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SEMI E124-1103 © SEMI 2003 9 critical WIP ( W 0 = R max × T min ) Worst Case ( throughput-rate & cycl e-time efficiency =1 / W 0 ) T min 1 Best Case ( throughput-rate & cycle-tim e efficiency = 1) actual throughp…

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SEMI E124-1103 © SEMI 2003 8
RELATED INFORMATION 1
MANUFACTURING SCIENCE BACKGROUND
NOTICE: This related information is not an official part of SEMI E124 and was derived from work by the task
force. This related information was approved by full letter ballot procedures on July 27, 2003.
R1-1
R1-1.1 To understand the production metrics given in
Section 6, we need to understand the underlying science
behind factory dynamics. The most important concept
is Little’s law given in the following equation, which is
the same as Equation 15 in Section 6:
(
)
(
)
(
)
average average actual
WIP cycle time throughput rate
=× (1)
R1-1.2 In Factory Physics
1
, this identity is called the
“F = ma” of manufacturing science. Little’s law relates
the three most significant fundamental quantities of
production systems. Unfortunately, it says that all three
metrics cannot be optimized simultaneously. Little’s
law is shown graphically in Figure R1-1. In all of the
figures in this Related Information, the colors denote
different values of the normalized production efficiency
metric with green representing values close to one (at
the bottleneck throughput rate and theoretical cycle
time), yellow representing values close to ½ (the
threshold case as discussed in Section R1-1.7), and red
representing values close to zero (when the throughput
rate goes to zero or the cycle time gets large). On the
floor of Figure R1-1 are the linear contours of the cycle
time level sets. Note that the boundaries of the
operating region are determined by the theoretical cycle
time (T
min
), the bottleneck throughput rate (R
max
), and
the WIP capacity (W
max
).
Figure R1-1
Surface Plot of Little’s Law
SEMI E124-1103 © SEMI 2003 9
critical WIP
(W
0
= R
max
×T
min
)
Worst Case (throughput-rate & cycle-time efficiency =1/W
0
)
T
min
1
Best Case (throughput-rate
& cycle-time efficiency = 1)
actual
throughput rate
1/T
min
bottle-
neck
through-
put rate
(R
max
)
1
Threshold Case (normalized
production efficiency = ½)
WIP capacity
(W
max
)
average WIP
Green
Yellow
Red
Figure R1-2
Plot of Actual Throughput Rate vs. Average WIP
R1-1.3 If we look at two of these fundamental quantities at a time, the factory dynamics become more clear. For
example, Figure R1-2 above shows actual throughput rate as a function of average WIP levels. Here the diagonal
solid black lines represent different constant cycle times, but no known strategy will keep the factory operating
exactly on one of these lines.
R1-1.4 Now suppose the factory is managed with a push strategy where a constant throughput rate is enforced so
that WIP levels are allowed to reach their equilibrium state. As shown below in Figure R1-3, this amounts to
choosing to operate the factory on one of the diagonal solid black lines (each of which represent different constant
throughput rates). We try to drive the factory along that line toward the bottom left (for lower average cycle time
and average WIP levels) by using better operating principles, but we are resisted by the inherent variability of the
factory.
average
cycle time
theo-
retical
cycle
time
(T
min
)
average WIP
1
bottleneck throughput
rate (R
max
)
Threshold Case (normalized
production efficiency = ½)
critical WIP
(W
0
= R
max
×T
min
)
WIP capacity
(W
max
)
Worst Case (throughput-rate
& cycle-time efficiency = 1/W
0
)
T
min
1
1
Best Case (throughput-rate
& cycle-time efficiency = 1)
W
max
R
max
G
r
e
e
n
Y
e
l
l
o
w
Red
Figure R1-3
Plot of Average Cycle Time vs. Average WIP
SEMI E124-1103 © SEMI 2003 10
R1-1.5 Now suppose the factory is managed with a
pull strategy where a constant WIP level is enforced so
that throughput rates are allowed to reach their
equilibrium state. In general, this is a better strategy,
because studies have shown that a constant WIP level
will result in a higher average throughput rate than the
constant throughput rate that results in the same average
WIP level. As shown below in Figure R1-4, this
constant WIP strategy (known as CONWIP) amounts to
choosing to operate the factory on one of the solid black
curves (each of which represents a different constant
WIP level). We try to drive the factory along that curve
toward the bottom right (for lower average cycle time
and a higher actual throughput rate) by using better
operating principles, but we are resisted by the inherent
variability of the factory.
actual throughput rate
1/T
min
bottleneck
throughput
rate (R
max
)
Threshold Case
(normalized
production
efficiency = ½)
critical WIP (W
0
= R
max
×T
min
)
WIP capacity (W
max
)
Best Case (throughput-rate & cycle-time efficiency = 1)
average
cycle time
theo-
retical
cycle
time
(T
min
)
W
max
R
max
Worst Case (throughput-rate
& cycle-time efficiency = 1/W
0
)
G
r
e
e
n
Yellow
Red
Figure R1-4
Plot of Average Cycle Time vs. Actual Throughput Rate