[From Bill Powers (980917.various)]
Bob Eberlein (980915) --
Your idea of including PCT submodels for the individual decision making is
intriguing. I am attaching a fairly simple project model in which the
individual has to decide whether or not a project is done. The current
formulation is completely mechanical. Take a look at the formula for
"project is done" and think about how you might change this to output a
zero >or one based on other variables in the model.
Some preliminary thoughts:
The initial project definition says only that the total work done should be
greater than or equal to 1000. The work done is the integral of [work
flow-rework discovery rate]. And work remaining is [rework discovery
rate-work flow].
It seems to me that the job is not done until there is no rework left, and
the work accomplished >= 1000. If the work accomplished happens to reach
1000 before the rework is all finished, and you stop the work, there will
be unfinished reworking left in the pipeline. If you don't stop the flow
until all the discovered reworking is finished, you'll end up with a
production overrun.
It also seems to me that this is not a model of the actual system and the
actual flow of production, but of abstractions about the flow. While it may
be true to say
undiscovered rework = INTEG[work flow*(1-work quality)-rework discovery
rate]
this does not reveal all the problems that are involved.
It helps to visualize the physical process.
···
+
raw materials ----> production line ----> output ----> inspection ----->
+ | | | |
-->-reworking -->- | | |
> > > >
> > > >
----parts for reworking ---<-- discards |
>
Total good parts for sale <-----------
If this is the way the plant is organized, we can see that the criterion
for being finished should be that there are N total good parts for sale,
and NO parts left in the reworking pipeline. If we assume a constant error
rate for either new or reworked parts, and (1 - work quality) parts fail
each time through inspection, then the time that has to elapse before the
total number of parts can be known is determined by the number of passes
through the reworking loop required to make (1 - quality)^n < 1 part.
This says that the count of parts should be the total parts accumulated for
sale so far PLUS the number of parts in the reworking pipeline (because
most of them will eventually be good parts). And as that total approaches
the number in the project definition, the rate of production of new parts
should be reduced, slowing the approach of the total to the specified
number while the reworking pipeline is emptied. It should be possible to
make the total number of good items produced exactly match the specified
number.
If the above diagram represents the physical plant and the workers, there
should be a control agent sitting on top of it, capable of acting by
varying the speed at which the production line makes new items, and
perceiving the total of good items accumulated for sale and items still in
the reworking pipeline.
target number
of good items
>
v error
--------->[Comparison] ------>-
> >
perceived total items |
> >
> >
[SUM] CONTROLLING |
^ ^ AGENT |
/ \ |
/ \ |
/ \ |
> > v
good items items to be speed of producing
reworked new items
(PROPORTIONAL TO ERROR]
I haven't tried a model of this yet (it's the middle of the night), so feel
free to complete it yourself. Notice that the production line will slow
down as the "total items" perceived approaches the target number. You can
make the output function nonlinear so the slowdown occurs only near the
end. As items are removed from the to-be-reworked bin, the production line
will speed up, slowing down again as some (most) of the reworked items show
up in the "good items" bin. That's just a verbal way of describing the
action; it will look more like a continuous approach to the specified
number of good items. This control system will automatically adjust itself
to account for discards and for variations in the rate of failed items.
Eventually the perceived items will all be good items, there will be zero
items to be reworked, the error will be zero, and the production line will
stop. There should be no production overruns if the time constants in the
production line are set right.
So the principle seems to be: first lay out the physical processes and
their connections. Then superimpose a controlling agent who perceives the
appropriate measures of the state of doneness, acting continuously on the
plant to make the perceived state match the definition of "done."
Best,
Bill P.