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MVA/PLSWe will discuss some verybasic concepts, just so youcan get a generalunderstanding of theprocedure and then wewill illustrate the power ofthis tool for solving majortechnical problems.

MVA/PLSWhat is it???

MVA/PLSIt Stands for:Multivariate Analysis- Partial Least SquaresAlso known as:Multivariate Analysis - Projection to Latent StructuresThe 2nd title is moredescriptive of thetechnique

MVA/PLSBut whatdoes it do forme???

n2n3n4n5.MVA/PLSLike regression, it helps youdetermine the relationshipamong process variables, butunlike regression it allows you tohave more variables thanobservations. The variables inthe X matrix can be correlatedand you can predict a set ofresponse variables with only onemodel.

MVA/PLSBecause of these features itis ideal for examininghistorical data.Yes, this is the processanalysis tool that we havebeen waiting for.. lo thesemany years!!!Graphically it lookslike this ......

MVA/PLSn1n2n3n4n5..njX1 X2 X3 X4 X5 X6 X7 X8 ... XiX MatrixOf Raw DataPredictsn1n2n3n4n5..njy1 y2 y3 ...ymY MatrixOfResponsesWhere i can be >> jand can be in the 1000'sHmmm and I see that you canhave more than one Y

MVA/PLSSince you have moreterms than observations,wouldn't you always getan artificially perfectfit???

MVA/PLSI see why you might thinkthat but the answer is...Noand this is because of theway MVA/PLS representsdata. For example....

MVA/PLSObs. x1 x21 300 23x2Plot of x1 and x2Data are scaled.MVA/PLS represents thevalues for the variables x1and x2 as coordinates fora single observation inmultidimensional space.This is known asEuclidean space.x1

MVA/PLSObs x1 x2 x31 300 23 50x3 .x2x1And if there arethree variables x1,x2 and x3 they arealso the coordinatesfor just a singleobservation inEuclidean space

MVA/PLSIn general if there is oneobservation and 1000variables, it would be shownas only one point in 1000dimensional space. Eachobservation determines thenumber of points and thenumber of variablesdetermines the number ofdimensions in Euclideanspace.

MVA/PLSI get it. The number ofdata points in spacewon't increase as youadd variables to the dataset. All that wouldchange are the numberof coordinates used todefine the location ofthat observation inspace.

MVA/PLSThat's absolutelycorrect!!!

MVA/PLSThe following graphsillustrate the basicconcept of a projection ofa model into its latentstructure.

MVA/PLSThis is an exampleof projecting datadown to onecomponent. Thismeans that theshadow that isformed is aligned inone direction. Thisis called theprincipalcomponent becauseit is the first andstrongestcomponent.Original Data Setin MultidiminsionalSpace. .. .... ..... . . .... . .... .Projected Data Set.

.MVA/PLSThis exampleshows aprojection intoa twocomponentmodel. Afterthe projectionthe shadows ofthe data aresitting on a twodimensionalplane.... ... . . . . ........ .. . ... .

MVA/PLSIn MVA/PLS the model isbased on the number ofcomponents that was usedfor the final model and notthe number of variables. Soyou can see that diagnosticsof MVA/PLS models arealso very different fromRegression models.

MVA/PLSDoes MVA/PLS allowyou to developMultivariate ControlCharts??

MVA/PLSYes, it does !!

MVA/PLSWhat do youmean byMultivariateControlcharts???

MVA/PLSA multivariatecontrol chart is asingle control chartthat monitors manyvariables at thesame time.

MVA/PLSYou can plot a response variablesuch as Moisture and when theMoisture begins to drift out, youcan click on a point and a screenwill appear showing you whichvariables in the processcontributed to the change inMoisture. This will allow theoperator to take corrective actioneven before the reel is made.

MVA/PLSSounds Great!!! Buthow does it knowwhich variables arethe important ones??

MVA/PLSWe would first have todevelop a mathematicalmodel that would isolate thevariables that have a realimpact on the responsevariable or variables ofinterest using an MVA/PLSmodeling technique.

MVA/PLSThis mathematicalmodel is thenprogrammed into theMultivariate ControlChart routine that ishard wired into theprocess.

MVA/PLSWho would developthis mathematicalmodel and hardwirethis program intothe process???

MVA/PLSThe on-line programcan be purchasedthrough Umetrics, Inc.17 Birch Road, Kinnelon,NJ 07405Telephone 973 492-8355They also providetraining in thistechnique.

MVA/PLSThe following aresome of theprojects that weworked on usingMVA/PLS

MVA/PLSAndroscoggin Mill Slip WrinklesAndroscoggin MillIP FinanceSuccessful EmployeeGeorgetown MillDecorative ProductsMasonite, LaurelCoating Machine Scale Build UpIsolate The Attributes Of TheImprove Fluff Pulp Fiber QualityIsolate Factors Effecting Greenness VariationIsolate Factors Causing Wet Line VariabilityPrinting Papers Cost of Increasing Machine SpeedArizona Chemical Factors Effecting Solvent Load in the EffluentNatchez MillFactors Effecting Product Filterability

MVA/PLSNow I willdemonstrate the use ofthis method on a realproject.