Matrix Data Analysis

7/31/2019 Matrix Data Analysis

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Quality Circle Forum ofIndiapresents

- simplified NEW SEVENTOOLS& PRIORITIZATION ANYLYSIS


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MATRIX DATA ANALYSIS


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What is matrix Data Analysis?

Matrix Data Analysis is a multivariateanalysis technique called 'PrincipalComponent Analysis'. This techniquequantifies and arranges data presented in aMatrix Diagram, to find more generalindicators that would differentiate and giveclarity to large amount of complexly

intertwined information. This will help us tovisualise properly and get an insight into thesituations.


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We know problems aremany and of different

nature. Everycompany needs abattery of tools and

techniques in solvingproblems of cost,quality and

productivity. The oldseven tools of QualityControl are simple tounderstand and apply.

NEW SEVEN TOOLSSEVEN TOOLS


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As mentioned byDr.K.Ishikawa, seven

tools (old) can solvearound 95% of the work

related or shop floor

and managementrelated problems.


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What about the balance problems?They are normally more difficult chronic

problems. They call for experience and the needof understanding and analysing the verbal data.


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AFFINITY DIAGRAM

NEW SEVEN TOOLS

TREE DIAGRAM

PDPC

RELATIONS DIAGRAM

MATRIX DATA ANALYSIS

MATRIX DIAGRAM

NEW SEVEN TOOLS

This gave rise to development of new seven tools to beused by mostly management personnel. Among theseAffinity Diagram, Tree Diagram, Matrix Diagram, ArrowDiagram and Process Decision Programme Chart areessentially planning tools and useful in analysing and

processing verbal data.


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Still you find

certain problemspersist andapplication of these

tools cannot help tosolve them. As you

know many timeproblems areintertwined.


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What you try toapply as

remedialmeasure to onemay cause an

adverse effecton others.Often you do

not solve theentire problem.

Why am I not able toapply the same

solutions to all theproblems?


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Let us say in a factory they are operating amachine.

This machine over a period has worn outand is giving rise to variations in manyaspects.


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For example in a rubber factory they have processproblem in the calendering area (Calendering is aprocess of insulating the warp sheets with rubbercompound in rubber industry ). The rolls of thecalender were worn out and it had to be sent forregrooving.

When I said problems

with calender, I did

NOT mean this

CALENDAR!!!


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There is variation in the pressureapplied to the rolls and also the watercirculated inside the rolls for coolingis not to the required level due to

defective cooling system. Added tothat warp sheet received fromsupplier is baggy and slightly

damaged. Even the compound iscausing problem.


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1

2

34 SYNCHRONOUS

FABRIC


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Production needs to be carried out without any

major violation of quality norms.Under these circumstances, the production manafter analysing the various problem aspectsdecides on a course, which is best under thegiven circumstances. He may decide that a littlemore of rubber gauge is alright as it is onlyleading to excess consumption of rubber

compound (causing monetary loss), but ensuresthe warp Sheet is not crushed by the roll whichmay have adverse effect on quality.


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Often in process area when problemsare faced it calls for certaincompromise.


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They call for analysing the situations and

deciding on important parameters whichneed to be identified for effectivefunctioning.


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Such analysis calls for first pooling upand studying the accumulated data.


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In case of the above example we must have a

a) fresh look into the number of warp sheetrolls available,

b) number of compound batches available andthe variation in its properties (lab data),

c) how best the cooling water temperature canbe managed and

d) what will be the effect of variation in rollpressure when applied to the various typesof fabrics etc.


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All these information are more in number,complex and intertwined. We should knowhow to analyse these data to get a bestcombination under the given circumstances.


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Do we face suchsituations only inprocessingcondition?

No, not necessarily,we may face them

even in normal life.


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For example in our countrycoalition government has

become a way offunctioning. Under this,election becomesinevitable when the ruling

party loses the support.We have faced thissituation many time. Undersuch circumstances

normally question beforeus is to whom we shouldcast our vote.

V

OT

EFOR

V

OT

EFOR


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If we belong to a party our problem is simple.We vote to that party candidate. But most of ushave no party affiliation.


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Do we vote for Congress,BJP, United Front or an

independent? How do wedecide that? Is there anymethod available?


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Yes we can decide about it in asystematic way. First write down in apaper what are our expectations.


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We want poverty to be eradicated and abetter living condition


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better communication system


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favourable balance of trade,


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corruption free

government andthe list goes on..

Each one ofthem again can

be split intovarious aspects.


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In our fifty years of freedom we have also

acquired certain experiences about thevarious parties. Each party has certainplus points and many minus points. Wealso know none of them will be able tofulfill all our expectations. Not only that,they may do well in an area but in theprocess may cause further aggravation to

an existing problem.


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So we

shouldknow the

prioritiesand basedon that

choose theparty.

BJP

CONGRE

SS

UNITEDFRONT

INDEPENDENT


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From these twoexamples we

can noticesome problemscall for

processing oflarge amount ofnumerical data,

which arecomplex andintertwined.

(x-x)

(y

(x-x

)2

(y

-

y

)2

K-B-M=16

(A+B)e

xp2=Ae

xp2

+2AB+B

exp2

Y=mc

2

A+B+C=

P+Q

M-N+

u

KA

-B=16


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Matrix Data Analysis is a tool with whichwe can quantify and arrange these dataand using certain formula can get aclarity of the situation. Matrix DataAnalysis is a Multivariate Analysistechnique called Principal ComponentAnalysis. Unlike the other six tools

belonging to this group it uses numericaldata. Why was this selected?


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According to Mr.Yoshinobu Nayatani, who was amember of the group which identified these newseven tools "Every company needs a battery of

techniques for sorting out large quantities ofcomplex interrelated data and identifying andsolving problems. Such techniques are needed inaddition to the original seven Quality Control tools

and other statistical methods. There are twotypes of complex interrelationships: Those amongverbal data and those among numerical data. Webelieve it is now essential for companies to

acquire and use techniques for sorting out bothtypes. This is why Matrix Data analysis wasincluded in the Seven New Quality Control Toolswhen they were first proposed".


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a) Few years back in the railways

one steam engine repair shop whichwas employing more than 500people faced a problem.


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Since the steam engines were phasedout they had to close their workshop.What to do with the workmen?

W t k th


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They cannot be thrown out of the job. Thealternative available to them was transferringthese people to various places.

We cant sack them.

Transferring them is an easy

way out, John, but that will

not solve the problem.


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At that time the Chief Engineer of thatplace came out with an idea. He

suggested that why not convert thesteam engine repair shop as DieselEngine repair shop.


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But that would call for application of QualityFunction Deployment method. He discussed

it with all the workers and made them tounderstand that this idea was better as theyneed not leave from the place where theywere for more than twenty years.


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But allocation of new job would be based

on various parameters like age,experience, job knowledge, physicalcondition, educational qualification, etc.

You dont botherabout their present

position.

Advantagesoutweigh the egoproblem.


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Against the present job requirementthese aspects will be compared giving

due weightage to them.

You prepare the listshowing their age,

experience, physical

condition etc. andcompare it with the jobrequirement giving due

weightage


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He used the Matrix Data Analysis methodand the problem was resolved to the

satisfaction of everyone involved.


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b) Marketing of consumer productsof different variations based on theeconomic strata.


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A famous well established soap and detergent

manufacturer, lost a very good marketsegment, as they did not work out the market

strategy based on different economic strata of

the people

(ONE PRODUCT FOR ALL SEGMENT)

TURF

TURF


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Another manufacturer came out with adetergent which was slightly inferior inquality compared to the one marketed by theestablished organisation, but the price wasmuch less, suiting lower income group

SURMA!!!THE CHEAPEST

AND THE BESTDETERGENT AVAILABLE

IN THE MARKET.

ANYBODY CAN AFFORD

IT!!!!!


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This lured the low income group which is thehighest in the country and the new manufacturer

captured the market.

What the hell are you doing as themarketing head? You could not

inform me about Surma which has

been launched?


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A consumer product

marketing calls for collectingrelevant data about people of

different income, age,education, habit etc., Withthe help of Matrix Data

Analysis they can workoutthe market strategy.


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This is applicable to not only soap, butalso to other products like Television,Washing Machine, Refrigerator etc.


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c) Long back a fiction was written byEugene Burdick an American novelist

titled '480'. It is not PL 480. It is divisionof American population into 480 groups.


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Various parameters were chosenand they were applied to thepeople and they werecategorised into 480 groups.The aspects which wereattractive to each group wasidentified and a strategy wasworked out to lure them usingthat. The purpose was to showhow even the so calledintelligent people could befooled and made to choose whatthe manipulator had decided.


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In that book it was to makethe American Citizens to

elect a particular personas President of thecountry. Even thoughEugene Burdick did nottalk about 'Matrix DataAnalysis' the ideasuggested shows how

Matrix Data Analysis canbe used for this.(Politicians to note).

I knew I would win the

college elections this

year. I was equipped

with the knowledge ofMatrix Data Analysis


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There are many areas, situations

wherein the Matrix Data Analysis can beused effectively to achieve theobjective.

Can I use Matrix Data

Analysis to solve all

these problems???


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As can be seen, the MatrixDiagram arranges theinformation in a row-columnformat with the degree ofrelationship or correlationshown by symbols ornumerical values. When the

number of rows and columnsis large and numerical valuesof interrelationship areentered, it is almost

impossible to get a totalpicture of relative importanceof the sets of variables on theproblem at hand.

Oh!my God! Icant make head

or tail out ofit..


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Consider for example the

following tabulation of somefinancial indication of 30different companies.


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No FINANCIAL INDICATOR 1 2 ... 29 30

1. Net sales/Income from operations x1.1 x1.2 ... x1.29 x1.30

2. Other Income x2.1 x2.2 ... x2.29 x2.30

3. Total expenditure x3.1 x3.2 ... x3.29 x3.30

4. Interest x4.1 x4.2 ... x4.29 x4.30

5. Profit Before tax x5.1 x5.2 ... x5.29 x5.30

6. Depreciation x6.1 x6.2 ... x6.29 x6.30

7. Provision for tax x7.1 x7.2 ... x7.29 x7.30

8. Profit after tax x8.1 x8.2 ... x8.29 x8.30

9. Capital employed x9.1 x9.2 ... x9.29 x9.30

10. Resources x10.1 x10.2 ... x10.29 x10.30

11. Ratio of earning to dividends x11.1 x11.2 ... x11.29 x11.30

12. Ratio of total liabilities to net worth. x12.1 x12.2 ... x12.29 x12.30


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The data are represented by 'xij' i.e., theith indicator for the ith company. There

are thus 12 x 30 = 360 observations.

This volume of data makes it impossibleto obtain a clear over all picture of what

the data means. Our interest would be toidentify which indicators are best todifferentiate among the companies and

present in a chart which companies arein the stronger position and which are indanger.


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The 12 financial indictorsshown above were allselected as likely to affect

overall evaluation ofcompanies prosperity.


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However, a question arises as to whethershare holders or banks do really assessfrom so many dimensions.

S B IS B I

STOCK EXCHANGE


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Is it possible to narrow down to asuitable set of basic indicators?


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The answer is yes and the methodology is

called Multi Variate Analysis a well knownstatistical technique. It was developed longago and thus is not a new tool.


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Its application to quality improvementmakes it useful to quality control mangersand practitioners.


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One needs

knowledge of matrixalgebra as theanalysis of datarequires complexcalculations. Theparticular format ofthis analysis is the

principal componentanalysis.


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Computer packages are available to carry

out such analysis. It is not intended in thisbrief write up to explain as to how to carryout multi variate analysis.


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The basic analysis is to obtain

a correlation matrix. The

numerical value of strength of

relationship between two ormore variables is given by an

index called the CorrelationCoefficient.


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( x-x ) ( y-y )r =

( x-x )2 ( y-y )2

where = x = x and y =y and there are nindividuals.

n n

If x and y are the variables say height

and weight of individuals, then thecorrelation coefficient between heightand weight is given by


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How such a correlation matrixlooks can be seen by thefollowing published example in

the bookManagement forQuality Improvement: The NewSeven Tools,edited by ShigeruMizuno.


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The example is food preference amongmen and women in different age groupsfor 100 food types. Evaluation on a scale

1 to 9 (1 indicating higher preference and9 indicating the lower), is shown in thefollowing table:

Average preference of food product by men and women


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Average preference of food product by men and women

Group Product 1 Product 2 .....

Product 100Men

41 yrs 3.0 3.5 .....

2.5Women


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The correlation matrix

worked out for each groupwas as follows:


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Men Women

15 yrs 16-20 21-30 31-40 >41 15yrs 16-

20 21-30 31-40 >41

1 2 3 4 5

6 7 8 9 10

2 0.871

3 0.516 0.759

4 0.370 0.604 0.852

5 0.172 0.402 0.726 0.875

6 0.938 0.821 0.517 0.358 0.208

7 0.811 0.838 0.658 0.488 0.354 0.889

8 0.615 0.709 0.698 0.620 0.523 0.746 0.894

9 0.500 0.647 0.701 0.721 0.710 0.621 0.768

0.852

10 0.330 0.457 0.558 0.632 0.748 0.493 0.642

0.773 0.911


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The above table shows how to reducethe original 100 x 10 observations for

10 groups into a compact tableshowing the interrelationships.


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Further analysis is carried out by Principal

Component Analysis wherein, the totalvariation in the data is usually explained byone or two principal components. (Principalcomponent is basically a data transformation

used to make interrelated original variablesinto a plane/space that can be independentlystudied). The first two principal componentscan be graphically represented on a xy planeand the influence of the different variables andthe relation can be studied.


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Examples

No detailed examples of the use of MatrixData Analysis are given here. Use ofthese technique to such problems as

forecasting fashion cycle, Desired carstyles and Control of wrinkles in themanufacture of pressed products etc.,

are reported in literature.


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Summary

Matrix Data Analysis or PrincipalComponent Analysis is a very usefulmethod in all service and processindustries where complexity of theproblems are order of the day. Withthe availability of ready to usecomputer soft wares, it should not

pose as a problem to the organisationsto make use of this method.

Documents

Matrix Data Analysis