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
l
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)
=
3
a
m2
m1
m
Ta
Tat
exp)
T
t
(Q
(1)
where:
a
1
, a
2
, a
3
are parameters connected with factors
such as skills, knowledge, regulations;
T
m
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):
( )
( )
( )
( )
( )
1
12
1
12
1
12
exp ln
exp when exp
1.0 when exp
β
γ
γ
γ
σ
σ
σ



−−




−≥



=




<

j
j
j
j
j
u
u
n
h
u
tT Φx C
t CT Φx
C
Pt
t CT Φx
(2)
( )
{ }
'
hh h
x P P Pt
γ
=
(3)
where:
the most suitable estimated median of
time required to complete the behavior;
u
σ
logarithmic standard deviation of response
time about operator;
( )
1
Φ x
reverse standard normal accumulation
distribution function;
xratio 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-