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dP
1(
t
)
= (
λ
+
λDh
)
P
1(
t
)+(1
Pfs
) ·
μfs
·
P
2(
t
)
dt
dP
2(
t
)
=
μfs
·
P
2(
t
)+
Cλfsh
·
P
3(
t
)+
μd
·
P
4(
t
)
dt
dP
3(
t
)
=
μfsh
·
P
3(
t
)+
Pfs
·
μfs
·
P
2(
t
)+
λDh
·
P
1(
t
)
dt
dP
4(
t
)
=
μd
·
P
4(
t
)+(1
C
) ·
λP
1(
t
)
(1)
dt
For steady state probabilities we obtain the following equations:
μfsh · μfs · μd · (1 − Pfs )
( λ − λDh ) · μfsh · μd + μfsh · μfs · (1 − Pfs ) · ( μd + λ − λC )+ μd · μfs · ( λDh − λP fs )
P 1=
( λ − λDh ) · μd · μfsh
( λ − λDh ) · μfsh · μd + μfsh · μfs · (1 − Pfs ) · ( μd + λ − λC )+ μd · μfs · ( λDh − λP fs )
P 2=
μfs · μd ( λDh − λP fs )
( λ − λDh ) · μfsh · μd + μfsh · μfs · (1 − Pfs ) · ( μd + λ − λC )+ μd · μfs · ( λDh − λP fs )
P 3=
λ (1 − C ) · μfsh · μfs · (1 − Pfs )
( λ − λDh ) − μfsh · μd + μfs · (1 − Pfs ) · ( μd + λ − λC )+ μd · μfs · ( λDh − λ · Pfs )
P 4=
(2)
The result from the analysis has shown the importance of human factor
for a safe and secure transportation process.
The probability of the system being in a given dangerous state - P3 and
P4 in example (Fig.5) shows the positive influence of human-operator on the
safety of the system. The model is constructed on the basis of statistical data
concerning operator on the railway trac control desk.
For the probability Pfs (Probability of unsafe human operation), the
statistical data shows values from
10 1
10 3
-
and for λDh (unsafe human
10 3 -
10 6 .
violation failure rate) -
4
Conclusion
Human errors are predictable, and thus can be prevented by changing the
design of a system. Psychologists use their knowledge of human perception,
response time, and cognition to predict and prevent possible errors. Any orga-
nization that professes to have a safety culture should treat human behavior
as an important issue. Even the most highly automated systems are designed,
installed, and maintained by people. Human error plays a crucial part in most
accidents, if not all. In critical systems like transport systems, safety measures
against human errors play a substantial role. Human error can be committed
in different phases of the life cycle, namely, during system specification and
development; and in the longest phase of the life-cycle during operation. In
railway operation, several safety-critical tasks are assigned to the operators
and are not controlled by signaling and interlocking systems. Many tasks
are necessary in situations occurring very rarely. Since these situations are
unfamiliar to the operators, the demand for good interaction is high and
 
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