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The Relationship Between Cycle Time
and WIP
The relationship between cycle time
and WIP
was first documented in 1961 by J. D. C.
Little. Little’s
Law states that at a given WIP level,
the ratio of WIP to cycle time equals throughput,
as shown in the formulas below:
In other words, for a factory with
constant throughput, WIP and cycle time
are proportional. If throughput is held
constant, it is impossible to reduce
average WIP without reducing average
cycle time, and vice versa. It is
important to understand that this is a
known mathematical relationship. Over the
long term, it will hold true for an
entire factory, or for a single
workstation (as long as the units used
for each term are consistent with one
another).
Little’s Law can be illustrated
with a simple example: assume a factory
with a capacity of 500 wafers per week
and no variability. Although this is a
highly unrealistic assumption, we will
relax it later in the tutorial. Under
these assumptions, if we start 500 wafers
or less in each week, the cycle time for
each will be one week (because we have
enough capacity to process them all
during the week).
However, suppose that we start out
with a backlog of 500 wafers in the fab.
Each week we get 500 more in, so that the
total WIP is 1000. We can only process
500 of the wafers in a given week. On
average, each wafer will spend two weeks
in the factory (one week waiting for the
backlog of other wafers to be processed,
the next week being processed).
Similarly, if we have 1500 wafers in the
factory at a time, the average cycle time
will be three weeks, etc. This is shown
in the graph below.
As another way of looking at this, the
following graph shows average throughput
vs. average WIP. Up to the capacity of
the factory, the throughput (the amount
we get out per week) will equal the
amount that we start per week. However,
when the WIP in the factory reaches the
capacity of 500 wafers per week,
throughput can no longer increase. No
matter how much WIP we cram into this
factory, we will never get more than 500
wafers per week out (without increasing
the fab capacity in some way). And, as
shown in the first chart, the more WIP we
cram in, the longer the average cycle
time will be.
In this example, the best thing to do
is clear  start exactly 500 wafers each
week. This will maximize throughput,
while cycle time remains at the minimum
of one week. However, the situation is
only this black and white for systems
with no variability. For fabs that
operate in the real world, we have to
consider the relationship between cycle time and
variability.
