Statistical tools for multivariate six sigma
Download
1 / 66

Statistical Tools for Multivariate Six Sigma - PowerPoint PPT Presentation


  • 198 Views
  • Updated On :

Statistical Tools for Multivariate Six Sigma. Dr. Neil W. Polhemus CTO & Director of Development StatPoint, Inc. The Challenge. The quality of an item or service usually depends on more than one characteristic.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Statistical Tools for Multivariate Six Sigma' - lark


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Statistical tools for multivariate six sigma l.jpg

Statistical Tools for Multivariate Six Sigma

Dr. Neil W. Polhemus

CTO & Director of Development

StatPoint, Inc.


The challenge l.jpg
The Challenge

The quality of an item or service usually depends on more than one characteristic.

When the characteristics are not independent, considering each characteristic separately can give a misleading estimate of overall performance.


The solution l.jpg
The Solution

Proper analysis of data from such processes requires the use of multivariate statistical techniques.


Outline l.jpg
Outline

  • Multivariate SPC

    • Multivariate control charts

    • Multivariate capability analysis

  • Data exploration and modeling

    • Principal components analysis (PCA)

    • Partial least squares (PLS)

    • Neural network classifiers

  • Design of experiments (DOE)

    • Multivariate optimization


Example 1 l.jpg
Example #1

Textile fiber

Characteristic #1: tensile strength - 115 ± 1

Characteristic #2: diameter - 1.05 ± 0.05


Sample data l.jpg
Sample Data

n = 100









Multivariate capability l.jpg
Multivariate Capability

Determines joint probability of being within the specification limits on all characteristics




Mult capability indices l.jpg
Mult. Capability Indices

Defined to give the

same DPM as in the

univariate case.



More than 2 characteristics l.jpg
More than 2 Characteristics

Calculate T-squared:

where

S = sample covariance matrix

= vector of sample means



T squared decomposition l.jpg
T-Squared Decomposition

Subtracts the value of T-squared if each variable is removed.

Large values indicate that a variable has an important contribution.




Generalized variance chart l.jpg
Generalized Variance Chart

Plots the determinant of the variance-covariance matrix for data that is sampled in subgroups.


Data exploration and modeling l.jpg
Data Exploration and Modeling

When the number of variables is large, the dimensionality of the problem often makes it difficult to determine the underlying relationships.

Reduction of dimensionality can be very helpful.




Analysis methods l.jpg
Analysis Methods

  • Predicting certain characteristics based on others (regression and ANOVA)

  • Separating items into groups (classification)

  • Detecting unusual items



Principal components l.jpg
Principal Components

The goal of a principal components analysis (PCA) is to construct k linear combinations of the p variables X that contain the greatest variance.


Scree plot l.jpg
Scree Plot

Shows the number of significant components.






Partial least squares pls l.jpg
Partial Least Squares (PLS)

Similar to PCA, except that it finds components that minimize the variance in both the X’s and the Y’s.

May be used with many X variables, even exceeding n.


Component extraction l.jpg
Component Extraction

Starts with number of components equal to the minimum of p and (n-1).




Classification l.jpg
Classification

Principal components can also be used to classify new observations.

A useful method for classification is a Bayesian classifier, which can be expressed as a neural network.




Bayesian classifier l.jpg
Bayesian Classifier

  • Begins with prior probabilities for membership in each group

  • Uses a Parzen-like density estimator of the density function for each group


Options l.jpg
Options

  • The prior probabilities may be determined in several ways.

  • A training set is usually used to find a good value for s.








Design of experiments l.jpg
Design of Experiments

When more than one characteristic is important, finding the optimal operating conditions usually requires a tradeoff of one characteristic for another.

One approach to finding a single solution is to use desirability functions.


Example 3 l.jpg
Example #3

Myers and Montgomery (2002) describe an experiment on a chemical process:









Combined desirability l.jpg
Combined Desirability

where m = # of factors and 0 ≤ Ij ≤ 5. D ranges from 0 to 1.






References l.jpg
References

  • Johnson, R.A. and Wichern, D.W. (2002). Applied Multivariate Statistical Analysis. Upper Saddle River: Prentice Hall.Mason, R.L. and Young, J.C. (2002).

  • Mason and Young (2002). Multivariate Statistical Process Control with Industrial Applications. Philadelphia: SIAM.

  • Montgomery, D. C. (2005). Introduction to Statistical Quality Control, 5th edition. New York: John Wiley and Sons.

  • Myers, R. H. and Montgomery, D. C. (2002). Response Surface Methodology: Process and Product optimization Using Designed Experiments, 2nd edition. New York: John Wiley and Sons.


Powerpoint slides l.jpg
PowerPoint Slides

Available at:

www.statgraphics.com/documents.htm