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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 inform …
SEMI E124-1103 © SEMI 2003 7
bottleneck
throughput
rate
average average
number of
tools in
bottleneck of bottleneck
equipment equipment
type * type *
number of
units of
product
type in
availability
finished
efficiency
units
out
ee
p
fini
××
=
*
for product type
in step on
bottleneck
equipment
type *
pe
theoretical
production
time per unit
ps
pP sS
shed
units out
e
×
∈∈
∑∑
(17)
NOTE 15: One of the factors in this metric is the average
number of available tools in the current bottleneck equipment
set, not the total number of tools nominally in the set.
()
()
-
max ,
average
best
WIP
case theoretical
cycle cycle time
bottleneck
time
throughput
rate
=
(18)
NOTE 16: See Related Information 1 for why Equations (18)
and (20) theoretically represent the best possible cases.
actual
finished units out
throughput
total time
rate
=
(19)
(
)
()
-
min ,
average
best case bottleneck
WIP
throughput throughput
theoretical
rate rate
cycle time
=
(20)
(
)
()
min ,
WIP
theoretical
bottleneck
capacity
throughput throughput
theoretical
rate
rate
cycle time
=
(21)
(
)
f
inished units out
WIP
turnover
average WIP
=
(22)
7 Related Documents
7.1 SEMI Standards
SEMI E35 — Cost of Ownership for Semiconductor
Manufacturing Equipment Metrics
SEMI E58 — Automated Reliability, Availability, and
Maintainability Standard (ARAMS): Concepts,
Behavior, and Services
SEMI E116 — Provisional Specification for Equipment
Performance Tracking
NOTICE: Unless otherwise indicated, all documents
cited shall be the latest published versions.
NOTICE: SEMI makes no warranties or
representations as to the suitability of the standards set
forth herein for any particular application. The
determination of the suitability of the standard is solely
the responsibility of the user. Users are cautioned to
refer to manufacturer's instructions, product labels,
product data sheets, and other relevant literature,
respecting any materials or equipment mentioned
herein. These standards are subject to change without
notice.
By publication of this standard, Semiconductor
Equipment and Materials International (SEMI) takes no
position respecting the validity of any patent rights or
copyrights asserted in connection with any items
mentioned in this standard. Users of this standard are
expressly advised that determination of any such patent
rights or copyrights, and the risk of infringement of
such rights are entirely their own responsibility.
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