University of Cagliari

Master Science in Chemical and Process Engineering

Statistical control of FTIR measurements in commercial detergents production

Supervisor:Ing. Massimiliano GROSSO

Co-supervisor: Student: Ing. Vincenzo GUIDA Alessandra TARIS

Scientific committee: in collaboration withProf. Ing. Roberto BARATTI

2011-2012

• potassium hydroxide

• surfactants (anionic, amphoteric, non ionic)

• Chelating agents

• sodium carbonate

• perfume

• ethanol

• Fatty acid

• polymers

• etc.

Aim: ensure standard quality in detergents

Focus on surfaces detergents

Complex formulations containing:

• ingredients mixing

• packaging

• quality control

Problems:

• Interpretation and manipulation of collected process variables may be difficult

• Online quality control is not always feasible

• Analytical techniques are slow (e.g. concentration measurements)

Steps in liquid detergents production:

Process deviations due to compositionvariations of detergent

FTIR spectroscopy: fast analytical technique, can be used online

Reproduction using a 142 samples set ofdetergentJoint variation of 11 experimentalconditions (compounds concentration)

Samples FTIR spectra

NPNN

P

P

PN

yyy

yyy

yyy

Y

21

22221

11211

N=142, P=1738Numero d'onda (cm-1)

Assorb

anza

Numero d'onda (cm-1)

Assorb

anza

Experimental campaign (P&G, Bruxelles)

142 spectra1738 absorbances for each spectrum

Samples FTIR spectra

Deviations reflect on spectra

Problem: How can weidentify samples differencesusing spectra analysis?

Thesis aims:

1. Development of methods for statistical control on experimentalmeasurements (spectra) using Multivariate StatisticalTechniques (to be implemented online in the future)

2. Detect compounds that significantly affect the spectra

Numero d'onda (cm-1)

Assorb

anza

PCA goals: data compression, informations extraction

Example: Bidimensional case-study (x1-x2 set)

Original variables Principal components (PC)

High dimensionsExtremely correlated

• PC1 greatest variance

• PC2 residual variance

• PC1 and PC2 indipendent (orthogonal)

fewerindipendent

x1

x2

x1

x2

x1

x2

PC1

PC2

Score1 (t1): projections on PC1 direction

Score2 (t2): projections on PC2 direction

Sscore1>>Sscore2PCA model : only one principal component (PC1)

Data coordinates in the newspace: scores (T)

Scores variance:

PC1

PC2

x1

x2

x1

x2

x1

x2

x1

x2

PC2

PC1

Hotelling T2

Measures distance from O′within PCA model

Q Statistic

Measures sample distance from PCA model

(that is from orthogonal projection on PC1 line)

Bidimensional case-study: 2 samples supposed to be out-of-control

Out-of-control samples identification using Q and T2 statistics

x1

x2

x1

x2

x1

x2

Low T2

High Q

High T2

Low Q

If T2 > T2lim or Q>Q lim Sample is out-of-control

O′

Q and T2 geometric interpretation

PTYJJJNJN

Y original experimental measurements

T scores matrix (new coordinates)

P loadings matrix (space rotation)

1) Components decomposition

2) PCA model

How many A principal components?

YY ˆ

N=142, J=1738

Multivariate data: N° variables >> 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2055

60

65

70

75

80

85

90

95

100

Numero componenti principali

Va

ria

nza

sp

ieg

ata

(%

)

Explained variance = 95%

1738Original variables (absorbances)

16Principal Components

16 components

Cumulative variance explained by principal components

Spectra can be well characterized using 16 PC

Synthetic chart, easy interpretation

Determination of the region (rectangular-shaped) in which in-controlsamples have to fall

T2 e Q limits(confidence level 95%)

T 2lim = 31.13 (MacGregor, 1995)

Qlim = 109.6 (Jackson, 1979)

False-positive samples

Joint region of multivariate gaussian distribution(limits more selective for outliers)

Ellipse

Determination of T2 e Q statistics foreach spectrum (Jackson, 1991)

0 10 20 30 40 50 60

40

60

80

100

120

140

160

180

T2

Q

Tlim

2

Qlim

Auto-validation

New definition of normal operating region

0 10 20 30 40 50 60

40

60

80

100

120

140

160

180

T2

Q

Tlim

2

Qlim

T2 T2

bx

3. Confidence ellipse equation:

1. Gaussian test for T2 and Q :

• Q approchable as gaussian

• T2 not gaussian

2. Non linear transformation

cost 212 )()( yyVxx

T2

bx

Q

T2

bx

Q

T2

bx

Q

New control region limits

Confidence limits:

• 95% e 99% (red)

• 100-th percentile (green)

T2

bx

Q

Statistical control simulation: identification out-of-control spectra

Load FTIR spectrum

Projection on PCA model(developed on training set)

Calculus T2bx and Q statistics

Statistical control using joint confidence region calculated on

training set

Joint confidence region

)()( XfYPTYXfT AAA

• Linear model

• Goal: Define relationship Y-X

• Significant variables choise

N=142 samplesM=11 experimental conditions (concentrations)A=16 scores (16 regressive models)

Stepwise Methods (Draper and Smith, 1998 )

Identification of variables that are most significant

perfumeNaCObuffer pHssurfactantsoda

surfactant ionicnonsoda

3

252423222122

121111

bbbbbat

bbat

• Models examples:

Influential variables :Sodium Hydroxide and surfactants

Non influential variables :Co-solvent (ethanol)

non ionic

surfactant

Sodium

hydroxideAnionic

surfactant

Amphoteric

surfactant

Sodium

Carbonate

• Qualitative compounds influence on spectra:

Qualitative relationship between experimental conditions (X) and scores (TA):

• Solvent does not influence spectra

• Spectra depend on soda, surfactants and sodium carbonate

Developments of general methods for statistical control:

• Spectra analysis and compression using PCA

• Variables reduction from 1738 to 16

• T2-Q control chart definition

• New different joint confidence region T2bx-Q

This work has been realized in cooperation with the

Procter & Gamble Research Centre in Pomezia (RM)