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1
Factory Physics Principles
Law (Little's Law): WIP = TH £ CT
Law (Best Case Performance): The minimum cycle time for a given WIP level, w, is given by ( T0 ; if w · W0 CTbest = w=rb ; otherwise. The maximum throughput for a given WIP level, w is given by, THbest =
(
w=T0 ; if w · W0 rb ; otherwise.
Law (Worst Case Performance): The worst case cycle time for a given WIP level, w, is given by, CTworst = wT0 The worst case throughput for a given WIP level, w, is given by, THworst = 1=T0
De¯n

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1
Factory Physics Principles
Law (Little's Law):
WIP = TH
£
CT
Law (Best Case Performance):
The minimum cycle time for a given WIP level,
w
, is given by CT best
=
(
T
0
;
if
w
·
W
0
w=r
b
;
otherwise.The maximum throughput for a given WIP level,
w
is given by,TH best
=
(
w=T
0
;
if
w
·
W
0
r
b
;
otherwise.
Law (Worst Case Performance):
The worst case cycle time for a given WIP level,
w
, is given by,CT worst
=
wT
0
The worst case throughput for a given WIP level,
w
, is given by,TH worst
= 1
=T
0
De¯nition (Practical Worst Case Performance):
The practical worst case(PWC) cycle time for a given WIP level,
w
, is given by,CT
PWC
=
T
0
+(
w
¡
1)
r
b
The PWC throughput for a given WIP level,
w
, is given by,TH
PWC
=
wW
0
+
w
¡
1
r
b
Law (Labor Capacity):
The maximum capacity of a line sta®ed by
n
cross-trained operators with identical work rates isTH
max
=
nT
0
2
Law (CONWIP with Flexible Labor):
In a CONWIP line with
n
identical workers and
w
jobs, where
w
¸
n
, any policy that never idles workers when unblocked jobs are available will achieve a throughput level TH
(
w
)
bounded by TH
CW
(
n
)
·
TH
(
w
)
·
TH
CW
(
w
)
where TH
CW
(
x
)
represents the throughput of a CONWIP line with all machinessta®ed by workers and
x
jobs in the system.
Law (Variability):
Increasing variability always degrades performance of a pro-duction system.
Corollary (Variability Placement):
In a line with where releases are indepen-dent of completions, variability early in a routing increases cycle time more than equivalent variability later in the routing.
Law (Variability Bu®ering):
Variability in a production system will be bu®ered by some combination of:1. inventory,2. capacity,3. time.
Corollary(Bu®er Flexibility):
Flexibility reduces the amount of variability bu®er-ing required in a production system.
Law (Conservation of Material):
In a stable system, over the long run, the rateout of a system will equal the rate in, less any yield loss, plus any parts production within the system.
Law (Capacity):
In steady state, all plants will release work at an average ratethat is strictly less than the average capacity.
Law (Utilization):
If a station increases utilization without making any other changes, average cycle time will increase in a highly nonlinear fashion.
Law (Process Batching):
In stations with batch operations or with signi¯cant changeover times:
3
1. The minimum process batch size that yields a stable system may be greater than one.2. As process batch size becomes large, cycle time grows proportionally with batch size.3. Cycle time at the station will be minimized for some process batch size, which may be greater than one.
Law (Move Batching):
Cycle times over a segment of a routing are roughly proportional to the transfer batch sizes used over that segment, provided there is nowaiting for the conveyance device.
Law (Assembly Operations):
The performance of an assembly station is de-graded by increasing any of the following:1. number of components being assembled,2. variability of component arrivals,3. lack of coordination between component arrivals.
De¯nition (Station Cycle Time):
The average cycle time at a station is madeup of the following components:cycle time
=
move time
+
queue time
+
setup time
+
process time
+
wait-to-batch time
+
wait-in-batch time
+
wait-to-match time
De¯nition (Line Cycle Time):
The average cycle time in a line is equal to thesum of the cycle times at the individual stations less any time that overlaps two or more stations.
Law (Rework):
For a given throughput level, rework increases both the mean and standard deviation of the cycle time of a process.
Law (Lead Time):
The manufacturing lead time for a routing that yields a given service level is an increasing function of both the mean and standard deviation of the cycle time of the routing.
4
Law (CONWIP E±ciency):
For a given level of throughput, a push system will have more WIP on average than an equivalent CONWIP system.
Law (CONWIP Robustness):
A CONWIP system is more robust to errors in WIP level than a pure push system is to errors in release rate.
Law (Self-Interest):
People, not organizations, are self-optimizing.
Law (Individuality):
People are di®erent.
Law (Advocacy):
For any program, there exists a champion who can make it work, ...at least for a while.
Law (Burn-out):
People get burned out.
Law (Responsibility):
Responsibility without commensurate authority is demor-alizing and counterproductive.

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