adequately with technical uncertainties
& Quality Management
In contrast to Russia, markov analysis
is not very common in the western civilization. Markov is an
alternative for fault tree analysis
(FTA) and reliability block diagram
(RBD) and can handle most scenarios that are usually tackled with FTA
or RBD. Furthermore, Markov can handle specific scenarios which FTA and
RBD can not.
mathematically being simpler than FTA and RBD, markov requires
more abstraction from the reliability analyst:
Instead of breaking the
system down into evident pieces (functional blocks or faults), markov
requires the system to be divided into so called states.
state represents the complete system in a specific
Like RBD, markov diagrams consist of blocks. Each block
represents a specific system state. System states should be named as
precisely as possible.
The quantitative information, namely the
transition rates (# of transitions per time unit) is kept in the
A twin engine aircraft is a very good example in order to demonstrate
the strength of markov. This example is also used in the FTA and the
RBD paragraphs for the purpose
of showing the limitations of these methods.
It is worthwhile to look a little bit closer to the markov twin engine
aircraft diagram. All transition rates are in units of [per hour].
It can be seen that, in contrast to
FTA and RBD, markov is capable to handle the twin engine aircraft
situation thoroughly, in particular:
- In normal operation, the system is in the state "Both Engines OK".
The engine failure rate, under normal condition, shall be 0,000001 /
hour, which is written beneath the respective arrows. If the right
engine fails, the system will transit to the "Right Engine Failed" state.
For left engine failure, the same applies vice versa. From the one engine faild states there
is no arrow back to the "Both Engines OK"
state because the preferred procedure upon engine failure is not a
restart; instead, the crew must head for the nearest eligible
alternate airport with the remaining engine.
one engine failed, the remaining engine must work harder in order to
keep the aircraft airborne. As a consequence, its failure rate will be
in this example, the engine failure rate for the remaining engine shall
0,000002/ h, which is twice as high compared to normal condition.
both engines failed, there is a high priority on restarting at least
one engine. The state diagram accounts for that by having arrows from
the "Both Engines
Failed" state towards the one engine failed states.
The transition rates for restarts is 4/h, which means that it takes a
quarter hour in order to get a failed engine running. In some cases
however the crew might fail in restarting engines. But even then there
is some chance for a successful emergency landing.
Markov is the preferred method for
such systems, whose behavior can not satisfactorily be modeled by
system components and their interaction.
- higher failure rate of the remaining engine when the other
engine has failed
- despite system failure (both engines failed), the system is
still working in some way (aircraft gliding), and there is even a
chance to get the system back into working condition (engine restart)
before"real" system failure (crash landing).
Like other Methods, there are some
problems associated with markov:
As a result of these problems, markov
is only used in cases where other methods fail.
- poor acceptance in western civilization among reliability analysts
- no problems however with authorities and appraisers
- For most systems it is easier to use RBD or FTA instead of
- e.g. redundant power supply. Here, RBD would not only be
easier, but also be more intuitive compared with markov.
rates between markov states are very often more
difficult to obtain than failure rates for system components. While
there are manyestablished methods available for determining component
failure rates, markov transition rates usually need unique assumptions.