IEOR 130 Methods of Manufacturing Improvement Fall, 2013 Prof ...

IEOR 130 Methods of Manufacturing Improvement
Fall, 2013
Prof. Leachman
Homework Problems #6
Due Tuesday Oct. 17, 2013
1. Data in a factory has been collected on the performance of five types of machines, as
displayed in the following table. The machines are all used in the same process flow.
Shown in the table for each machine type are the theoretical production time per lot
(TPT) in hours, the number of lots (NL) processed, the actual production time (PT) in
hours and the down time (DT) in hours. Total time for each machine type is 24 hours.
Machine TPT NL PT DT
Type
A 1.0 20 21.0 2.5
B 1.0 21 21.5 1.5
C 0.5 38 20.0 0.5
D 0.5 36 20.0 3.0
(a) Calculate the availability, the utilization of total time and the utilization of availability
for each machine type. Calculate the OEE of each machine type. Assume quality
efficiency is 100% for all machine types.
(b) Suppose it is possible to reduce down time by 0.5 hours per day for any of the four
machine types. However, it is not possible to reduce down time for more than one of the
machine types, i.e., you must pick one machine type and reduce down time of that
machine type. For which one do you think it would be most beneficial to fab
performance? Why? How will fab performance improve?
(c) Suppose it is possible to increase rate efficiency of any of the four machine types. For
which one do you think it would be most beneficial to fab performance? Why? How will
fab performance improve?
2. A wafer fabrication plant produces 800 wafers per day of a memory device. The line
yield is 100%. The steppers are the bottleneck equipment. At present, the OEE of the
steppers averages 0.667, the down time averages 10% and the idle time averages 5%. The
quality efficiency for the steppers is 100%. Considering all photo steps to make the
memory device, the total theoretical process time per wafer is 0.5 hours.
(a) How many steppers are operating in the plant?
(b) What is the rate efficiency of the steppers?
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(c) What rate efficiency would be sufficient to reduce the number of operating steppers
by one without reducing the output?
3. Two alternative processing machines are under consideration. Statistics about machine
performance and maintenance are as follows:
Machine Rework Scrap Avg. PM Avg. Machine Avg. Process time
Rate Rate Hours/Week Failures (Hours) (Hours/lot-pass)
MTBF MTTR
A 0.01 0.001 16 200 8 0.55
B 0.02 0.006 18 100 6 0.50
Assume the fab operates 168 hours per week. The machines process one lot at a time.
When rework is required, the lot must be processed a second time. The average
process time for the second pass is the same as for the first pass. The chance of a third
pass is negligible.
(a) What is the average availability of each machine type?
(b) The two machines have the same price. From a productivity point of view, which one
would you recommend? Explain.
4. An I Line stepper is the bottleneck of a small fabrication facility, and management
desires to maximize its output rate. When equipped with a brand new bulb, the lamp
intensity of the stepper is approximately 1,000 mW/cm2. The intensity declines after
every wafer exposure until the bulb is replaced. The photo engineer has estimated the
lamp intensity function to be LI(n) = 1,000(0.9994) n , where n refers to the nth wafer
exposed since the bulb was replaced and LI(n) is the lamp intensity realized for the nth
wafer. The total machine down time to replace the bulb and re-qualify the stepper is four
hours. Other stepper data: wafer exchange time XT = 13 seconds, initial alignment time
AT = 27.5 seconds, and move and align time MT = 0.5 seconds. There is only one
exposure step performed by the stepper, with NE = 60 and EE = 1,000 mJ. No blading is
required.
Consider three possible frequencies for changing the bulb: once every 100 wafers, once
every 1,000 wafers, or once every 5,000 wafers. Which frequency would maximize
n
n
i 1
a
stepper output rate? Explain. (Useful fact from algebra: a a .)
i1
1
a
5. In a 24-hour period, a particular photo exposure machine had 2.5 hours of down time.
Its rate efficiency was 85 percent. It completed processing of 35 lots, but 5 of these were
the second run on a lot previously processed (i.e., 5 lots were reworked). The average
process time per machine cycle was 0.5 hours. (One lot is processed per machine cycle,
and a rework lot takes the same amount of time as a first-pass lot.)
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(a) Estimate the availability, the utilization of availability and the OEE of the
machine for that 24-hour period.
(b) An engineering change to the machine is under consideration. The change will
reduce the rework rate to about 6 percent, but it will increase the average process
time by 2 percent. (Theoretical process time will not be changed.) Assuming the
24-hour period reflected average conditions, estimate what the OEE score will be
if the engineering change had been implemented. Assume the number of fab starts
will be increased just enough so that the utilization is held constant.
Now suppose it is not known how low the rework rate will be after the engineering
change, but it is known that average process time would rise by 2 percent. Find the upper
limit on the rework rate after the change such that the engineering change will not
decrease OEE from its value in part (a). Once again, assume the fab starts would be
adjusted so that the utilization is held constant.
6. A semiconductor factory producing 0.8 micron products utilizes 5X G Line stepper
machines to perform photolithography. The machine works as follows. One or two
cassettes of 25 wafers each may be placed in the stepper by the operator. The operator
must enter a recipe into the machine and place the proper reticle (i.e., the photomask) in
the machine before starting the machine. The machine accommodates up to six reticles in
an internal magazine. A new cassette, recipe and/or reticle can be tendered to the machine
while it is running on another cassette/reticle/recipe combination.
Mechanical apparatus inside the machine move wafers one at a time out of the input
cassette and onto an X-Y stage where the exposures will take place. The machine
performs the lithography exposures on the first wafer, then the completed wafer is moved
to an empty cassette while the second wafer is moved onto the X-Y stage. The fixed time
to move a completed wafer off the stage and replace it with the next wafer to be
processed is called the wafer exchange time (XT).
After a wafer is moved onto the X-Y stage, the machine performs an aligning procedure
to properly orient the wafer level and straight with the camera lens. The fixed time to
perform this initial alignment is called the alignment time (AT).
The 5X stepper performs multiple exposures, one at a time. (The name "stepper" comes
from the fact that it performs multiple "steps" across the wafer surface.) Each exposure
encompasses a small number of die. The number of exposures (NE) required to fully
process a particular wafer type is a given factor which depends on the size of the die and
the exposure field size of the machine.
The process recipe calls for a certain exposure energy (EE) to be achieved, measured in
milli-Joules (mJ). The time required to perform this exposure (ET) equals EE divided by
the lamp intensity (LI) of the machine, where LI is measured in milli-Watts per square
centimeter (mW/sq cm). LI depends on the condition of the exposure bulb and the quality
of the optical path inside the machine.
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After a single exposure is completed, the X-Y stage moves the wafer over for the
exposure of the next field. The fixed time for the mechanical apparatus to move the wafer
and re-align the camera is called the move time (MT). There is no MT before exposing
the first die; all initial motion of the wafer on the X-Y stage is included in AT.
For the die types produced in this factory, there are no "test keys" printed on the wafers.
The entire wafer surface is printed with product dice.
After exposures of all wafers in the cassette are completed, the cassette can be removed
from the machine and the exposed wafers are then sent through a development process.
(Similar to the way the machine can hold two cassettes of inbound wafers, there is room
in the machine for two outbound cassettes. A full outbound cassette can be removed from
the machine while it continues to process wafers into the other cassette.) After
developing, the wafers are inspected under a microscope. If for some reason the exposure
was mis-aligned with earlier mask layers, the current layer can be stripped off in an acid
bath, and the wafers sent back through the stepper for a second try. This repetition is
known as rework. Let RW denote the fraction of total wafer operations performed on the
5X stepper that are rework.
The operational procedures followed in the factory sometimes result in the machine being
completely flushed out of wafers and falling idle. For quality control purposes, the
machine might be deliberately stopped after processing one wafer and held idle while
waiting for the results of the after-develop inspection. When the machine is to be used
again after becoming idle, the machine is inactive while the operator puts in a new reticle,
puts in a new cassette, enters the appropriate recipe, and starts the machine. It then takes
the machine some time to bring the first wafer from the inbound cassette to the X-Y stage
in order to start the basic processing cycle described above. The sum of all these delay
times is called a setup time (ST). Let WPS denote the average number of wafers
processed between setups.
The industrial engineer for the fab has collected the following data about a particular 5X
stepper in the factory:
Parameter Theoretical Average
LI 770 mW/sq cm 720 mW/sq cm
MT 0.46 sec 0.47 sec
AT 27.0 sec 29.0 sec
XT 12.0 sec 12.0 sec
ST
150 sec
(a) Provide a formula for the theoretical processing time (seconds per wafer) as a function
of the number of exposures per wafer (NE), the exposure energy (EE), and the numerical
parameters above.
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(b) Provide a formula for the average processing time (seconds per wafer). Assume the
average rework rate RW and the average number of wafers per setup WPS parameters are
given. Assume rework does not result in extra stepper setups.
(c) The Photo Process Engineering Manager would like some help prioritizing the efforts
of her staff. She would like to know: Which would reduce average processing time more,
a 5% reduction in exposure time, or a 5% reduction in the rework rate? Assume the
average number of exposures NE is 60, the current average exposure time is 0.3 seconds,
and the current average rework rate is 2.6%. Answer her question and explain.
(d) Suppose the average processing time for the stepper is reduced. Would this translate
into a higher OEE score for the stepper? Explain.
7. At present, the process specifications for the operation of a metal etcher require the
operator to perform a test run of the machine on a single blank wafer before processing
each production lot. The blank wafer must be inspected for particles using a measurement
machine that counts particles on the wafer surface. During this time, the metal etcher is
held idle. If the particle count is low enough, the operator may proceed to process the
production lot through the metal etcher. If the particle count is too high, the metal etcher
machine is declared out-of-control and a cleaning of the machine must be performed
before any production lots can be processed. The relevant parameters are as follows:
Parameter Average Theoretical
Time to process blank wafer 10.2 minutes 9.1 minutes
Time to inspect blank wafer 8.5 minutes 6.2 minutes
Time to process production lot 30.5 minutes 28.0 minutes
Cleaning time per 24 hours 2.0 hours
Other down time per 24 hours 1.2 hours
Production lots processed per day 25.0
(a) What is the current OEE of the metal etcher? Assume that, theoretically, test runs are
not necessary.
(b) Estimate the current availability of the metal etcher. Suppose we define utilization (of
total time) for the metal etcher to include processing time plus the enforced idleness
during inspection of test runs. Estimate the current utilization (of total time) of the metal
etcher.
(c) Optimistically, what is the potential increase in OEE if test runs are eliminated but no
other improvements are made? That is, what is the ratio of potential OEE to current
OEE? (To estimate this increase, assume there will be no change in idle time, cleaning
time, other down time or in rate of quality after the test runs are eliminated. Moreover,
assume the metal etcher is the fab bottleneck by a very wide margin.)
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(d) Pessimistically, there might be a major drop in die yield if the test runs are not
performed. By what factor would the die yield need to drop to offset the gains in wafer
throughput? Do you think such a drop is likely?
(e) How would the trade-off change if the metal etcher was not the fab bottleneck?
Would we be more inclined or less inclined to eliminate test runs? Explain very briefly.
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