Equipment failure forecast in a semiconductor production...

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Equipment failure forecast in a semiconductor production line

GENUA Caterina Maria, PAPPALARDO Maria Vittoria

STMicroelectronics

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Purpose

Improve the data model of the mathematical simulator used in STMicroelectronics fabs, predicting equipment failures (unscheduled down or preventative maintenance), through the application of non-parametric inferential statistics techniques on historical equipment data.Obtainable benefits: Equipment failure prediction can improve STAP simulator data model accuracy, thus providing better indications to the shop floor for dispatching, and giving more reliable commitment to customers.

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Catania STMicroelectronics production lines

Catania site aerial view

M5

Catania STMicroelectronics shop floor

25-wafers lot

Grey area equipment

Diffusion area

Etching area

Photolithography area

Diffusion Furnace

Clean room operator

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Production software tools

WorkstreamDB

APF reporting system

COBOLextracts

Production data extracts Simulator input

STAP toolbox STAP engine

Simulator output

STAPtoolbox

Reports

Fab Performance Viewer framework

FPV repository

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Production software tools used in this project

Production control Group uses Shop Floor Scheduling toolsfor data analysis and for production process dispatchingindications.

Among those tools, the following have been used in thisproject:STAP (ST Autosched Accelerated Processing) : mathematical simulator produced by Amat, which, through fab data model, reproduces the whole production process and generates reports, such as production targets.FPV (Fab Performance Viewer): framework for graphical and statistical analysis of production data related to process flows, shop floor equipment, operators.

Reliability theory (1/2)

Availability: proportion of time a system is in a functioning conditionAvailability indicators

MTBF – Mean Time Between FailMTTF – Mean Time To FailMTTR – Mean Time To Repair

up

down

MTBF

MTTR MTTF

7

Reliability theory (2/2)

Probability distributions mainly used in reliability theory

Exponential distribution, if the system has a constant failure rate, i.e. the rate does not vary over the life cycle of the system with agingWeibull distribution, if the failure rate of the system grows as the system grows older, due to aging and use, so the older the system is, the more it tends to fail

STAP data model

Product file

Route files

Order files

Stations file

Generic resources file

Calendar files

STAP simulator engine

Reports

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STAP calendar files (1/3)

Equipment down (unscheduled failure) calendarAssociation of down calendar file to single stationEquipment PM (Preventative Maintenance) calendar Association of PM calendar file to single station

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up

down

MTTF MTTR

DOWNCALNAME DOWNCALTYPE MTTFDIST MTTF MTTF2 MTTF3 MTTFUNITS MTTRDIST MTTR MTTR2 MTTR3 MTTRUNITS

DN_LAM4520 mttf_by_cal exponential 144.86 hr exponential 15.5 hrs

Equipment down (unscheduled failure) calendar

RESTYPE RESNAME CALTYPE CALNAME FOADIST FOA FOA2 FOA3 FOAUNITS

stn LAM4520O207 down DN_LAM4520 weibull 0.571429 10.26469 hr

Association of down calendar file to single station

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Equipment PM (Preventative Maintenance) calendar

RESTYPE RESNAME CALTYPE CALNAME FOADIST FOA FOA2 FOA3 FOAUNITS

stn LAM4520O207 pm PM_LAM4520O207 weibull 0.571429 10.26469 hr

Association of PM calendar file to single station

PMCALNAME PMCALTYPE MTBPMDIST MTBPM MTBPM2 MTBPMUNITS MTTRDIST MTTR MTTR2 MTTRUNITS

PM_LAM4520O207 mtbpm_by_cal exponential 27.06 hr weibull 0.425532 1.009563 hr

up

down

MTBPM

MTTR

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Exponential distribution (1/2)

βμ =

Probability density function:

altrimenti0 xse

0

1)(

≥

⎪⎩

⎪⎨⎧

=− β

β

xexf

Cumulative distribution function:

altrimenti0 xse

01)(

≥

⎪⎩

⎪⎨⎧ −=

− βx

exF

Mean:

Variance:22 βσ =

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Exponential distribution (2/2)

STAP exponential distribution data modelMTTFDIST exponentialMTTF 10MTTFUNIT hr

Properties:Skewed distributionUsed for events with high variability (e.g. equipment

MTTF)

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Weibull distribution (1/2)

altrimenti0 xse

0)(

1 ≥

⎪⎩

⎪⎨⎧

=⎟⎠⎞⎜

⎝⎛−−−

α

βαααβx

exxf

altrimenti0 xse

01)(

≥

⎪⎩

⎪⎨⎧−=

⎟⎠⎞⎜

⎝⎛−

αβx

exF

Mean:

⎟⎠⎞

⎜⎝⎛Γ=αα

βμ 1

Variance:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛Γ−⎟

⎠⎞

⎜⎝⎛Γ=

222 1122

ααααβσ

( ) ∫∞

−−=Γ0

1 dtetz tzwhere: (gamma function)



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Weibull distribution (2/2)

Weibull distribution STAP data modelMTTFDIST weibullMTTF 1MTTF2 17MTTFUNIT hr

Properties:Distribution family including exponentialWidely used in reliability theory to analyze system life cycleUnimodal and skewedwhen α=1, it’s an exponential with mean βwhen α<1, it’s very skewed to the right and high values

probability is bigger than exponential

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Gamma distribution (1/2)

( ) altrimenti0 xse

0)(

1>

⎪⎩

⎪⎨⎧

Γ=

−−

αβ βαα xex

xf

( )altrimenti

0 xse

0!

1)(1

1

>

⎪⎩

⎪⎨⎧−= ∑

−

=

−α

β βj

jx

jxexF

βαμ =

Mean:

Variance:

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βασ =

( ) ∫∞

−−=Γ0

1 dtetz tzwhere: (gamma function)



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Gamma distribution (2/2)

Gamma distribution STAP data modelMTTFDIST gammaMTTF 1MTTF2 17MTTFUNIT hr

Properties:Distribution family including exponentialUnimodal, can be skewed or almost symmetricwhen α=1, it’s an exponential with mean 1/βwhen α>10, can be approximated by a normal with mean μ and

variance σ2

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STAP data model improvement

golden tools selectionPM and down calendar files update, applying inferential statistics to historical data of golden toolswhat-if analysis: compare two simulation runs

sim_before: calendar files updated with deterministic approachsim_after: calendar files updated with probabilistic approach

Simulation results comparisonBenefits

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Calendar files updateDeterministic approach

Calendar manual update

Periodical (e.g. every three months)Exponential distributionMTTF, MTBPM, MTTR values extracted from production reports and communicated by production people to production control people in charge of updating STAP data model

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Deterministic approachsim_before (1/2)

Equipment down calendar

DOWNCALNAME DOWNCALTYPE MTTFDIST MTTF MTTFUNITS MTTRDIST MTTR MTTRUNITS

DN_LAM4520 mttf_by_cal exponential 144.86 hrs exponential 15.5 hrs

Association of down calendar file to single station

RESTYPE RESNAME CALTYPE CALNAME FOA FOAUNITS

stn LAM4520O207 down DN_LAM4520 122676 sec

stn LAM4520O303 down DN_LAM4520 57458.9 sec




stn LAM4520O210 down DN_LAM4520 27500.5 sec


stn ALLIAN112 down DN_LAM4520 245064 sec

NOTE: The same calendar is associated to more than one station.

Deterministic approachsim_before (2/2)

Equipment PM calendar

PMCALNAME PMCALTYPE MTBPMDIST MTBPM MTBPMUNITS MTTRDIST MTTR MTTRUNITS

PM_LAM4520 mtbpm_by_cal exponential 300 hrs exponential 11.7 hrs

Association of PM calendar file to single station

RESTYPE RESNAME CALTYPE CALNAME FOA FOAUNITS

stn LAM4520O207 pm PM_LAM4520 254057 sec




stn LAM4520O209 pm PM_LAM4520 1.03E+06 sec

stn LAM4520O210 pm PM_LAM4520 56952.7 sec


stn ALLIAN112 pm PM_LAM4520 507520 sec

NOTE: The same calendar is associated to more than one station.

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Calendar files updateProbabilistic approach

Calendar update based on inferential statistics techniques on equipment data found in hystorical repository

Extraction of golden tools data related to failures and preventative maintenance, from Fab Performance Viewer, FPV framework archiveApplication of Kolmogorov- Smirnov test to golden tools data, to determine probability distribution related and associated parametersUpdate STAP calendars with the calculated parameters

Probabilistic approach Data extraction from FPV archive

EQP_ID EQP_NAME

1070 ALLIAN112

482 LAM4520O207

715 LAM4520O208

1069 LAM4520O209

624 LAM4520O210

1068 LAM4520O213

892 LAM4520O303

895 LAM4520O306

EQP_ID OLD_STATE NEW_STATE TRANSACTION_INSTANT STATUS

482 DOWN UP 27-Nov-2010 03:26:45 PM STAND-BY

482 UP DOWN 27-Nov-2010 01:54:49 PM UNSCHEDULED

485 UP DOWN 28-Nov-2010 06:25:50 PM SCHEDULED

485 DOWN UP 27-Nov-2010 04:47:22 PM STAND-BY

485 UP DOWN 27-Nov-2010 12:46:16 PM UNSCHEDULED

485 DOWN UP 27-Nov-2010 09:43:47 AM STAND-BY

EQP_ID DAY MTBF MTTR DOWN_PERCENT STATUS

482 25-Nov-2010 12:00:12 AM 33.2769 1.5875 .0477 UNSCHEDULED

876 25-Nov-2010 12:12:51 AM 11.5636 3.1258 .2703 SCHEDULED

626 25-Nov-2010 12:35:28 AM 18.7222 4.3786 .2339 SCHEDULED

728 25-Nov-2010 12:44:10 AM 7.1517 .1236 .0173 UNSCHEDULED

1030 25-Nov-2010 12:48:53 AM 83.9725 2.0039 .0239 UNSCHEDULED

987 25-Nov-2010 12:59:56 AM 16.5936 .465 .028 UNSCHEDULED

820 25-Nov-2010 01:09:35 AM 48.0644 1.2867 .0268 SCHEDULED

1140 25-Nov-2010 01:23:17 AM 54.0175 1.4156 .0262 SCHEDULED

Stations table

up_down_transaction table

down_data table

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Probabilistic approachKolmogorov-Smirnov test (1/4)

“goodness-of-fit” test, proposed by Kolmogorov in 1933 and developed by Smirnov

compare a sample with a reference probability distributionThe Kolmogorov–Smirnov statistic quantifies the distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distributionThe computed distance will be compared to a threshold value to verify the null hypothesis that the samples are drawn from the reference distribution.

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X1,...,XN – N Independent and identically-distributed random variables Empirical distribution function SN for N iid observations Xiis defined as

iiN FN

XS 1)( =

Where Fi is the number of observations ≤ Xi

F0(.) - completely specified cumulative distribution functionF0(Xi) – expresses the expected value of samples <= Xi

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Kolmogorov–Smirnov statistic is

( ) ( )iNi

N

iXSXFD −=

= 01max


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test significance will be computed as

( ) ( )∑∞

=

−−−=1

21 22

12j

jjKS eQ λλ

[ ]( )DNNQobservedD KS /11.012.0)Pr( ++=>

Where QKS is defined as:

is a monotonic function with:

QKS(0)=1 QKS(∞)=0


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Probabilistic approachApplication of K-S test to data extracted from FPV(1/4)

MTTR results for golden tools failures

Lowest K-S test

Test significance Distribution type Distribution parameters

Station #data

Avg Standard deviation

D gamma D exponential D Weibull threshold Gamma Exponential

Weibull Gamma Exponential

Weibull α β

LAM4520O207 78 3.49 8.88 0.987179 0.433173 0.20363 0.153763 0 0 0.002552 no no no 0.454545 1.439969

LAM4520O303 108 6.32 34.78 0.990741 0.529611 0.401984 0.130674 0 0 0 no no no 0.298507 0.667273

LAM4520O208 102 5.46 9.94 0.990196 0.317283 0.167916 0.134462 0 0 0.005468 no no no 0.588235 3.535006

LAM4520O213 123 5.55 33.07 0.99187 0.548473 0.351509 0.122447 0 0 0 no no no 0.285714 0.476918

LAM4520O209 116 2.91 14.12 0.991379 0.507595 0.435371 0.126087 0 0 0 no no no 0.31746 0.40053

LAM4520O210 135 3.57 9.16 0.992593 0.328891 0.229257 0.116878 0 0 0.000001 no no no 0.454545 1.472084

LAM4520O306 111 7 54.42 0.990991 0.676216 0.495541 0.128896 0 0 0 no no no 0.25641 0.339019

ALLIAN112 59 1.75 2.77 0.983051 0.28751 0.253574 0.176797 0 0.000082 0.000776 no no no 0.645161 1.268947

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MTTF results for golden tools failures


Station #data


D gamma D exponential D Weibull threshold Gamma Exponential Weibull Gamma Exponential Weibull α β

LAM4520O207 78 16.51 31.38 0.987179 0.190428 0.083977 0.153763 0 0.005888 0.622476 no no yes 0.571429 10.26469

LAM4520O303 108 17.07 53.34 0.990741 0.178551 0.280952 0.130674 0 0.001717 0 no no no - 17.07

LAM4520O208 102 28.54 53.24 0.990196 0.186742 0.094751 0.134462 0 0.001352 0.304325 no no yes 0.571429 17.74648

LAM4520O213 123 12.65 21.51 0.99187 0.169067 0.086951 0.122447 0 0.001497 0.297043 no no yes 0.625 8.847901

LAM4520O209 116 11.46 33.31 0.991379 0.140527 0.26001 0.126087 0 0.01832 0 no no no - 11.46

LAM4520O210 135 9.28 10.44 0.140484 0.106748 0.09012 0.116878 0 0.086074 0.212239 no no yes 0.909091 8.867484

LAM4520O306 111 11.31 20.61 0.990991 0.109366 0.136451 0.128896 0 0.131517 0.028919 no yes no - 11.31

ALLIAN112 59 21.36 54.01 0.983051 0.221482 0.21944 0.176797 0 0.004994 0.005575 no no no 0.454545 0.81333

Lowest K-S test


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MTTR results for golden tools PMs


Station #data


D gamma D exponential D Weibull threshold Gamma Exponential Weibull Gamma Exponential Weibull α β

LAM4520O207 194 2.85 8.22 0.994845 0.464547 0.280585 0.097499 0 0 0 no no no 0.425532 1.009563

LAM4520O303 197 3 9.95 0.994924 0.472284 0.320832 0.096753 0 0 0 no no no 0.384615 0.809296

LAM4520O208 118 3.64 6.98 0.991525 0.360658 0.216121 0.125014 0 0 0.000025 no no no 0.555556 2.169273

LAM4520O213 276 2.73 7.64 0.996377 0.454566 0.178707 0.081742 0 0 0 no no no 0.425532 0.964051

LAM4520O209 285 2.55 6.78 0.996491 0.495555 0.204094 0.080441 0 0 0 no no no 0.444444 0.999823

LAM4520O210 227 4.65 26.78 0.995595 0.456195 0.456734 0.090134 0 0 0 no no no - 4.65

LAM4520O306 233 2.68 7.27 0.995708 0.380725 0.251248 0.088966 0 0 0 no no no 0.434783 0.998243

ALLIAN112 184 3.76 28.83 0.994565 0.52887 0.622604 0.100113 0 0 0 no no no - 3.76

Lowest K-S test


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MTBPM results for golden tools PMs


Station #data


D gamma D exponential D Weibull threshold Gamma Exponential

Weibull Gamma Exponential Weibull α β

LAM4520O207 194 27.06 33.74 0.310447 0.165252 0.243772 0.097499 0 0.000041 0 no no no - 27.06

LAM4520O303 197 21.30 20.8 0.163803 0.149983 0.149983 0.096753 0.00042 0.000241 0.000241 no no no 1 21.296

LAM4520O208 118 28.3 30.57 0.161027 0.104668 0.118599 0.125014 0.003796 0.141556 0.066777 no yes no - 28.3

LAM4520O213 276 16.5 18.78 0.186568 0.155111 0.141913 0.081742 0 0.000003 0.00025 no no no 0.869565 15.382

LAM4520O209 285 17.44 16.96 0.170783 0.151519 0.148993 0.080441 0 0.000003 0.000005 no no no 1.052632 17.794

LAM4520O210 227 22.31 29.35 0.366045 0.167081 0.21617 0.090134 0 0.000005 0 no no no - 22.31

LAM4520O306 233 20.33 18.86 0.211389 0.156893 0.150686 0.088966 0 0.000017 0.000043 no no no 1.052632 20.750

ALLIAN112 184 29.47 32.5 0.22515 0.250833 0.277687 0.100113 0 0 0 no no no 0.822394 0.027

Lowest K-S test


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Probabilistic approachSTAP calendars update (1/2)

Equipment failures calendar

DOWNCALNAME DOWNCALTYPE MTTFDIST MTTF MTTF2 MTTFUNITS MTTRDIST MTTR MTTR2 MTTRUNITS

DN_LAM4520O207 mttf_by_cal weibull 0.571429 10.26469 hr weibull 0.454545 1.439969 hr

DN_LAM4520O303 mttf_by_cal exponential 17.07 hr weibull 0.298507 0.667273 hr






DN_ALLIAN112 mttf_by_cal weibull 0.454545 0.81333 hr weibull 0.645161 1.268947 hr

Association of calendar file to single stations

RESTYPE RESNAME CALTYPE CALNAME FOADIST FOA FOA2 FOAUNITS

stn LAM4520O207 down DN_LAM4520O207 weibull 0.571429 10.26469 hr

stn LAM4520O303 down DN_LAM4520O303 exponential 17.07 hr






stn ALLIAN112 down DN_ALLIAN112 weibull 0.454545 0.81333 hr

NOTE: Each station has its own calendar

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Equipment PM calendar

Association of calendar file to single stations

PMCALNAME PMCALTYPE MTBPMDIST MTBPM MTBPM2 MTBPMUNITS MTTRDIST MTTR MTTR2 MTTRUNITS


PM_LAM4520O303 mtbpm_by_cal weibull 1 21.296 hr weibull 0.384615 0.809296 hr


PM_LAM4520O213 mtbpm_by_cal weibull 0.869565 15.38174 hr weibull 0.425532 0.964051 hr


PM_LAM4520O210 mtbpm_by_cal exponential 22.31 hr exponential 4.65 hr


PM_ALLIAN112 mtbpm_by_cal gamma 0.822394 0.027905 hr exponential 3.76 hr

RESTYPE RESNAME CALTYPE CALNAME FOADIST FOA FOA2 FOAUNITS

stn LAM4520O207 pm PM_LAM4520O207 exponential 27.06 hr

stn LAM4520O303 pm PM_LAM4520O303 weibull 1 21.296 hr






stn ALLIAN112 pm PM_ALLIAN112 gamma 0.822394 0.027905 hr

NOTE: Each station has its own calendar

Probabilistic approachSTAP calendars update (2/2)

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Results – application of KS-TEST to golden tools

4 days run horizon8 Golden tools in ETCHING areaParameters used as reference for comparison

Transactions up-down and viceversa (occurrence and duration)Moves – transition of a wafer from one operation to the next one

Results – golden tools (1/2)

0

1000

2000

3000

4000

5000

6000

Total MTTR (hrs) Total MTTF (hrs)

ActualSim_beforeSim_after

0

5

10

15

20

25

30

down % fails #

0

200

400

600

800

1000

1200

1400

1600

Average MTTR (hrs)

Results – golden tools (2/2)

1000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

1

Moves simul_before-moves actual

Moves simul_after-moves actual

14000

14500

15000

15500

16000

16500

17000

17500

18000

1

Actual

sim_before

sim_after

0

20

40

60

80

100

120

140

25/01

/2008

125

/01/20

08 2

25/01

/2008

326

/01/20

08 1

26/01

/2008

226

/01/20

08 3

27/01

/2008

127

/01/20

08 2

28/01

/2008

128

/01/20

08 2

28/01

/2008

3

90

90.5

91

91.5

92

92.5

93

93.5

94

94.5

95

1

Adherence sim_before

Adherence sim_after

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Results – application of KS-TEST to whole simulation model

4 days run horizon~ 500 stations in 10 homogeneous areasParameters used as reference for comparison

By stationPCCOMPS – number of wafers processed by stationDown and PM % per shift

Moves by area

Results – whole model % stations adherent to reality, by area

FOTOATT FOTOSVI DIFF METAL

Sim_before 36% 27% 8% 36%

Sim_after 64% 73% 92% 64%

Results – whole modelmoves by area and by shift

Shift 1 Shift 2

FOTOATT FOTOSVI METAL FOTOATT FOTOSVI METAL

Sim_before 14640 8370 8730 15112 8193 9341

Sim_after 14625 8330 8551 13754 7856 7932

Actual 17052 9491 10887 12902 7824 7629

Results – whole modelPCCOMPS by station - figures

Results – whole modelDOWN and PM % by station - figures

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BenefitsSimulation nearer to reality

Number and frequency of transitions and up and down times are next to realityMoves target better estimated (not over-estimated)Better Adherence

Deterministic approach drawbacksData manual update is not always based on correct data and executed at right timesDoes not consider products mix variability

Probabilistic approach advantagesWeekly data update based on historical equipment behaviorReal-time dataBetter usage of simulator potential

Equipment failure forecast in a semiconductor production...

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