Download presentation

Presentation is loading. Please wait.

Published byJosiah Aven Modified about 1 year ago

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

2
Agenda 1.Introduction 2.SPC 3.MSPC 4.Passive optimization (E-MSPC) 5.Active optimization (MSPO) 6.Conclusions

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

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

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 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

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

9
Low Dimensional Presentation

10
MSPC Charts (Chemical Reactor) SamplesKey Variables

11
Panel Process Control (not just a game)

12
Cruise Ship Control (by Kim Esbensen)

13
Key Process Variables

14
PLS1 Prediction of Fuel Consumption SamplesPredicted vs. Measured Weather conditions X1, X2, X3, X4 PLS1 Fuel Consumption Y Cap’s setup X5, X6, X7

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

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

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 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

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
SIC Prediction. Selected Test Samples Sample NoQuality statusSIC Status 1NormalInsider 2HighOutsider 3NormalAbsolute outsider 4LowOutsider 5NormalInsider Insiders Outsiders Abs. Outsiders

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

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) 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

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
Optimization Problem Weather conditions X1, X2, X3, X4 PLS1 Fuel Consumption Y Cap’s 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

32
Interval Prediction of X opt PLS2 X opt

33
Dubious Result of Optimization Predicted X opt 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 X opt 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
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

41
Conclusions Thanks and... Bon Appetite!

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google