Download - 10.02.04 1 Multivariate Statistical Process Control and Optimization Alexey Pomerantsev & Oxana Rodionova Semenov Institute of Chemical Physics Russian

10.02.04 1

Multivariate Statistical Process Multivariate Statistical Process Control and OptimizationControl and OptimizationAlexey Pomerantsev & Oxana Rodionova

Semenov Institute of Chemical PhysicsRussian Chemometrics Society

© Chris Marks

10.02.04 2

AgendaAgenda

1. Introduction

2. SPC

3. MSPC

4. Passive optimization (E-MSPC)

5. Active optimization (MSPO)

6. Conclusions

10.02.04 3

Statistical Process Control (SPC)Statistical Process Control (SPC)

SPC Objective

To monitor the performance of the process

SPC Method

Conventional statistical methods

SPC Approach

To plot univariate chart in order to monitor key process variables

SPC Concept

To study historical data representing good past process behaviour

10.02.04 4

Historical Process Data (Chemical Historical Process Data (Chemical Reactor)Reactor)

X17

9.74E-031.01E-02

-1.43E-039.07E-035.78E-03

-9.49E-04-6.79E-03-3.42E-03-9.86E-034.18E-03

-4.84E-039.44E-03

-4.99E-03-6.81E-031.23E-039.90E-033.65E-03

-6.78E-03s54 6.61E-02 -5.40E-01 7.19E-03 -2.85E-01 -5.19E-04 -5.78E-01 1.81E-04 -2.67E-04 -6.23E-05

…

…

X1 X2 X3 X4 X5 X6 X7 X8 X9

s1 -1.19E-01 7.28E-01 -2.15E-02 5.22E-01 7.06E-04 7.32E-01 3.10E-04 -6.13E-04 -5.92E-05s2 -1.37E-01 7.28E-01 -2.89E-02 6.08E-01 7.09E-04 7.02E-01 6.58E-04 -1.22E-03 -1.49E-04s3 2.51E-02 -9.15E-02 6.73E-03 -1.13E-01 -9.07E-05 -7.58E-02 -2.29E-04 4.10E-04 5.65E-05s4 -1.14E-01 6.70E-01 -2.18E-02 5.04E-01 6.50E-04 6.65E-01 3.83E-04 -7.34E-04 -7.96E-05s5 -7.93E-02 4.14E-01 -1.69E-02 3.51E-01 4.04E-04 3.98E-01 3.96E-04 -7.35E-04 -9.05E-05s6 1.51E-02 -6.38E-02 3.74E-03 -6.75E-02 -6.28E-05 -5.67E-02 -1.15E-04 2.07E-04 2.78E-05s7 7.44E-02 -5.24E-01 1.11E-02 -3.24E-01 -5.06E-04 -5.45E-01 -1.73E-05 7.92E-05 -1.07E-05s8 3.65E-02 -2.66E-01 5.12E-03 -1.59E-01 -2.56E-04 -2.78E-01 1.43E-05 -3.95E-07 -1.14E-05s9 1.36E-01 -7.06E-01 2.89E-02 -6.01E-01 -6.88E-04 -6.77E-01 -6.83E-04 1.26E-03 1.56E-04s10 -2.74E-02 3.60E-01 1.82E-03 1.12E-01 3.42E-04 4.12E-01 -4.31E-04 7.24E-04 1.22E-04s11 7.47E-02 -3.31E-01 1.80E-02 -3.34E-01 -3.25E-04 -2.99E-01 -5.30E-04 9.62E-04 1.28E-04s12 -1.17E-01 7.02E-01 -2.16E-02 5.13E-01 6.81E-04 7.03E-01 3.40E-04 -6.63E-04 -6.76E-05s13 1.06E-01 -2.82E-01 3.23E-02 -4.82E-01 -2.85E-04 -1.87E-01 -1.25E-03 2.21E-03 3.14E-04s14 7.39E-02 -5.28E-01 1.07E-02 -3.21E-01 -5.09E-04 -5.50E-01 2.49E-06 4.48E-05 -1.59E-05s15 -9.87E-03 1.02E-01 -3.21E-04 4.17E-02 9.75E-05 1.13E-01 -8.29E-05 1.36E-04 2.44E-05s16 -1.06E-01 7.68E-01 -1.52E-02 4.62E-01 7.41E-04 8.03E-01 -2.54E-05 -2.68E-05 2.88E-05s17 -4.76E-02 2.66E-01 -9.52E-03 2.10E-01 2.59E-04 2.61E-01 1.92E-04 -3.61E-04 -4.19E-05

P

rod

uct

ion

cyc

les

s1,

s2,

...

,s5

4

Key process variables (sensors) X1, X2, ... , X17

10.02.04 5

Shewart Charts (1931)Shewart Charts (1931)

X1 Normal

X2 Normal

X1 Control

X1 Control

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

s1 s3 s5 s7 s9

s11

s13

s15

s17

s19

s21

s23

s25

s27

s29

s31

s33

s35

s37

s39

s41

s43

s46

s49

s51

s54

s56

Cycles (time)

X1

Se

ns

or

X2 Normal

X2 Normal

X2 Control

X2 Control

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

s1 s3 s5 s7 s9

s11

s13

s15

s17

s19

s21

s23

s25

s27

s29

s31

s33

s35

s37

s39

s41

s43

s46

s49

s51

s54

s56

Cycles (time)

X2

Se

ns

or

X1 Normal

X2 Normal

X1 Control

X1 Control

X2 Normal

X2 Normal

X2 Control

X2 Control

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

s1 s3 s5 s7 s9

s11

s13

s15

s17

s19

s21

s23

s25

s27

s29

s31

s33

s35

s37

s39

s41

s43

s46

s49

s51

s54

s56

Cycles (time)

X1

& X

2 S

en

so

rs

Normal

Normal

Control

Control

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

s1 s3 s5 s7 s9

s11

s13

s15

s17

s19

s21

s23

s25

s27

s29

s31

s33

s35

s37

s39

s41

s43

s46

s49

s51

s54

s56

Cycles (time)

All

Se

ns

ors

10.02.04 6

Panel Process Control (just a game)Panel Process Control (just a game)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.31 -0.4 0.26 -0.3 -0.3 -0.4 -0.1 0.13 0.08 -0.3 -0.3 #### -0.3 -0.3 #### -0.1 -0.4

Time till the end of shift: 7:59:10

0.31

-0.36

0.26

-0.31-0.27-0.37

-0.09

0.13 0.08

-0.35 -0.35

0.01

-0.28-0.35

-0.01

-0.06

-0.38

OnOff Exit

-3

-2

-1

0

1

2

3

-4 -3 -2 -1 0 1 2 3 4

PC1

PC

2

10.02.04 7

Multivariate Statistical Process Control Multivariate Statistical Process Control (MSPC)(MSPC)

MSPC Objective

To monitor the performance of the process

MSPC Method

Projection methods of Multivariate Data Analysis (PCA, PCR, PLS)

MSPC Approach

To plot multivariate score plots to monitor the process behavior

MSPC Concept

To study historical data representing good past process behavior

10.02.04 8

Projection MethodsProjection Methods

Initial Data

Data Plane

Data Center

PCs

Data Projections

10.02.04 9

Low Dimensional PresentationLow Dimensional Presentation

10.02.04 10

Loadings

X1

X2

X3

X4

X5

X6

X7

X8X9

X10X11

X12

X13

X14

X15X16

X17

-0.3

0

0.3

0.6

-0.4 -0.2 0 0.2 0.4

PC1

PC2

MSPC Charts (Chemical Reactor)MSPC Charts (Chemical Reactor)

Scores

s53

s52

s51s50

s49

s48s47

s46s45 s44

s43

s42s41

s40

s39 s38 s37

s36s35s34

s33

s32s31

s30

s29s28

s27 s26

s25

s24

s23

s22

s21s20

s19s18

s17

s16

s15

s14

s13

s12

s11

s10

s9s8

s7

s6 s5

s4

s3 s2

s1

-3

-2

-1

0

1

2

3

-4 -3 -2 -1 0 1 2 3 4

PC1

PC2

Samples Key Variables

10.02.04 11

Panel Process Control (not just a game)Panel Process Control (not just a game)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.31 -0.4 0.26 -0.3 -0.3 -0.4 -0.1 0.13 0.08 -0.3 -0.3 #### -0.3 -0.3 #### -0.1 -0.4

Time till the end of shift: 7:59:10

0.31

-0.36

0.26

-0.31-0.27-0.37

-0.09

0.13 0.08

-0.35 -0.35

0.01

-0.28-0.35

-0.01

-0.06

-0.38

OnOff Exit

-3

-2

-1

0

1

2

3

-4 -3 -2 -1 0 1 2 3 4

PC1

PC

2

10.02.04 12

Cruise Ship Control (by Kim Esbensen)Cruise Ship Control (by Kim Esbensen)

10.02.04 13

Key Process VariablesKey Process Variables

10.02.04 14

PLS1 Prediction of Fuel Consumption PLS1 Prediction of Fuel Consumption

Scores

-3

-2

-1

0

1

2

3

-4 -3 -2 -1 0 1 2 3 4

PC1

PC2

Samples Predicted vs. Measured

Slope: 0.95Offset: 0.02Correl: 0.98RMSEP: 0.23SEP: 0.24Bias: -0.005

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Measured Fuel

Pre

dic

ted

Fu

el

Weather conditionsX1, X2, X3, X4

PLS1Fuel Consumption Y

Cap’s setupX5, X6, X7

10.02.04 15

Passive OptimizationPassive Optimization

Weather conditions

Order!!! Prediction !Order!!!X5, X6, X7

Prediction !

Prediction ?

Fuck

Captain StudentComputer

4242

X1, X2, X3, X4X5, X6, X7

censored

10.02.04 16

Active OptimizationActive Optimization

Weather conditions

Advice!!!

Censored

Order?

CaptainStudent Computer

X1, X2, X3, X4

X5 X6, X7

Optimal

X5, X6, X7

42

10.02.04 17

In Hard Thinking about PC and PCsIn Hard Thinking about PC and PCs

Forty twocensored

10.02.04 18

Multivariate Statistical Process Multivariate Statistical Process Optimization (MSPO)Optimization (MSPO)

MSPO Objective

To optimize the performance of the process (product quality)

MSPO Methods

Projection methods and Simple Interval Calculation (SIC) method

MSPO Approach

To plot predicted quality at each process stage

MSPO Concept

To study historical data representing good past process behavior

10.02.04 19

Technological Scheme. Multistage Process Technological Scheme. Multistage Process

S1 S2 S3

M1 M2 M3 CM1 CM2 CM3

W1 W2 W3 CW1 CW2 CW3

WR1 WR2

MR1 MR2

S

W CW

M CM PA1 A2 A3 A4 A5 A6

S1 S2 S3

M1 M2 M3 CM1 CM2 CM3

W1 W2 W3 CW1 CW2 CW3

WR1 WR2

MR1 MR2

S

W CW

M CM PA1 A2 A3 A4 A5 A6

I6

II8

III11

IV14

V16

VI19

VII25

10.02.04 20

Historical Process DataHistorical Process Data

X preprocessing Y preprocessing

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

M1

M2

M3

MR

1

MR

2

CM

1

CM

2

CM

3

A1

A2

A3

A4

A5

A6 Y

Tra

inin

g

Se

t (1

02

)

Y

Tes

t S

et

(52

)

Y

XV XVI XVII

XI XII XIII XIV XV XVI XVII

XI XII XIII XIV

10.02.04 21

Quality Data (Standardized Y Set)Quality Data (Standardized Y Set)Training Set Samples

Lowest Quality Y=-1

Highest Quality Y=+1

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1 21 41 61 81 101

Y

Test Set Samples

Lowest Quality Y=-1

Highest Quality Y=+1

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1 11 21 31 41 51

Y

10.02.04 22

General PLS ModelGeneral PLS Model

0

0.1

0.2

0.3

PC_0 PC_2 PC_4 PC_6 PC_8

PCs

RMSE Calbration

Validation

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

M1

M2

M3

MR

1

MR

2

CM

1

CM

2

CM

3

A1

A2

A3

A4

A5

A6 Y

Y

YXTEST

XTRAINING

^

^PLS

6 PCs

10.02.04 23

SIC Prediction. All Test SamplesSIC Prediction. All Test SamplesSIC Prediction

1

2

3

4

5

6

7

8

9

1011

12 15

17

18

19

20

21

2223

25

26

27

28

29

30

3132

33

34

35

38

40

41

42

44

45

46

47

48

49

5051

13

16

24

43

36

52

3739

14

-1.0

-0.5

0.0

0.5

1.0

Test Samples

Y SIC PLS1 Test

Status plot

5251

50

49

48

4746

454443

42

41

40

393837

36

35

34

33 32

31 30

29

2827

26

25

24

23

22

21

20

19

18

17

16

1514

13 1211

10

9

8

7

6

5

4

3

21

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

Status plot

12

3

4

5

6

7

8

9

10

111213

1415

16

17

18

19

20

21

22

23

24

25

26

2728

29

3031

3233

3435

36

3738 39

40

41

42

43 4445

4647

48

49

50

5152

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

SIC Prediction

1

2

3

4

5

6

7

8

9

1011

12 15

17

18

19

20

21

2223

25

26

27

28

29

30

3132

33

34

35

38

40

41

42

44

45

46

47

48

49

5051

14

3937

52

36

43

24

16

13

-1.0

-0.5

0.0

0.5

1.0

Test Samples

Y SIC PLS1 Test

10.02.04 24

SIC Prediction. Selected Test SamplesSIC Prediction. Selected Test Samples

Sample No Quality status SIC Status

1 Normal Insider

2 High Outsider

3 Normal Absolute outsider

4 Low Outsider

5 Normal Insider

SIC Prediction

5

4

31

2

-1.0

-0.5

0.0

0.5

1.0

Selected Test Samples

YObject Status plot

1.01

2

34

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

Insiders

Outsiders

Outsiders

Ab

s. O

uts

ider

s

10.02.04 25

Passive Optimization in PracticePassive Optimization in Practice

Objective

To predict future process output being in the middle of the process

Method

Simple Interval Prediction

Approach

Expanding Multivariate Statistical Process Control (E-MSPC)

Concept

To study historical data representing good past process behaviour

10.02.04 26

Expanding MSPC, Sample 1Expanding MSPC, Sample 1S

1

S2

S3

W1

W2

W3 Y

Tra

inin

g

Se

t (1

02

)

Y

1 yxI XI

Sample 1, Normal Quality Insider

-1.0

-0.5

0.0

0.5

1.0 SIC PLS1

Y x1

S1

S2

S3

W1

W2

W3

WR

1

WR

2

Y

Tra

inin

g

Se

t (1

02

)

Y

1 yxI xII

XI XII Sample 1, Normal Quality Insider

-1.0

-0.5

0.0

0.5

1.0 SIC PLS1

Y x1

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

Y

Tra

inin

g

Se

t (1

02

)

Y

1 y

xI xII xIII

XI XII XIII


-1.0

-0.5

0.0

0.5

1.0 SIC PLS1

Y x1

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

M1

M2

M3 Y

Tra

inin

g

Se

t (1

02

)

Y

1 yxI xII xIII xIV XI XII XIII XIV


-1.0

-0.5

0.0

0.5

1.0 SIC PLS1

Y x1

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

M1

M2

M3

MR

1

MR

2

Y

Tra

inin

g

Se

t (1

02

)

Y

1 yxVxI xII xIII xIV

XVXI XII XIII XIV Sample 1, Normal Quality Insider

-1.0

-0.5

0.0

0.5

1.0 SIC PLS1

Y x1

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

M1

M2

M3

MR

1

MR

2

CM

1

CM

2

CM

3

Y

Tra

inin

g

Se

t (1

02

)

Y

1 yxV xVI xI xII xIII xIV

XV XVI XI XII XIII XIV


-1.0

-0.5

0.0

0.5

1.0 SIC PLS1

Y x1

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

M1

M2

M3

MR

1

MR

2

CM

1

CM

2

CM

3

A1

A2

A3

A4

A5

A6 Y

Tra

inin

g

Se

t (1

02

)

Y

1 y

XV XVI XVIIXI XII XIII XIV

xV xVI xVIIxI xII xIII xIV


-1.0

-0.5

0.0

0.5

1.0 SIC PLS1

Y x1

10.02.04 27

Expanding MSPC , Samples 2 & 3Expanding MSPC , Samples 2 & 3Sample 2, High Quality, Outsider

-1.0

-0.5

0.0

0.5

1.0

x2 SIC

PLS1 Y

Sample 3, Normal Quality, Absolute Outsider

-1.0

-0.5

0.0

0.5

1.0

x3 SIC

PLS1 Y

10.02.04 28

Expanding MSPC , Samples 4 & 5Expanding MSPC , Samples 4 & 5

Sample 4, Low Quality, Outsider

-1.0

-0.5

0.0

0.5

1.0 x4 SIC

PLS1 Y

Sample 5, Normal Quality, Insider

-1.0

-0.5

0.0

0.5

1.0x5 SIC

PLS1 Y

10.02.04 29

Active Optimization in PracticeActive Optimization in Practice

Objective

To find corrections for each process stage that improve the future process output (product quality)

Method

Simple Interval Prediction and Status Classification

Approach

Multivariate Statistical Process Optimization (MSPO)

Concept

Corrections are admissible if they are similar to ones that sometimes happened in the historical data in the similar situation

10.02.04 30

Linear Optimization Linear Optimization

Linear function always reaches extremum at the border.

So, the main problem of linear optimization is not to find a

solution, but to restrict the area, where this solution should

be found.

x

y=a*x

x

y=a*x

x

y=a*x

x

y=a*x

10.02.04 31

Optimization ProblemOptimization Problem

Weather conditionsX1, X2, X3, X4

PLS1Fuel Consumption Y

Cap’s setupX5, X6, X7

Fixed variables Xfix

PLS1 Quality measure Y

Optimized Xopt

Y = X*a = Y0 + Xopt*a2, where Y0 = Xfix*a1 = Const

Model

For given Xfix and a1 to find Xopt that maxi(mini)mizes Y

Task

max (Y) = Y0 + max (Xopt)*a2, as all a > 0 (by factor)

Solution

10.02.04 32

Interval Prediction of Interval Prediction of XXoptopt

Borders

1 2 3 4 5

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2


M1

S1

S2

S3

W1

W2

W3

WR

1

WR

2

CW

1

CW

2

CW

3

M1

M2

M3

X fix X opt

XIVXI XII XIII PLS2

PLS Prediction

54321

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2


M1 PLS±2*RMSEP

1 2 3 4 5

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2


M1 SIC Prediction

54321

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2


M1 SIC Prediction

5

4

3

21

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4


M1Xopt

10.02.04 33

Dubious Result of OptimizationDubious Result of Optimization

Optimized

III III IV V VI VII

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Y x4 Opt

x4 Test

Optimized

VIIVIVIVIIII II

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

SIC PLS

Y x4 Opt

x4 Test

Optimized

III III IV V VI VII

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

SIC PLS

Y x4 Opt

x4 Test Limits

Predicted Xopt variables are out of model!

10.02.04 34

Adjustment with SIC Object Status Adjustment with SIC Object Status Concept

Corrections are admissible if they are similar to ones that sometimes happened in the historical data in the similar situation.

Optimal variables Xopt should be within the model !

Object Status plot

Insiders

1

2

3

4

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

SIC Prediction

1 2 43 5

-0.4

-0.2

0.0

0.2

0.4


M1 Object Status plot

Insiders

1

2

3

4

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

SIC Prediction

1 2 43 5

-0.4

-0.2

0.0

0.2

0.4



Insiders

1

2

3

4

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

SIC Prediction

1 2 43 5

-0.4

-0.2

0.0

0.2

0.4



Insiders

1

2

3

4

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

SIC Prediction

1 2 43 5

-0.4

-0.2

0.0

0.2

0.4


M1

10.02.04 35

Sample 1 Normal Quality InsiderSample 1 Normal Quality InsiderOptimized

VIIVIVIVIIII II-1.0

-0.5

0.0

0.5

1.0 SIC PLS

Y x1

Test III III IV V VI VII-1.0

-0.5

0.0

0.5

1.0 SIC PLS

Y x1

Object Status plot

1.05

43

2

1

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

10.02.04 36

Sample 2 High Quality OutsiderSample 2 High Quality OutsiderOptimized

III III IV V VI VII-1.0

-0.5

0.0

0.5

1.0

SIC PLS

Y x2

Test VIIVIVIVIIII II-1.0

-0.5

0.0

0.5

1.0

SIC PLS

Y x2

Object Status plot

1.01

2

34

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

10.02.04 37

Sample 3 Normal Quality Abs. OutsiderSample 3 Normal Quality Abs. OutsiderOptimized


-0.5

0.0

0.5

1.0

SIC PLS

Y x3


-0.5

0.0

0.5

1.0

SIC PLS

Y x3

Object Status plot

1.01

2

34

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

10.02.04 38

Sample 4 Low Quality OutsiderSample 4 Low Quality OutsiderOptimized

III III IV V VI VII

-1.0

-0.5

0.0

0.5

1.0 SIC PLS

Y x4


-0.5

0.0

0.5

1.0 SIC PLS

Y x4

Object Status plot

1.05

43

2

1

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

10.02.04 39

Sample 5 Normal Quality InsiderSample 5 Normal Quality InsiderOptimized


-0.5

0.0

0.5

1.0 SIC PLS

Y x5


-0.5

0.0

0.5

1.0 SIC PLS

Y x5

Object Status plot

1.01

2

34

5

-1.0

-0.5

0.0

0.5

1.0

SIC-Leverage

SIC

-Re

sid

ua

l

10.02.04 40

Philosophy of MSPO. Food IndustryPhilosophy of MSPO. Food IndustryF

oo

d Q

ual

ity

Production Effectiveness

Restaurant qualityStandard (descriptive) control

Fast Food qualityISO-9000

Home-made qualityMSPO

Home-made qualityIntuitive (expert) control

10.02.04 41

ConclusionsConclusions

Thanks and ...

Bon Appetite!

Download - 10.02.04 1 Multivariate Statistical Process Control and Optimization Alexey Pomerantsev & Oxana Rodionova Semenov Institute of Chemical Physics Russian

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