Ron,

The following may assist:

Monte Carlo simulation
When it is necessary to investigate more complicated operation and failure
patterns, or detailed aspects of equipment repair, such as spares holding,
delays before repair can start, or priorities where there are repair
resource limitations, the mathematical analysis can be extremely difficult
or impossible to solve.

Monte Carlo simulation is a method which can be used to bypass the complex
mathematics of an analytical solution. It can only be used effectively with
a computer and was, at one time, considered too expensive to use routinely.
However, with the advent of the microcomputer and the appearance of Monte
Carlo simulation programmes on the market, the technique is becoming more
accessible.

The technique is to generate a computer model of the system to be
investigated, and then to simulate the operation of the system for a
predetermined period, during which random failures and repairs can occur to
the components of the system. The operational states which the system takes
up as a result of each failure or repair (or other event) are logged, and
from the percentages of time spent in each state, the overall system
availability can be calculated and other useful information may be inferred.

a) The computer model - The computer model is usually based on a Reliability
Block Diagram (RBD) of the system, and controlled by a set of rules which
specify exactly the model's response to each type of event which can occur.
Each block in the RBD (which can represent a component or group of
components, or even one aspect of a single component), can be assigned an
individual Failure Rate, Repair Rate, and number of spares available. The
set of rules specifies such details as which blocks (components) have to be
'taken out of service' if a block fails, which other blocks have to be 'put
into service', which repair strategy is put into practice, for example,
whether the 'component' is to be repaired in situ or changed for a spare,
and whether an exchanged component should be scrapped or refurbished, and
the effect of the block failure on the percentage throughput of the whole
system. For example, if a system model includes two 100 per cent throughput
feed pumps in parallel, and each pump set is treated as four components in
series (that is, high pressure pump, booster pump, electric motor, and
balance of plant) the rules will probably require that if the electric motor
of the running pump fails, the remaining components of the running pump are
shut down and the standby pump is started. At the same time the rules will
initiate the repair of the failed motor, perhaps replacing it with a spare
if one is available and to do so would be quicker than repairing it in situ.
In this case, if the standby pump is permitted to start without failure, the
availability of the whole system model is unaffected. Further rules are
required to determine whether the failed pump is returned to service as soon
as it has been repaired or remains as standby until the other pump fails.
b) Simulation of events - When the model has been set up in the computer,
it is run by simulating sequences of events (failures, repairs, consumption
of spares, and so on) which occur independently to each component of the
model. For the model to mimic the real system properly, the events must
occur at intervals related to those which could occur in the real system.
If, for instance, a real component has an MTBF of 3000 hours and the
distribution of the times to failure is known (say, exponential
distribution), then the set of times to failure which occur to that
component in the model must be drawn from that distribution and must
represent an MTBF which approximates to 3000 hours. The computer must,
therefore, generate an independent series of random times for each component
parameter, to suit the specified mean times and distributions. Unlike Markov
analysis, the Monte Carlo simulation method is not restricted to use of the
exponential distribution, but can simulate times drawn from any distribution
which seems appropriate (for example, Weibull, log-normal, rectangular, and
so on). When the simulation is set in motion, failures, repairs, and such
like occur to the components of the model at the times specified by the set
of random time series and controlled by the model's set of rules. The state
of each component is logged after either each unit time interval or each
change of state of any component. The length of the simulation may be
expressed in terms of the time for a specified number of failures to occur
in the model (perhaps several thousand) or the time for a number of cycles
of specified length, for example, the time between major overhauls or the
complete life cycle. Because the model can run so much faster in the
computer than a system in real time, very long runs are possible. In
general, the longer the run, the closer the sets of random time series will
approximate to the desired distributions, and the closer the overall system
availability will approach a steady-state value.
c) Results - At the end of the simulation, the programme totals the time
spent by each component in its running, standby, and failed states, and the
time spent by the overall system in all its possible states, from which the
overall system availability can be calculated. Other subsidiary information
can also be obtained, such as the number of times each component failed, or
standby plant was called to start, the number of times components were
exchanged for spares, and whether there would have been advantage in having
more spares available.

The above description is not of a specific computer programme but shows,
rather, how a Monte Carlo simulation can be carried out and some of the
features which may be found in programs. Not all commercially-available
programmes will have all the features in this description, but may have some
additional features.

Monte Carlo simulation is a powerful technique, which is capable of
producing an answer to any problem posed by the reliability engineer,
subject only to the ingenuity of the computer programmer (and the cost of
their time). However, it is not an analytical technique, and the more
complex the problem, the more difficult it is to check if the programme has
been written correctly and, therefore, if the result can be relied upon.
Also, the more components and rules in the model, the longer it will have to
run in order to achieve a steady-state result. While a substantial
simulation may be carried out in seconds on a large computer, it can take
perhaps several hours on a microcomputer, so that there will usually have to
be a compromise between computing time and costs and the desire to ensure
that the steady-state solution has been reached. This is particularly so
when several runs of the same model are required, with different sets of
random time series to check consistency, or when the model is run many times
with different component parameter values or configurations when searching
for an optimum design for a real system.

Possibly the above explanation serves to illustrate the marked difference
that exists between Reliability Engineering, and Reliability Centred
Maintenance. Especially when other techniques such as Markov Analysis and
Baye's Theorem are introduced.

Peter B.
==========

----- Original Message -----
From: Ron Doucet <doucetr@...>
To: <plantmaint@...>
Sent: Wednesday, July 18, 2001 2:09 AM
Subject: Re: [plantmaint] Manning ratio : Monte Carlo


> What is Monte Carlo simulation?
>
>
> Ron
>
>
>
>
> "Selvarajan Murugan" <selva@...> on 07/17/2001 05:49:31 AM
>
> Please respond to plantmaint@...
>
> To: plantmaint@...
> cc: (bcc: Ron Doucet/CR/IOC/North)
> Subject: [plantmaint] Manning ratio : Monte Carlo
>
>
>
> I am currently working on factory manning indices
> and I want some advice on how to go about doing this
> with the aid of the Monte Carlo simulation.
> Is there any other simulation or method for doing
> the operator to machine and technician to machine
> ratio.
> Any one out can share with me on the matter.
>
> Regards,
> selva
>
>
>
> If you ever need to get in contact with the owner of the list, (if you
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>
>
>
>
>
>
>
>
> If you ever need to get in contact with the owner of the list, (if you
have
> trouble unsubscribing, or have questions about the list itself) send email
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If you ever need to get in contact with the owner of the list, (if you have
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