Minimum
Inventory Variability Dispatching Policies MIVP®
(MIVP®
Donald W.
Collins, Ph.D. and Professor
ABSTRACT
This paper illustrates the use of
discrete event stochastic simulation modeling to compare two scheduling
(dispatching) policies for machines in a factory when a machine becomes
available for processing. The two policies are first-in-first-out (FIFO) and
Minimum Inventory Variability Policies™ (MIVP®), both control the items in the queue (buffers) in front of the
machine or resource [8,9,10,11]. The simulation model is run with FIFO for each
queue for 100 days to establish a baseline set of data. This baseline cycle
time and work-in-progress (WIP) data are collected for comparison to MIVP®. The only change between the model runs is the queues in the model
are switched to run the rule set of MIVP®.
With discrete event simulation
modeling, the user can play “what if” scenarios without expended a lot of
capital [4,5,8,9,10,11,19,20]. The results from simulation give the user an
additional input in making decisions. The model below is basically simple, i.e.
5 machines and 6 buffers, but the user can glean a lot of information. For
example, machine utilization’s can be observed and compared, queue statistics
can be recorded, mean cycle time and mean WIP can be plotted, production
throughput can be calculated, bottleneck capacity can be pushed to it’s limit,
setup rules and machine controllers can be tested, preventive maintenance
schedules can be tried, and personnel (operator) requirements can be
determined. Simulation allows you to play these “what-if” scenarios at minimal
cost without disturbing the factory.
The System to be Modeled
The following figure and
specification was taken from a test-bed designed by Karl Kempf, Manufacturing
Systems Principal Scientist, of the INTEL Corporation. This test-bed is an
example of a very small section in the Semiconductor FAB and is referred to as
a Mini-FAB [6,14,16].
Diffusion Photolithography Implant
Figure 1.
Schematic diagram of the 5 machines 6 steps process flow
The Mini-FAB included two products
and test wafers with their process flows (production recipes) of six steps
utilizing three different machine sets. There was one re-entrant step at each
machine group, steps 4, 5 and 6. The machine groups included Diffusion-C1 (2
machines Ma and Mb), Implant-C2 (2 machines Mc and Md) and Photolithography-C3
(1 machine Me).
Machines Ma and Mb in the Diffusion
bay used predictive machine controllers (a PID controller compared to an
H-infinity controller) [11,20] to establish when the machines were to be taken
down for emergency maintenance. Predictive controllers are being researched for
yield improvement to determine a potential failure prior to its occurrence so
the product being processed is not scraped [7,11,13,17,18,19,20]. Machines Mc
and Md in the Implant bay used historical data of Mean-Time-Before-Failure
(MTBF) and Mean-Time-To-Repair (MTTR) as the emergency maintenance. All
machines had a specific Preventive Maintenance Schedule (PM) with rules for
when the machines could be taken off line for PM.
The objective of this Mini-FAB
example was to compare Minimum Inventory Variability Policies® - MIVP® queue to
machine dispatching policy to the first-in-first-out (FIFO) dispatching policy.
The MIVP® decreased
cycle time by 19% when compared to FIFO [11]. This example demonstrates an
advantage of MIVP® over FIFO
even in the small number of process steps and machine groups. The best
advantage of MIVP® is when you
have multiple products with large number of process steps (300+ average steps)
and many machine groups (130+ parallel machine groups) and multiple reentrant
levels (15+ layers on the wafer). A recent implementation of MIVP® in a real Semiconductor-FAB with 55 different micro-controller
devices has seen a decrease in product average cycle time of 32.9% (going from
49 days to 31 days in less than six months). The average process flow, in this
FAB, of each device was 285 steps (ranging from 164 steps to 350 steps) with
reentrant levels averaging 10 layers on the wafer. The FAB included 132 machine
groups (with 485 machines). This reduction was evaluated at $100+ million US
savings per year [8,9].
The MIVP® set of heuristic rules looks at the queue wait time at every
resource in the factory and not just at the known bottleneck sections of the
FAB. MIVP® will enhance (not
eliminate) company specific dispatching policies such as proprietary polices for
setup at specific machine groups and/or bottleneck sections of the FAB. MIVP® are
distributed throughout the factory and respond dynamically in real time to
variability’s that occur on the FAB floor making decisions for the next set of
wafers to be processed.
Product Entry
The following diagram shows the
arrival of the two products and test wafers at a constant rate of 1 lot (48
wafers) every 2 hours using the arrival stats
Generator icon from the Extend™ Discrete
Event Library. Each product/device and test wafers are timed by a clock-in and
clock-out routine called the Timer icon,
also from the Discrete Event Library. This icon maintains the average cycle
time over the production run. The products are counted using the Count Items icon. The process time attributes
are assigned for each step in the process flow with the Set A(5) icon from the Discrete Event Library. Each product/device
and test wafers are sent to the router using the Throw icon to start the manufacturing process.
The Production Router for the
Reentrant Process Flow
The manufacturing design team has
preset the process flow of each product through its production life. This
process flow plan establishes the number of steps and the machine or machine
groups the product will visit through its production cycle. This sequence
(routing) must be followed precisely for the production yield to be achieved.
In a simulation model attributes assigned to the product such as the process
step can be used to determine where the product is to be sent next, i.e. to
which machine group.
The following diagram shows the
routing and the reentry for each product and test wafers. The first step in the
process flow is when the products and test wafers arrive from the previous
diagram by the Throw to routing icon.
The Catch (To Routing) icon receives
the lots and begins the routing process. The reentry for the three stages
allows the product to reenter the router for the next step in the process flow.
The routing (or process flow) for all products and test wafers includes six
steps as follows: Machine Group 1, Machine Group 2, Machine Group 3, Machine
Group 2, Machine Group 1, Machine Group 3, then Exit.
The
three Machine Groups, Diffusion,
Implant, and Photolithography
The following diagram shows the three
machine groups, which are utilized in the process flow and the router of the
previous page. The diffusion bay receives step 1 and step 5 and requires a
setup or batching of wafers in a specific manner required by INTEL (see next
two pages for batching rules). Each machine group has a queue pick selector block, a hierarchical block that can be
switched from FIFO to MIVP®. See pages
7, 9, and 11 for the details for each “Que
Pick Selector” in front of the three machine groups. After the lot has been
processed it is sent to the router for the next step in the process flow
(ReEntry 1, 2, 3).
Company
Specific Batching Rules for Diffusion Furnaces for Step 1
The products to be batched arrive at
machine group 1 for steps 1 and 5. The first Get A icon (get
attribute) determines the step for which the products are to be batched. All
products that arrive for step 1 are sent to the “Batcher for Step 1” (see
below) and the products for step 2 are sent to the “Batcher for Step 2” (see
next page). All step 1 batches have 7 possible combinations and step 5 batches
have 4 combinations. Products A and B are used in 5 of the combinations for
step 1 and 2 of the combinations in step 5. The test wafers are used in 3 of
the combinations in step 1 and in 2 combinations of step 5.
The following diagram shows the rule
set for the batching requirement for step 1 in the process flow. The rules are
you may have 3 lots of product Pa (PaPaPa), 3 lots of product Pb (PbPbPb), 1
lot of product Pa, 1 lot of Pb and 1 lot of test wafers TW (PaPbTW), 2 lots of
product Pa and 1 lot of Pb (PaPaPb), 2 lots of product Pb and 1 lot of Pa
(PbPbPa), 2 lots of product Pb and 1 lot of test wafers TW (PbPbTW), 2 lots of
product Pa and 1 lot of test wafers TW (PaPaTW). The batch icon from the Discrete Event Library of Extend™ allows you to assemble three combinations of product in any order
and quantity that you wish. The Set A
icon (set attribute) icon allows you to set the batch type for ordering the
priority in the queue with MIVP® for Machine
Group 1, process step 1.
Company
Specific Batching Rules for Diffusion Furnaces for Step 5
The following diagram shows the rule set for the batching requirement for step 5 in the process flow. The rules are you may have 3 lots of product Pa (PaPaPa), 3 lots of product Pb (PbPbPb), 2 lots of product Pb and 1 lot of test wafers TW (PbPbTW) and 2 lots of product Pa and 1 lot of test wafers TW (PaPaTW),. The batch icon from the Discrete Event Library of Extend™ allows you to assemble three combinations of product in any order and quantity that you wish. The Set A icon (set attribute) allows you to set the batch type for ordering the priority in the queue with MIVP® for the reentry of Machine Group 1, process step 5.
Queue
Pick Selector (FIFO or MIVP®) for Machine
Group C1 – Diffusion Furnaces
The following diagram shows the queue
pick selector for steps 1 and 5 in the process flow at machine group 1. Several
custom icons produced for the semiconductor industry by ACADZ inc. are used in
this hierarchical block. The key icon is the MIVP® 20 Que Pick, which can
be switched from the MIVP® rules to
FIFO. When the switch is set to FIFO, the first product batch that arrives is
the first to be processed on the next available machine. FIFO does not care if
the batched products is for step 1 or step 5. MIVP® on the other hand makes a choice using its rule structure, e.g.,
if machine Me (step 6) is down for maintenance, MIVP® will select a batched product for machine group C2 (step 2) if one
is available. The rule here is to “correlate the present available process time
with the next process step availability”. This is one of the many rules within
MIVP®.
The switch is set to FIFO for the baseline data
collection. Once the model has been run and the data has been collected for
FIFO, the MIVP® schedule policies are
switched on and the model is run again for the same production time. The average
cycle time results from MIVP® are then compared to FIFO.
Machine
Group C1 – Diffusion Furnaces with PID and H-Infinity Controllers for Predictive
Emergency Maintenance
The diagram below represents machine
group C1, the two machines Ma and Mb, diffusion furnaces. The batched lots will
arrive and be processed on the next available machine (furnace). The furnace
will be taken down for emergency maintenance according to the controller being
tested, either a PID Controller or an H-Infinity Controller. The diagram shows
that the PID controller is being tested.
Queue
Pick Selector (FIFO or MIVP®) for Machine
Group C2 - Implant
The following diagram shows the queue pick selector for step 2 and step 4 in the process flow for the Implant Machines Mc and Md. The rules are switched to FIFO for the baseline data collection. Once the model has been run and the data has been collected for FIFO, the MIVP® schedule policies are switched on and the model is run again for the same production time. The average cycle time results from MIVP® are then compared to FIFO.
Machine
Group C2 – Implant with Historical Emergency Maintenance
The diagram below represents the two
machines Mc and Md, for Implant. The lot will arrive and be processed on the
next available machine. The Implant Machines will be taken down for emergency
maintenance according to historical data for mean time before failure MTBR and
mean time to repair MTTR. The diagram also shows preventive maintenance with a
specific rule set for PM.
Queue Pick
Selector (FIFO or MIVP®) for Machine
Group C3 - Photolithography
The following diagram shows the queue pick
selector for step 3 and step 6 in the process flow for the Photolithography
Machine Me. The rules are switched to FIFO for the baseline data collection.
Once the model has been run and the data has been collected for FIFO, the MIVP® schedule policies are
switched on and the model is run again for the same production time. The average
cycle time results from MIVP® are then compared to FIFO.
Machine
Group C3 – Photolithography with Setups and Preventive Maintenance
The diagram below represents the
Photolithography Bay machine Me, the Photo Stepper. The lot will arrive and be
processed on the machine. This machine has a set of rules for setup because the
reticule requires changing for each different product as well as each different
layer. The Photo Stepper Machine will be taken down for emergency maintenance
according to historical data for MTBR and MTTR. The diagram also shows
preventive maintenance with a specific rule set for PM.
Data
Collection for Production, Cycle Time, Work-in-Progress and Model Statistics
The following diagram shows the icons
for collecting statistics during the production run. Work-In-Progress (WIP),
average cycle time and product exit information is displayed in numerical form
as well as graphically. Queue statistics of arrivals, departures, size of
queue, and utilization are important for playing “What If” scenarios. The mean
and variance of each machine is also displayed numerically and graphically.
Results
Table 1.
Kempf Mini-FAB Model Results, no setup’s and 1 lot per 120 minutes
|
|
Products Average |
Product Pa |
Product Pb |
Product TW |
PID Mean Cycle
Time, FIFO
|
4134.0±88.3 |
4155.1±90.8 |
4858.7±85.3 |
3388.1±96.0 |
|
H¥ Mean Cycle Time, FIFO |
3462.4±23.5 |
3499.4±14.6 |
4194.1±25.3 |
2693.5±60.4 |
|
PID Mean Cycle Time, MIVP® |
3899.3±62.6 |
4176.7±75.5 |
4605.4±63.4 |
2915.7±63.3 |
|
H¥ Mean Cycle Time, MIVP® |
3373.8±22.3 |
3519.4±16.0 |
4082.1±30.9 |
2520.0±45.8 |
|
Raw Processing Time[1] |
1277.915±0.909 |
1277.915±0.909 |
1277.915±0.909 |
1277.915±0.909 |
|
TQT[2], PID FIFO |
2856.1235 |
2877.2493 |
3580.8557 |
2110.2656 |
|
TQT, H¥ FIFO |
2184.5004 |
2221.5628 |
2916.255 |
1415.6834 |
|
TQT, PID MIVP® |
2621.3977 |
2898.8603 |
3327.5275 |
1637.8051 |
|
TQT, H¥ MIVP® |
2095.9532 |
2241.5301 |
2804.1914 |
1242.1381 |
|
PID Mean WIP[3],
FIFO |
39.20±2.18 |
23.23±1.73 |
15.03±1.50 |
0.933±0.373 |
|
H¥ Mean WIP, FIFO |
29.83±1.60 |
17.40±1.19 |
11.56±1.17 |
0.866±0.343 |
|
PID Mean WIP, MIVP® |
36.40±1.56 |
22.86±1.76 |
12.36±1.54 |
1.166±0.671 |
|
H¥ WIP, MIVP® |
29.16±1.23 |
16.66±0.805 |
11.90±0.897 |
0.600±0.219 |
Comparison
among the Mean Cycle Time for different strategies