1 / 41

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

fraley
Download Presentation

Multivariate Statistical Process Control and Optimization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

  3. Statistical Process Control (SPC) SPC Objective To monitor the performance of the process SPC Concept To study historical data representing good past process behaviour SPC Method Conventional statistical methods SPC Approach To plot univariate chart in order to monitor key process variables

  4. Production cycles s1, s2, ... ,s54 Key process variables (sensors) X1, X2, ... , X17 … … Historical Process Data (Chemical Reactor)

  5. Shewart Charts (1931)

  6. Panel Process Control (just a game)

  7. Multivariate Statistical Process Control (MSPC) MSPC Objective To monitor the performance of the process MSPC Concept To study historical data representing good past process behavior MSPC Method Projection methods of Multivariate Data Analysis (PCA, PCR, PLS) MSPC Approach To plot multivariate score plots to monitor the process behavior

  8. Projection Methods Initial Data Data Plane Data Center PCs Data Projections

  9. Low Dimensional Presentation

  10. MSPC Charts (Chemical Reactor) Samples Key Variables

  11. Panel Process Control (not just a game)

  12. Cruise Ship Control (by Kim Esbensen)

  13. Key Process Variables

  14. Cap’s setupX5, X6, X7 Fuel Consumption Y PLS1 PLS1 Prediction of Fuel Consumption Samples Predicted vs. Measured Weather conditionsX1, X2, X3, X4

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

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

  17. In Hard Thinking about PC and PCs Forty two censored

  18. Multivariate Statistical Process Optimization (MSPO) MSPO Objective To optimize the performance of the process (product quality) MSPO Concept To study historical data representing good past process behavior MSPO Methods Projection methods and Simple Interval Calculation (SIC) method MSPO Approach To plot predicted quality at each process stage

  19. Technological Scheme. Multistage Process

  20. Historical Process Data X preprocessing Y preprocessing

  21. Quality Data (Standardized Y Set)

  22. General PLS Model

  23. SIC Prediction. All Test Samples

  24. Outsiders Outsiders SIC Prediction. Selected Test Samples Abs. Outsiders Insiders

  25. Passive Optimization in Practice Objective To predict future process output being in the middle of the process Concept To study historical data representing good past process behaviour Method Simple Interval Prediction Approach Expanding Multivariate Statistical Process Control (E-MSPC)

  26. Expanding MSPC, Sample 1

  27. Expanding MSPC , Samples 2 & 3

  28. Expanding MSPC , Samples 4 & 5

  29. Active Optimization in Practice Objective To find corrections for each process stage that improve the future process output (product quality) Concept Corrections are admissible if they are similar to ones that sometimes happened in the historical data in the similar situation Method Simple Interval Prediction and Status Classification Approach Multivariate Statistical Process Optimization (MSPO)

  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.

  31. Fixed variablesXfix Model Y=X*a=Y0 + Xopt*a2, where Y0 = Xfix*a1 = Const Task For given Xfix and a1 to find Xopt that maxi(mini)mizes Y Solution max (Y) = Y0 + max (Xopt)*a2, as all a> 0 (by g factor) Weather conditionsX1, X2, X3, X4 Cap’s setupX5, X6, X7 Optimized Xopt Fuel ConsumptionY Quality measureY PLS1 PLS1 Optimization Problem

  32. PLS2 Xopt Interval Prediction of Xopt

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

  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 Xopt should be within the model !

  35. Sample 1 Normal Quality Insider

  36. Sample 2 High Quality Outsider

  37. Sample 3 Normal Quality Abs. Outsider

  38. Sample 4 Low Quality Outsider

  39. Sample 5 Normal Quality Insider

  40. Home-made qualityIntuitive (expert) control Home-made qualityMSPO Food Quality Restaurant qualityStandard (descriptive) control Fast Food qualityISO-9000 Production Effectiveness Philosophy of MSPO. Food Industry

  41. Conclusions Thanks and ... Bon Appetite!

More Related