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Multivariate Statistical Process Control and Optimization: 

Multivariate Statistical Process Control and Optimization Alexey Pomerantsev & Oxana Rodionova Semenov Institute of Chemical Physics Russian Chemometrics Society © Chris Marks

Agenda: 

Agenda Introduction SPC MSPC Passive optimization (E-MSPC) Active optimization (MSPO) Conclusions

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

Historical Process Data (Chemical Reactor): 

Historical Process Data (Chemical Reactor)

Shewart Charts (1931): 

Shewart Charts (1931)

Panel Process Control (just a game): 

Panel Process Control (just a game)

Multivariate Statistical Process Control (MSPC): 

Multivariate Statistical Process Control (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

Projection Methods: 

Projection Methods

Low Dimensional Presentation: 

Low Dimensional Presentation

MSPC Charts (Chemical Reactor): 

MSPC Charts (Chemical Reactor) Samples Key Variables

Panel Process Control (not just a game): 

Panel Process Control (not just a game)

Cruise Ship Control (by Kim Esbensen): 

Cruise Ship Control (by Kim Esbensen)

Key Process Variables: 

Key Process Variables

PLS1 Prediction of Fuel Consumption : 

PLS1 Prediction of Fuel Consumption Samples Predicted vs. Measured Weather conditions X1, X2, X3, X4

Passive Optimization: 

Passive Optimization Weather conditions Order!!! Prediction ! Order!!! X5, X6, X7 Prediction ! Prediction ? Fuck Captain Student Computer 42 42 X1, X2, X3, X4 X5, X6, X7 censored

Active Optimization: 

Active Optimization Weather conditions Advice!!! Censored Order? Captain Student Computer X1, X2, X3, X4 X5 X6, X7 Optimal X5, X6, X7 42

In Hard Thinking about PC and PCs: 

In Hard Thinking about PC and PCs Forty two censored

Multivariate Statistical Process Optimization (MSPO): 

Multivariate Statistical Process 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

Technological Scheme. Multistage Process : 

Technological Scheme. Multistage Process

Historical Process Data: 

Historical Process Data X preprocessing Y preprocessing

Quality Data (Standardized Y Set): 

Quality Data (Standardized Y Set)

General PLS Model: 

General PLS Model

SIC Prediction. All Test Samples: 

SIC Prediction. All Test Samples

SIC Prediction. Selected Test Samples: 

SIC Prediction. Selected Test Samples Insiders Abs. Outsiders

Passive Optimization in Practice: 

Passive 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

Expanding MSPC, Sample 1: 

Expanding MSPC, Sample 1

Expanding MSPC , Samples 2 & 3: 

Expanding MSPC , Samples 2 & 3

Expanding MSPC , Samples 4 & 5: 

Expanding MSPC , Samples 4 & 5

Active Optimization in Practice: 

Active 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

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.

Optimization Problem: 

Optimization Problem

Interval Prediction of Xopt: 

Interval Prediction of Xopt

Dubious Result of Optimization: 

Dubious Result of Optimization Predicted Xopt variables are out of model!

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 !

Sample 1 Normal Quality Insider: 

Sample 1 Normal Quality Insider

Sample 2 High Quality Outsider: 

Sample 2 High Quality Outsider

Sample 3 Normal Quality Abs. Outsider: 

Sample 3 Normal Quality Abs. Outsider

Sample 4 Low Quality Outsider: 

Sample 4 Low Quality Outsider

Sample 5 Normal Quality Insider: 

Sample 5 Normal Quality Insider

Philosophy of MSPO. Food Industry: 

Philosophy of MSPO. Food Industry

Conclusions: 

Conclusions Thanks and ... Bon Appetite!

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