10.02.04 1 multivariate statistical process control and optimization alexey pomerantsev & oxana...

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10.02.04 1 Multivariate Statistical Multivariate Statistical Process Control and Process Control and Optimization Optimization Alexey Pomerantsev & Oxana Rodionova Semenov Institute of Chemical Physics Russian Chemometrics Society © Chris Marks

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10.02.04 1 Multivariate Statistical Process Control and Optimization Alexey Pomerantsev & Oxana Rodionova Semenov Institute of Chemical Physics Russian Chemometrics Society Chris Marks Slide 2 10.02.04 2 Agenda 1.Introduction 2.SPC 3.MSPC 4.Passive optimization (E-MSPC) 5.Active optimization (MSPO) 6.Conclusions Slide 3 10.02.04 3 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 Slide 4 10.02.04 4 Historical Process Data (Chemical Reactor) Production cycles s1, s2,...,s54 Key process variables (sensors) X1, X2,..., X17 Slide 5 10.02.04 5 Shewart Charts (1931) Slide 6 10.02.04 6 Panel Process Control (just a game) Slide 7 10.02.04 7 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 Slide 8 10.02.04 8 Projection Methods Initial Data Data Plane Data Center PCs Data Projections Slide 9 10.02.04 9 Low Dimensional Presentation Slide 10 10.02.04 10 MSPC Charts (Chemical Reactor) SamplesKey Variables Slide 11 10.02.04 11 Panel Process Control (not just a game) Slide 12 10.02.04 12 Cruise Ship Control (by Kim Esbensen) Slide 13 10.02.04 13 Key Process Variables Slide 14 10.02.04 14 PLS1 Prediction of Fuel Consumption SamplesPredicted vs. Measured Weather conditions X1, X2, X3, X4 PLS1 Fuel Consumption Y Caps setup X5, X6, X7 Slide 15 10.02.04 15 Passive Optimization Weather conditions Order!!! Prediction ! Order!!! X5, X6, X7 Prediction ! Prediction ? Fuck CaptainStudentComputer 42 X1, X2, X3, X4 X5, X6, X7 censored Slide 16 10.02.04 16 Active Optimization Weather conditions Advice!!! Censored Order? CaptainStudentComputer X1, X2, X3, X4 X5 X6, X7 Optimal X5, X6, X7 42 Slide 17 10.02.04 17 In Hard Thinking about PC and PCs Forty two censored Slide 18 10.02.04 18 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 Slide 19 10.02.04 19 Technological Scheme. Multistage Process Slide 20 10.02.04 20 Historical Process Data X preprocessing Y preprocessing Slide 21 10.02.04 21 Quality Data (Standardized Y Set) Slide 22 10.02.04 22 General PLS Model Slide 23 10.02.04 23 SIC Prediction. All Test Samples Slide 24 10.02.04 24 SIC Prediction. Selected Test Samples Sample NoQuality statusSIC Status 1NormalInsider 2HighOutsider 3NormalAbsolute outsider 4LowOutsider 5NormalInsider Insiders Outsiders Abs. Outsiders Slide 25 10.02.04 25 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 Slide 26 10.02.04 26 Expanding MSPC, Sample 1 Slide 27 10.02.04 27 Expanding MSPC, Samples 2 & 3 Slide 28 10.02.04 28 Expanding MSPC, Samples 4 & 5 Slide 29 10.02.04 29 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 Slide 30 10.02.04 30 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. Slide 31 10.02.04 31 Optimization Problem Weather conditions X1, X2, X3, X4 PLS1 Fuel Consumption Y Caps setup X5, X6, X7 Fixed variables X fix PLS1 Quality measure Y Optimized X opt Y = X*a = Y 0 + X opt *a 2, where Y 0 = X fix *a 1 = Const Model For given X fix and a 1 to find X opt that maxi(mini)mizes Y Task max (Y) = Y 0 + max (X opt )*a 2, as all a > 0 (by factor) Solution Slide 32 10.02.04 32 Interval Prediction of X opt PLS2 X opt Slide 33 10.02.04 33 Dubious Result of Optimization Predicted X opt variables are out of model! Slide 34 10.02.04 34 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 X opt should be within the model ! Slide 35 10.02.04 35 Sample 1 Normal Quality Insider Slide 36 10.02.04 36 Sample 2 High Quality Outsider Slide 37 10.02.04 37 Sample 3 Normal Quality Abs. Outsider Slide 38 10.02.04 38 Sample 4 Low Quality Outsider Slide 39 10.02.04 39 Sample 5 Normal Quality Insider Slide 40 10.02.04 40 Philosophy of MSPO. Food Industry Food Quality Production Effectiveness Restaurant quality Standard (descriptive) control Fast Food quality ISO-9000 Home-made quality MSPO Home-made quality Intuitive (expert) control Slide 41 10.02.04 41 Conclusions Thanks and... Bon Appetite!