-

tems

2.2 Navigational system

Since half on twenty century rules concerning vessel

technical condition, crew knowledge and operational

action proving vessel safety are have been defined

by International Maritime Organization. The meas-

ure of vessel safety is a risk defined as a function of

threats and consequences relating to theoretical and

actual risk, (Soliwoda 2008).

Figure 24. Vessel reliability conditions according to naviga-

tional system and navigational situation.

Figure 25. Model of ship encounter situations (Pietrzykowski

2007)

2.3 Human error

Human reliability is one of main factors which in-

fluence safety at maritime transport. Generally we

can select the sources of human error into intended

and unintended.

Unintended errors can be classified as :

1 Errors of Omission

− Involve failure to do something.

2 Errors of Commission

− Involve performing an act incorrectly.

3 Sequence Error

− Involve performs some step in a task or tasks

out of sequence.

4 Timing Error

− Involve fails to perform an action within an al-

lotted time or performing too fast or to slow.

Figure 26. Sources of human error

Table 1. Human errors sources statistic, ABS REVIEW AND

ANALYSIS OF ACCIDENT DATABASES: 1991 – 2002

__________________________________________________

Sources %

__________________________________________________

Situation assessment and awareness 15,2

Task omission 10,4

Management 10,1

Knowledge, skills, and abilities 7,3

Mechanical / material failure 6,6

Weather 6,6

Complacency 5,6

Risk tolerance 4,8

Business management 4,8

Navigation vigilance 4,6

Lookout failures 4,3

Maintenance related human error 4,1

Fatigue 3,5

Unk

nown cause 3,3

Procedures 2,8

Manning 2,0

Commission 1,5

Uncharted hazard to navigation 1,3

Substance abuse 1,3

__________________________________________________

Factors Contributing to Accidents, (Clem-

ens 2002)

− Management

− Physical Environment

− Equipment Design

225

− Work Itself

− Social/Psychological Environment

− Worker/Co-worker

− Unsafe Behavior/Chance (Risk)

Exposure to Hazardous Situation, (Lawton, Mil-

ler, Campbell 2005)

− Perception of Hazard

− Cognition of Hazard

− Decision to Avoid

− Ability to Avoid

− Safe Behavior

Probability of operator error (Clemens 2002)

































⋅

⋅−

−=

Tat

exp)

(1)

where:

− a

, a

are parameters connected with factors

such as skills, knowledge, regulations;

− T

is an average time for analyzed operation;

− t is time which operator has for this operation.

Figure 27. Probability of operator error for different skills and

knowledge parameters, (Smolarek & Soliwoda, 2008)

Also the Human Cognitive Safety Model

(HCSR) can be used as a method for computing fac-

tor of human’s safety degree for the whole safety

degree of HMESE, (Wang Wuhong, at al 1997). If

the uncertainties of human’s conduct operation are

taken into consideration, the error probability of

human cognitive activities can be re-written as

(Wang Wuhong, at al 1997):

( )

exp ln

exp when exp

1.0 when exp

−









−−











−≥



























tT Φx C

t CT Φx

(2)

( )

{ }

hh h

x P P Pt

= ≤

(3)

where:

−



－the most suitable estimated median of

time required to complete the behavior;

−

－logarithmic standard deviation of response

time about operator;

−

( )

Φ x

−

－reverse standard normal accumulation

distribution function;

− x－ratio between defined probability and non-

response.

3 SAFETY MODEL

Ship is the human-machine system in which the

functions of a human operator (or a group of opera-

tors - crew) and a machine are integrated. In safe

analysis it is necessary to emphases the view of such

a system as a single entity that interacts with exter-

nal environment so it’s obvious to take into consid-

eration, (Gucma, 2005). From the three aspects of

“human”, “machine”, “environment”, in this paper

qualitatively analyses the influence of two aspects,

human and machine on safety of Human-Machine-

Environment System in the ship transportation pro-

cess. The safety degree of a ship is the function of

the three sub-systems about human, machine and

environment and can be regarded as the functional

system according to human error and technical fail-

ure. The human error and technical failure are ex-

press interaction human-environment and ship-

environment, (Smolarek, 2008):.

The graph of ship system safety states changes is

presented at figure 8. We take into consideration the

ship safety model which is discreet in state and time

domain.

Figure 28. Graf of system state changes.

Where state 2 is partially unsafe state according

to human error and state 3 is partially unsafe state

according to technical failure of the ship or its any

subsystem.

Corresponding transition matrix of one-step tran-

sition probabilities













4441

343231

242321

1312

p00p

p0pp

pp0p

0pp0

(4)

Q(t/T

)

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7

t/T

probability

0,4

0,8

1,2

226

According to matrix (4) we have

4441

343231

242321

1312

=++

ppp

(5)

Using the total probability and memoryless prop-

erty of Markov chains we obtain the Chapman

Kolmogorov equations

{ }

.0,4,3,2,1,

),(),(),(

nmji

nkmkpmkkpnkkp

rkirij

≤≤∈

++⋅+=+

∑

(6)

If it is an irreducible non periodic Markov chain

consisting of positive recurrent states then a unique

stationary state probability vector π exists













⋅=

(7)

where:

−

- is a steady state probability, k = 1,2,3,4;

and the matrix equation for vector π is given by

























⋅













−

1111

2313

3212

413121

ppp

(8)

where:

−

- is a transition probability from state j to

state k, j,k=1,2,3,4.

If the condition

1111

det

2313

3212

413121

≠⋅













−

ppp

(9)

is satisfied, then the solution is given by

))(())(()1)(1(

)1(

41311323124121123213322341

3223

ppppppppppppp

−++−++−+

−

))(())(()1)(1(

41311323124121123213322341

321312

ppppppppppppp

ppp

−++−++−+

−−

))(())(()1)(1(

41311323124121123213322341

231213

ppppppppppppp

ppp

−++−++−+

−−

)pp)(ppp()pp)(ppp()1pp)(p1(

1pppppppppppp

41311323124121123213322341

122132231331312312133221

−++−++−+

−++++

If transition probabilities are equal to p, then

;

1 p

−

;

1 p

−

;

−

−=

(10)

Figure 29 Graf of tendency of stationary state changes for in-

creasing p

4 CONCLUSIONS

Vessel safety assessment carried out upon IMO

standards allows theoretical estimating of safety

without actual vessel conditions details and condi-

tion of crew. For more sophisticated cognitive mod-

eling is necessary to model numerous failure modes

or represent complex interdependencies between

human error sources, ship route, ship technical and

exploitations parameters. An alternative to repre-

senting the seaman as an element of a ship system is

to represent him as a subsystem in and of itself. It

means that the seaman should be modeled autono-

mously.

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Studia nr.44 AkademiaMorska w Szczecinie, Szczecin

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π1

π2

π3

π4