Equipment Utilization and Queuing TheoryMary Tang, Ph.D. – SNF Lab Manager

Nick Bambos, Ph.D., Professor of Electrical EngineeringMr. Neal Master, Graduate Student in Electrical Engineering

Mr. Jie Zhang, Operational Intelligence Managerand Kayvis Deon-Ofori Damptey, Operational Intelligence Analyst

But Research is NOT Production…So why does utilization matter? Because we make or inform decisions about:

Equipment› Investments› Removal› Maintenance priorities

Operational efficiency› What to do with idle equipment› Managing reservations

Strategic planning› Prioritizing customer needs› Indeed, determining who our customers are

Motivation: Understanding customer satisfaction surveysThe question: Equipment downtime affects your work…

1 – Never2 – Rarely3 – Sometimes4 – Often5 – Always

2008/9 – average of 4 (n=105)2012/13 – average of 2 (n=75)

Actual average overall equipment downtime:

2008 = 5.3%2012 = 5.2%

Could the activity in the lab explain this?

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Equipment Hours Logged/Month

Utilization = Equipment hours used (enabled) /Hours available Average %Utilization in 2008 ~ 14.7%Average %Utilization in 2013 ~ 10.8%

Is this enough a difference to affect user experience?

A comparison of equipment utilization

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%Utilization

20082013

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#Tools Above %Utilization

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Left: Utilization of all charged lab equipment, rank ordered. Right: The number of tools that are above a certain % Utilization.Utilization is defined simply as the number of billed hours for 24/7 operation over 50 weeks. The difference seems easier to see, but can it be significant?

Queuing TheoryThe mathematics of waiting lines, used to describe requests to a device.

A perfectly well-utilized system has regularly scheduled requests for processes that are equal in length.

https://www.utdallas.edu/~metin/Or6302/Folios/omqueue.pdf

https://www.utdallas.edu/%7Emetin/Or6302/Folios/omqueue.pdf

Queuing Theory

The reality… requests come in at somewhat random times, with process times that vary. The result is that even if there is excess capacity, there will be a queue.

Remember, sources of variation are:1. Request arrival times2. Length of time to process the request

Queuing Theory

Requests arrival times is described as the time between arrivals and is modeled as an exponential (left). The number of requests requiring a process service time of duration, t, is modeled as a Poisson distribution (right).

Queuing Theory

%Utilization

Wai

t Tim

e

The result:

Variability in the time of the request and duration of service cause the wait time to increase exponentially with utilization. Increase in variability causes nonlinear increases in wait time.

Variability in arrival times

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3501 5 9 13 17 21 1 5 9 13 17 21 1 5 9 13 17 21 1 5 9 13 17 21 1 5 9 13 17 21 1 5 9 13 17 21 1 5 9 13 17 21

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Barchart consolidating one year’s worth of equipment enables/disables (FY13) by day of the week and time of day.

This might be a proxy for describing the variability in arrival times of requests. The CoV for this behavior is 0.67.

Variability in process/service times

evalign2nikonstresstestrtaag

fusionp2

kscoat

alphastep

wbgen2-rfx

AG4108

micronic

ksbonderwhite-oven

thermcopoly2

wbnitride

tylan5

prometrix

thermconitride1

cpd

AG4100

cmp

semhitachi

epi

tylan6scttylan3wbgen2-hp

lampolyald

xactix

zygo

matrixwbsilicide

laurell-R

tylanfga

teos2tylansige

drytek1

tylanpoly

drytek4

evalign

telrtagaasfga2

tylannitridethermcopoly1gryphon

afm2

stsetch2

wbgaas-hprp5000etch

drytek2ebeam

woollam

karlsusswbgen-hpr

pquest

sts

wafersawwbsolvent

tylan4

gasonics

sem4160

metalica

wbgaas-hplmrcsvgcoat2headway2

svgdevwbmetal

karlsuss2wbgen-ctbthermco1svgcoatthermco2asml

amtetchertylanbpsg

tylan1tylan2evbondwbnonmetalsvgdev2

yesstsetchwbdiffbluem

innotecepi2 raith

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afm2

alphastepamtetcher

asmlaw610_l

aw610_r

bluemccp-depcmp

cpd

drytek2drytek4

ellipsomterepi2

epi2Bevalign

evalign2evbond

evgspraycoat

fga2 fiji1fiji2

fiji3

gasonics

hdpcvdheadway2

hummer

innotecintlvac_evap

intlvac_sputterkarlsusskarlsuss2

ksbonder

kscoat

lampoly

laurell-G

laurell-Rlithosolv

matrix

metalica

micromanipulator6000

mrc

nanospec

nanospec2Ox-35

p2

p5000etchpquest

prometrix

PT-DSEPT-MTLPT-Oxraith

savannahsem4160stresstest

sts

stsetchstsetch2

svgcoat svgcoat2svgdev svgdev2tel

teos2

thermco1thermco2

thermco3

thermco4thermcoltothermconitride

1

thermcopoly1thermcopoly2

tylan1tylan2tylan3

tylan4tylan5tylan6

tylanbpsg

tylanfga

tylannitride

uetchwafersaw

wbclean-3wbdiff

wbgaas-hpl

wbgaas-hpr

wbgen2-hp

wbgen2-rfxwbgen-ctb

wbgen-hpr

wbmetal

wbmiscreswbnitride wbnonmetal

wbsilicidewbsolvent

woollamxactix

yes

zygo

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CoV of process times (enable to disable time) versus % utilization. High CoV leads to longer wait times, but only for some significant level of utilization. Interesting clustering, but no smoking gun.

2008 2013

Queuing theory…

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#Tools Above %Utilization

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… offers a tantalizing explanation for why what might seem to be a modest change in utilization might lead to vast difference in customer experience. However, simple analysis isn’t clear cut.

Problems with queuing theory in a research fab

Fabrication consists of multiple processes in sequence; additional variability introduced. Fabrication requires repeating processes; “reentry” into the queue results in more complex math.

http://www.csus.edu/indiv/b/blakeh/mgmt/documents/opm101supplc.pdf

Problems with queuing theory in a research fab

There isn’t a handy way to measure wait time in our environment.

However, for high-in-demand tools, there will be wait times for reservations (wait times, sans queue.) Reservation game playing might be one proxy metric for customer satisfaction.

Takeaway…

Reservations: An effective reservation program is incredibly

effective at allocating resources. “Effective” means “flexible.” The aim is to

establish clear expectations for access.

Customer service skills Absolutely essential, more important, to limited

extent, than performance by standard metrics. We all need to be in the “experience

economy.”

And in closing…

a couple other topics related to utilization

Equipment Investments/Divestments

22 Furnaces in 2013Ave Utilization = 8%

13 Furnaces in 2015

Variable speed dry pump Collaboration with Oerlikon Leybold; custom factory upgrades to Leyvac LV80 dry screw pump Drop-in replacement for Hanbel PS80 line Tool enable: N2 purge on, full 60 Hz power; Tool disable: N2 off (15 min delay), power to 20 Hz. Annual savings estimated at $2K N2, $2.5K utilities. Pump received last week – data at the next UGIM! More info: Contact Carsen Kline (carsen@Stanford.edu)

Cost of Ownership Model LV80 PS80 Savings per year25% UtilizationPowerTotal hours per year 8,760.00 8,760.00operation hours per year 2,190.00 2,190.00idle hours per year 6,570.00 6,570.00full speed power consumption (kW) 3.00 3.00idle speed power consumption (kW) 1.70 3.00unit cost of power $/kWh 0.118 0.118chilled water (1.3 kWh) 1,507.00total cost of power per year 2,084.33 4,594.90 2,510.57

N2N2 purge flow during process (slm) 30.00 30.00N2 purge flow during idle (slm) 8.00 30.00process hours per year 2,190.00 2,190.00idle hours per year 6,570.00 6,570.00unit cost of utility N2 $/100scf 0.65 0.65total cost of N2 per year 1,629.73 3,621.63 1,991.89

Cost of Power + N2 Per Year 3,714.06 8,216.53 4,502.46

Sheet1

Cost of Ownership ModelLV80PS80Savings per year

25% Utilization

Power

Total hours per year8,760.008,760.00

operation hours per year2,190.002,190.00

idle hours per year6,570.006,570.00

full speed power consumption (kW)3.003.00

idle speed power consumption (kW)1.703.00

unit cost of power $/kWh0.1180.118

chilled water (1.3 kWh)1,507.00

total cost of power per year2,084.334,594.902,510.57

N2

N2 purge flow during process (slm)30.0030.00

N2 purge flow during idle (slm)8.0030.00

process hours per year2,190.002,190.00

idle hours per year6,570.006,570.00

unit cost of utility N2 $/100scf0.650.65

total cost of N2 per year1,629.733,621.631,991.89

Cost of Power + N2 Per Year3,714.068,216.534,502.46

N2 conservation panel PLC, solenoid valves, relays, based on Supertex design Tool enable: high flow mode Tool disable: switch to low flow, after 15 min. delay $1200 in materials to build $6200 saved across six pumps since installation 7/1/15 Complete plans available; contact Carsen

345 days since installation on 7/1/15Utilization Hi/Lo flow cu. ft. saved Savings

delta, cu. ft.since 7/1/150.18 0.3 122213 $794

oxford-rie 0.2 0.7 278208 $1,808PT-Ox 0.25 0.4 149040 $969PT-MTL 0.27 0.5 181332 $1,179p5000etch 0.23 0.3 114761 $746lampoly 0.23 0.3 114761 $746

960314 $6,242

Sheet1

Based on N2 overall cost of $6.50/1000 scf

345 days since installation on 7/1/15

UtilizationHi/Lo flowcu. ft. savedSavings

delta, cu. ft.since 7/1/15

0.180.3122213$794

oxford-rie0.20.7278208$1,808

PT-Ox0.250.4149040$969

PT-MTL0.270.5181332$1,179

p5000etch0.230.3114761$746

lampoly0.230.3114761$746

960314$6,242

Sample References“Family-Based Scheduling Rules of a Sequence-Dependent Wafer Fabrication System.” Ching-Chin-

Chern and Yu-Lien Liu. IEEE Transactions on Semiconductor Manufacturing, Vol. 16, No. 1, Feb. 2003.

“Control of Batch Processing Systems in Semiconductor Wafer Fabrication Facilities.” HareshGurnani, Ravi Anupindi, and Ram Akella. IEEE Transactions on Semiconductor Manufacturing, Vol. 5, No. 4, Nov. 1992.

“Queuing Theory for Semiconductor Manufacturing Systems: A Survey and Open Problems.” J. George Shanthikumar, Shenwei Ding, and Mike Tao Zhang. IEEE Transactions on Automation Science & Engineering, Vol. 4, No. 4, Oct. 2007.

“Implementation of Modeling and Simulation in Semiconductor Wafer Fabrication with Time Constraints Between Wet Etch and Furnace Operations.” Wolfgang Scholl and JeorgDomaschke. IEEE Transactions on Semiconductor Manufacturing, Vol. 13, No. 3, Aug. 2000.

“A Total Standard WIP Estimation Method for Wafer Fabrication.” Yu-Hsin Lin and Ching-Eng Lee. European Journal of Operational Research, Vol. 131. 2001.

Equipment Utilization and Queuing TheoryBut Research is NOT Production…Motivation: Understanding customer satisfaction surveysCould the activity in the lab explain this?A comparison of equipment utilizationQueuing TheoryQueuing TheoryQueuing TheoryQueuing TheoryVariability in arrival timesVariability in process/service timesQueuing theory…Problems with queuing theory in a research fabProblems with queuing theory in a research fabTakeaway…And in closing…��a couple other topics related to utilizationEquipment Investments/DivestmentsVariable speed dry pumpN2 conservation panelSample References