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allows us to consider and analyse effects of non-periodic preventive main-
tenance. If the failure rates of the components could rise over time, then
approximation could be made via modified constant failure rate in every con-
secutive phase.
3C e tudy
Let us assume safety relevant control system with 2-out-of-2 system architec-
ture. Such a system is depicted in the Fig. 2 via a simplified block diagram.
Fig. 2. Block diagram of a general 2oo2 control system
Further assumptions for this case study are: only units A and B directly
influence the safety of the system; both A and B units are identical, therefore
hardware failure rates are
λ
A
=
λ
; on-line diagnosis with its detection
mechanisms has the diagnostic coverage coe
cient
c<
λ
B
=
1
and the system is
able to reach the safe state after a detectable failure has occurred. Transition
rate to the safe state
δ
is determined through a time needed to detect a failure
and negate its consequences.
If all conditions stated above apply, then impacts of the hardware failures
on the SIL could be analysed by the CTMC shown in Fig. 3. Further meanings
of states and transitions is summarised in the Table 1 and Table 2.
Fig. 3. CTMC of a general 2oo2 control system
CTMC in the Fig. 3 is determined through the infinitesimal generator
matrix
