Z: Random Fuzz Generator.
Although many systems which are notionally deterministic are sufficiently complex
that their behaviour is indistinguishable from random, there are times when a random
(or, strictly speaking, a psuedo random) input is needed, if only to satisfy the boss.
Generally, 'Monte-Carlo' simulations need extremely long trials to give statistically useful answers,
especially where the intention is to optimize a design and small differences are being sought.
The McSimAPN approach is rather to make it easy to observe transient behaviour
and how a system responds to the varying demands put on it. But, recognizing the need,
this block type will generate a new 'random' value each time it is invoked.
However, since no process makes unbounded excursions in any physically realizable system,
I have made sure that the output of this block can always be constrained within finite bounds.
You don't have to use the bounds, but you will have to deliberately change them if you want to open them up,
or close them down.
Options and Values.
Mode 0: The default case; the block generates a uniformly distributed series of values
with width Av and mean Bv, where:
Av=Va+aa, Bv=Vb+bb and Va is the output of block An, etc.
This doesn't need to be constrained.
Mode 1:
Gaussian Distribution, SD is Av, Mean is Bv.
This is constrained to lie between Cv and Dv. If the unconstrained distribution frequently generates values
that would exceed a bound, then there will be a spike in the probability distribution at the bound.
Mode 2:
Poisson Distribution, mean is Av, base, i.e minimum value, is Bv.
Also constrained.
Mode 3:
Erlang Distribution, shape factor 3.
Also constrained.
Other Tricks with McSimAPN
If you add variables from these distributions, to give a new variable
the "central limit theorem" begins to show and the resulting distribution becomes more and more like Gaussian.
By the time the shape factor for Erlang is up to 4, most people would hardly distinguish it from Gaussian.
The A (activity), B (belt), D (Diverter) and T (Timer) blocks all have the built in ability to operate with a random
periods for their actions simply by defining the average period as negative.
They all use an Erlang distribution with shape factor 2.
However, if a positive random value is provided at the Pn connection,
that will be used whenever a next event time is to be assigned.
Any shape of probability distribution can be generated from a uniform random number stream,
by passing it through a suitable function generator, shaped with the cumulative probability distribution.
(Run the "Z-fuzzMakerTest.txt" model to see it done.)
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MJMcCann-Consulting
Help Index:
Index/Search
Background
Simulation Concepts
Continuous Systems
Discrete Systems
McSimAPN Structure
McSimAPN Operation
Using McSimAPN
Start McSimAPN
Save Model,data
Create Blocks
Run-Hold-Reset
Link Excel+VBA
PetriNet Block Types
A activity/action
B belt conveyor
C container/constant
D diverter(random)
Analogue Block Types
E exponents
F flux/flow
G function Generator
H hysteresis
I integrator
J inductor
K logic element
L logarithms
M memory
N note/label
O oscilloscope/graph
p not assigned
Q quantizer/rounding
R relay on/off
S sin/asin/atan
T timer/clock
U user link Excel
V visual voltmeter
W sWitch selector/MUX
X multiply
y not assigned
Z random (fuZZ)
& signed summation
% division/difference
@ access/move values
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Invitation. McCann can help if you have a
design or operational problem that needs some technical support that is outside your
team's experience, some quantitative assessment of what is really the cause of the
difficulties, some design alternatives or just a fresh look by an intelligent
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If you have a problem with the behaviour of a market sector, plant, process or item of
equipment and would like to get a quantitative handle on it to improve yield or optimise
performance, then contact us. We are always ready to give a little time
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POB 902,
Chadds Ford PA
19317 USA.
T: 1 302 654-2953
F: 1 302 429 9458
E: mjmccann@iee.org
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