RESEARCH AND CONCEPTS

Graph theory and matrixapproach for performanceevaluation of TQM in Indian

industriesSushma Kulkarni

Rajarambapu Institute of Technology, Sangli, Maharashtra, India

Abstract

Purpose – Once the decision is taken to implement total quality management (TQM) in anyorganization, achieving TQM is a journey. It takes significant effort over an extended period of time.Seeks to propose a TQM performance index.

Design/methodology/approach – An industry TQM performance index evaluates and ranks thevarious industries practicing TQM for a given period of time. Uses graph theory and a matrixapproach.

Findings – The index is obtained from industry performance function, which is useful foridentification and comparison of the different industries for their TQM performance. If the TQMevaluation is done correctly, the evaluation will present the profile of the organization to differentaudience, i.e. the customers, governments, other industries, funding agencies and public.

Originality/value – The model suggested for evaluation presents a logical approach to rank theindustries and other organization practicing TQM or other quality program.

Keywords Project evaluation, Total quality management, Graph theory

Paper type Research paper

IntroductionTotal quality management (TQM) is an all encompassing dynamic process in anorganization to promote never ending improvement in the effectiveness and efficiencyof all elements of a business (Hradesky, 1995). TQM is the integration of functions andprocesses within an organization in order to achieve continuous improvement of thequality of goods and services. The goal is customer satisfaction (CS) (Ross, 1996). Acompany’s continued success requires repeat business, which in turn depends upon thecustomers. A strong customer focus is therefore imperative. TQM is a means to thisend, and an attribute of good management. TQM is essentially customer driven. Ittakes a total system view. TQM measures are not merely confined to traditional rejects,reworks, down grades and the like. They also include global, balance sheet parameterssuch as profits, stock in trade, market share, etc.

The approach touches every operation, every individual and every activity. Each isa link with the ultimate purpose to provide durable satisfaction to the existing andpotential customers. The concept of TQM hinges on continuous, improvement as thecore mission of the upper management. Zero defect or non-conformance is theoperational objective of an organization. It is not a static restrictive concept. In itspolicy perspective and specification, the top management forges harmony between

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The TQM MagazineVol. 17 No. 6, 2005

pp. 509-526q Emerald Group Publishing Limited

0954-478XDOI 10.1108/09544780510627615

zero defects as the operational, objective and continuous improvements as thedynamics pursuit of the management (Bounds et al., 1994).

Some common principles that run through TQM interpretations (Dale and Cooper,1997):

. Every one in the organization is involved continuously improving the processunder his or her control and takes responsibility for his or her own qualityassurance.

. Each person is committed to satisfying his or her customer (internal or external).

. Team work is practiced in a number of forms. There is a commitment to thedevelopment of employees through involvement.

. Participation by everyone in the business is positively encouraged and practiced.

. A formal program of education and training is in place and this is viewed as aninvestment in developing people’s ability and knowledge and helping themrealize their potentials.

. Suppliers and customers are integrated into the improvement process.

. Honesty, sincerity, and care are integral part of daily business life and simplicityin process, systems, procedures and work instructions are pursued.

Graph theory and matrix approachOnce the decision is taken to implement TQM in any organization, achieving TQM is ajourney (Juran Institute, 1992). It takes significant effort over an extended period oftime. The journey can be divided into five phases as per Dr Juran namely decide,prepare, start, expand, integrate with a sixth phase as evaluation which will indicate asto how effective the implementation is as compared to other organizations practicingTQM. The model suggested for evaluation presents a logical approach to rank theindustries (other organization practicing TQM or other quality up gradation program)using graph theory and matrix approach. Industry TQM performance index (ITQMpi)is proposed which evaluates and ranks the various industries practicing TQM for agiven period of time. The index is obtained from industry performance function (IPF),which is useful for identification and comparison of the different industries for theirTQM performance.

If the TQM evaluation is done correctly, the evaluation will present the profile of theorganization to different audience, i.e. the customers, governments, other industries,funding agencies and public. The purpose served is given below.

. Customer – choice of best product from market and worth for money.

. Government – accountability, funding, policy and planning, national growthand development.

. Society – accountability.

. Funding agency – funding R & D, expansion projects, new projects feasibility,etc.

. Industry – for comparison in the competitive market.

Presently, bodies responsible for industrial development, quality control, etc. in Indialike CII, QCFI, TPM, etc. have already started propagating TQM and its benefits by

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conducting various training programs and various awards are also instituted atnational and international level to propagate and inculcate quality culture in Indianorganization. There is Malcom Balridge Award, European Quality Award, JapaneseQuality Award (Deming prize) at international level, Indian Juran Award, Dr ShahTrust Award, etc. at national level.

But their evaluation procedure for award is elaborate, and still it is felt that there is aneed for simple and effective evaluation procedures. When TQM is implemented in anyorganization, to evaluate its performance it is a total effect of large number ofparameter on each other as well as on the TQM performance. Thus theinterrelationship between the attributes (parameter) according to the importance ofone attribute over the other needs to be studied along with the independent effect ofeach parameter on TQM performance evaluation. Thus, efforts need to be extended todetermine factors which influence an industry’s performance based on TQM practice inthat particular organization for a particular period, using a logical approach toappraise the organization of their standing in the national and international scenariofor improvement or sustaining the performance according to the performance of TQMprocess evaluated.

Graph theory is a logical and system approach (Narsingh, 2001). The advancedtheory of graph and its application are very well documented. Graph theory is a verynatural and powerful tool in combinatorial operation research, transport network,activity of stochastic process useful for modeling representation proved to be useful formodeling and analyzing various kinds of system in many fields of science andengineering. A graph G ¼ ðV ;EÞ consists of a set of objects V ¼ {v1; v2; . . .} calledvertices, and another set E ¼ {e1; e2; . . .}; whose elements are called edges, such thatedge ek is identified with an unordered pair (vi, vj) of vertices. The vertices vi, vjassociated with edge ek are called end vertices of ek. The most common representationof a graph is by means of a diagram, in which the vertices are represented as points andeach edge as a line segment joining its end vertices. Often this diagram itself is referredto as graph. The object shown in Figure 1, e.g. is a graph. Matrix approach useful inanalyzing the graph models expeditiously is applied to derive useful system functionand system index to meet the objectives. The representations of graphs by matricesoffer case in computer handling. In view of their advantages, graph theory andmatrix approach is proposed for the evaluation and comparison of TQM in anorganization.

TQM performance evaluation attributesFor the purpose of evaluation of TQM in an organization which is a set of processimplemented at all stages right from input to the final output going out from the

Figure 1.Graph with five vertices

and six edges

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system. Let us consider an industry as a system; the system input, process and outputvariables for implementation of TQM is top management, infrastructure employeeempowerment (EE), supplier involvement (SI), strategic planning (SP) for TQMvision/mission and goals, measurement and analysis of products and processes,evaluation of cost of poor quality, quality culture, benchmarking and CS, etc. Theperformance attribute can be defined as the system variable, input, output or theprocess variable.

TQM evaluation attributes digraphTQM evaluation attributes digraph is defined, which models the importance orpresence of attributes and their interrelationship for a given organization. TrackingTQM can be tough. As one rolls out total quality initiative, one must continuouslymonitor it on every front to ensure that the process is delivering the right results.Concentrate on planning for quality but ignore infrastructure (IN) and the TQMinitiative will collapse. Allocate resources but forget to communicate with employeesand one will have a well budgeted, but utterly ineffective TQM exercise. May bethis is the reason that over 70 percent of the TQM initiatives in the worldeventually fail. To ensure that your TQM implementation is really working,measure it not just in overall terms, but in each area covered by the TQM processalong with the importance of each parameter (attribute) over the other with allattributes considered at a time.

A digraph (also called directed graph) G consists of a set of vertices V ¼{v1; v2; . . .}; a set of edges E ¼ {e1; e2; . . .} and a mapping function that maps everyedge onto some ordered pair of vertices (vi, vj). As in the case of undirected graphs,a vertex is represented by a point and an edge by a line segment between vi and vjwith an arrow from vi to vj. In Figure 2, an edge for which the initial and terminalvertices are the same forms the self loop, such as e7 and for edge e4, v3 is initialvertex from where the edge is incident out and v4 is terminal vertex where the edgeis incident into.

Thus, TQM evaluation attribute diagraph consists of a set of nodes. E ¼ {ei};with i ¼ 1; 2; . . . ;M and a set of edges, r ¼ {rij}: A node Ei represents ith TQMperformance attribute (i.e. A i) and the edges represent the interrelationship amongthe attributes. The number of nodes, M is equal to the number of TQM performanceevaluation attributes node j in the selection, then a directed edge or arrow is drawnfrom node i to node j (i.e. rij). If j is having relative importance over i, then directededge or arrow is drawn from node j to node i (i.e. rij), e.g. for two nodes e1 and e2

the graph can be represented as follows as shown in Figure 3 with r12

indicating relative importance of e1 over e2 and r21 indicating relative importance ofe2 over e1.

Figure 2.Diagraph with fivevertices and seven edges

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To demonstrate the TQM evaluation attributes diagraph, an example of TQMevaluation for a particular organization is considered. Suppose the most importantattributes for TQM evaluation are:

. infrastructure (IN);

. top management support (TMS);

. strategic planning (SP);

. employee empowerment (EE); and

. customer satisfaction (CS).

TMS is more important for TQM performance as compared to IN, however, IN is alsoimportant in TQM performance, even though less important than the TMS. Thus, thereexists relative importance between these attributes in both directions. Similarly, theattributes, EE and CS are equally important for the success of TQM in anyorganization. Thus, the interrelations can be represented among the other attributes. ATQM performance evaluation attribute diagraph is developed based on the above andis shown in Figure 3. The five nodes represent the five selected attributes and the edgestheir relative importance.

TQM performance evaluation attributes diagraph gives a graphical representationof the attributes and their relative importance for quick visual appraisal. As thenumber of nodes and their interrelations increases, the digraph becomes complex. Insuch a case the visual analysis of the diagraph is expected to be difficult and complex.To overcome this constraint, the diagraph is represented in matrix form as shown in(1), where E1; . . . ;E5 are nodes showing attributes. r12; r13; r14; . . . ; r51 are edgesshowing relative importance of attributes over each other.

Matrix representationMatrix representation of TQM evaluation attributes diagraph gives its one to onerepresentation. A matrix called the TQM performance attributes matrix (TQMpam) isdefined. This is M £ M matrix and considers the presence of attributes (i.e. Ei) andtheir relative importance (i.e. rij). This matrix A1 for TQM performance attributesdiagraph Figure 3 is represented as:

A ¼

Attributes IN TMS SP EE CS

IN Ei r12 r13 r14 r15

TMS r21 E2 r23 r24 r25

SP r31 r32 E3 r34 r35

EE r41 r42 r43 E4 r45

CS r51 r52 r53 r54 E5

ð1Þ

Figure 3.Relative importance

between edge and node

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Where, Ei is the value of its attribute (A 1) represented by node and Ei and rij is therelative importance of ith attribute over jth represented by the edge rij. Permanent ofthis matrix A, i.e. per (A), is defined as TQM performance evaluation function.Permanent is a standard matrix function and is used in combination mathematics(Venkate Rao, 2000).

TQM performance evaluation function for matrix expression (1) is written as perJurkat and Ryser (1966) formula as:

PerðAÞ ¼Y5

i¼1

Ei þ SiSjSkSlSmðrijrjiÞEkElEm þ EiEjEkElEmðrijrjkrki

þ rikrkjrjiÞElEm

{SiSjSkSlSmðrijrjiÞðrklrlkÞEm þ SSSSSðrijrjkrklrli þ rilrikrkjrjiÞEm}

þ {SiSjSkSlSmðrijrjiÞðrklrlmrmk þ rkmrmlrlkÞ

þ SiSjSkSlSmðrijrjkrklrlmrmi þ rimrmlrlkrkjrjiÞ}

ð2Þ

Expression (2) is a complete expression as it considers attributes presence and at thepossible relative importance among attributes. The term is the sets of distinct diagonalelements (i.e. Ei’s) and loops of off diagonal elements of different size (i.e. rijrji, rijrjkrkl,etc.).

In general, if there are M number of TQM performance evaluation attribute for agiven organization and the interrelationship exist among all the TQMpea, there theTQM performance evaluation attributes matrix B for the considered TQMperformance evaluation attribute digraph is written as expression (3):

B ¼

Attribute 1 2 3 · · · M

1 E1 r12 r13 · · · r1M

2 r21 E2 r23 · · · r2M

3 r31 r32 E3 · · · r3M

..

. ... ..

. ...

· · · ...

..

. ... ..

. ...

· · · ...

M rM1 rM2 rM3 · · · EM

ð3Þ

TQMP attribute functions for this matrix, B contains (M1) number of terms. In sigmaform, the TQM performance evaluation function is written as expression (4). Thisexpression contains (M þ 1) groupings.

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PerðBÞ ¼YM

a¼1

þ SiSjSk· · ·SmðrijÞElEk· · ·Em þ SSS· · ·SðrijrjiÞEkEl · · ·Em

þ SiSjSk· · ·Smðrijrjkrkl þ rikrkjrjiÞElEm· · ·EM

þ{SiSjSk· · ·SM ðrijrjiÞðrklrlkÞEmEn· · ·EM þ ½SiSjSk· · ·SM ðrijrjkrklrli

þ rilrlkrkirjiÞEmEn· · ·EM �}

þ {½SiSjSk· · ·SM ðrijrjiÞðrklrlmrmk þ rkmrmlrlkÞEnEo. . .EM �

þ ½SiSjSk· · ·SM ðrijrjkrklrlmrmi þ rimrmlrlkrkjrjiÞEnEo. . .EM �}

ð4Þ

Expression (4) is a TQM performance evaluation function that ensures a realistic TQMperformance evaluation in terms of evaluation attributes. The expression containsterms arranged in (M þ 1) groupings. The first grouping contains only one term and isa set of presence of M attributes. The second grouping, is absent as there are noself-loops in the digraph. The terms of the third grouping represent a set of twoattribute relative importance loops (i.e. rijrji) and is the resultant causality of attributei and j, and the severity of remaining ðM 2 2Þ attributes. Each term of the fourthgrouping is a set of three event relative importance loops (i.e. rijrjkrki or its pair rikrkjrji)and the severity of remaining ðM 2 3Þ attributes. The terms of the fifth grouping arearranged in two subgroupings, each term of the first subgrouping is a set of two2-attribute relative importance loops [(i.e. rijrji) and (rklrlk)] and the severity of ðM 2 4Þattributes. Each term of the second subgrouping is a set of 4-attributes relativeimportance loop [(i.e. rijrjkrkirli) or its pair rilrlkrkirji)] and the severity of ðM 2 4Þattributes. Similarly other terms of the expression are defined. Thus, the TQMperformance evaluation function characterizes an organization for its performanceevaluation as it contains all possible structural components of the attributes and theirrelative importance.

TQM performance evaluation index (TQMpei)TQMpei is a measure of the performance of an organization for its TQM processes. Ahigher value of the index means better performance. The TQM performance evaluationfunction defined above, i.e. expression (4) is appropriate for evaluation of the TQMpei asit contains presence of their attributes and their relative importance. The numericalvalue of the TQMpef (TQM performance evaluation function) is called the TQMpei. Asthe TQMpef contains only the positive terms, therefore higher values of Ei’s and rij’swill result in increased value of the TQMpei. To calculate the TQMpei the requiredinformation is the values of Ei’s and rij’s.

The value of Ei’s should be obtained from the data provided by the organizationpracticing TQM on the prescribed attributes evaluation from the ith attribute and suchquantitative value is then converted into a ranked value judgment on a scale, e.g. 0-10may be adopted. Table I is suggested which represents the TQMpea on a qualitativescale. It is seen that some of the attributes were not easy to measure in terms ofqualitative scale hence a questionnaire has been designed to measure each attribute interms of weightage (questionnaire enclosed in appendix). Each attribute has been

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measured in terms of eight subquestions each having a specified weightage. Thesequantitative weightage are then required to normalize the quantitative value of the Ei

on the same scale as the qualitative value, i.e. 0-10. If E1 has range Eii and Eiu. The otherintermediate value Eii of the TQMpea is assigned the value in between 0 and 10 as perthe following:

Ei ¼ {10=Eiu}Eii for Eii ¼ 0

¼ {10=ðEiu 2 EilÞ}ðEii 2 EilÞÞ for Eil . 0ð5Þ

Expression (5) is applicable for general beneficial attributes only, e.g. CS means, itshigher attribute values are more desirable for the given TQM performance evaluationfor a particular organization, whereas, non-beneficial attributes, e.g. decrease in marketshare is the one, whose lower attribute values are desirable. Therefore, in case of nonbeneficial TQMpea, the attribute value 0 (zero) on scale 0-10, is assigned to the highestrange value (Eiu) and value if 10 is assigned to the lower range value (Eii). The otherintermediate value (Eii) of the TQMpea is assigned the values in between 0 and 10 as perthe following.

Ei ¼ 10{1 2 ðEii=EiuÞ} for Ei ¼ 0

¼ 10{10=ðEiu=EiiÞ}ðEiu 2 EiiÞ for Ei . 0ð6Þ

The relative importance between two attributes (i.e. rij) is also assigned value on thescale 0-10. The relative importance rij implies that an attribute i is compared withanother attribute j in terms of relative importance for the given organization. Therelative importance between i, j and j, i is distributed on the scale 0-10 and is defined as

rji ¼ S 2 rij ð7Þ

It means that a scale is adopted (0 to S) on which the relative importance values arecompared. If rij represents the relative importance of ith attribute over jth attribute,then the relative importance of the jth attribute over ith attribute is evaluated using

Qualitative measure of TQM performanceevaluation attribute

Attribute value of TQM performanceevaluation (Ei)

Exceptionally low 0Extremely low 1Very low 2Below average 3Average 4Above average 5High 6Very high 7Most high 8Extremely high 9Exceptionally high 10

Table I.Value of TQMperformance evaluationattributes (Ei’s)

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expression (7). For example, if the jth attribute is slightly more important than ithattribute then rji ¼ 6 and rij ¼ 4. Table II is suggested which aids in assigning rijvalues based on the above.

The TQMpei value for each organization evaluated using expression (4) andsubstituting the values of Ei’s and rij’s. The organizations can be arranged in thedescending or ascending order of TQMpei, to rank them for their performance. Theorganization, for which the values of TQMpei are highest, is the best TQM performancestandard organization. However, the final decision may depend on factors likepersonnel interview of CEO, employees and some of the direct customers’ etc. and otherconstrains. But TQMpei can surely guide and help to select the best standards of TQMtoday.

MethodologyA methodology for the selection of best TQM performing organization is suggestedbased on digraph and matrix method. The main steps of the methodology are:

(1) Identify the TQM performance evaluation attributes (i.e. A1, A2, . . . ,AN) for thegiven organization. Also consider relative importance among the attributes.Obtain also the value of the attributes (Ei). Refer questionnaire Appendix andtheir relative importance (rij). Refer Tables I and II for details.

(2) Develop the TQMpea diagraph considering the identified TQMpe attributes andtheir relative importance. The number of nodes shall be equal to the number ofattributes considered in step 1. The edges and their directions will be decidedbased on the interrelations among the attributes (rij’s) (as explained earlier).

(3) Develop the TQMpea matrix for the TQMpea diagraph. This will be M £ Mmatrix with diagonal elements as Ei’s and off diagonal elements as rij’s.

(4) Obtain the TQMpe function for the matrix on the lines of expression (4).

(5) Substitute the values of Ei and rij, obtained in step 1, in expression (4) toevaluate TQMpei for the organizations to be evaluated.

(6) Arrange the organizations in the descending order of the TQMpei. Theorganization having the highest values of TQMpei is the best standard of TQMorganization. However, the final decision may depend on other factors likepersonnel interview, etc.

Relative importance ofattributes

Class description rij rij ¼ 10 2 rij

Two attributes are of equal importance 5 5One attribute is slightly important 6 4One attribute is very important over the other 7 3One attribute is most important over the other 8 2One attribute is extremely important over the other 9 1One attribute is exceptionally important over theother 10 0

Table II.Relative importance of

attributes (rij’s)

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Model suggested for TQM performance evaluation based on the data collected frompresent research studyAs per the methodology defined above, the first step is to identify the attributesaffecting the TQMpe for any organization or (industry):

. strategic planning for TQM in organization (SPO);

. top management support;

. employee empowerment;

. supplier involvement; and

. customer satisfaction.

The data regarding the above attributes can be collected from the organization with thehelp of questionnaire (Appendix) formulated on the basis of weightage. Each attributeis evaluated on the basis of eight subquestions each carrying a maximum weightage offive points hence maximum weightage given to each attribute is 40 points. Therefore,for five attributes maximum total weightage is 40 £ 5 ¼ 200 points. Thus (for thisevaluation of Ei attributes one can use Malcom Balridge award criteria also) but thequestionnaire is designed as per study of TQM in Indian context.

Once the attributes are identified and the Ei are calculated, next step is to define therelative importance of the attribute rij suggested as per Table II. With Ei’s and rij’sidentified draw the TQMpea digraph showing the presence of Ei as well as relativeimportance of the above attributes as shown in Figure 4. This diagraph consists of fivenodes 1, 2, 3, 4 and 5 representing the above mentioned attributes, respectively. TQMpe

matrix, C, of this diagraph is written as matrix expression (8) on the lines of matrixexpression (3). The TQMpea are abbreviated as SPO, TM, EE, SI, and CS.

The quantitative values of these attributes as collected by the questionnaire(Appendix) are tabulated in Table III (the data used in Table III are assumed values ofweightage). These values are to be normalized in the interval scale 0-10. In our fiveattributes identified all the attributes are beneficial attributes (the questions inquestionnaire are formatted in that manner Appendix and higher values are desirable.

Figure 4.Diagraph for TQMpef (fiveattribute model) showingrelationship of one nodewith all the other fournodes

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The attribute values are obtained using expression (5) and Table I. The values of theseattributes are normalized and given in Table IV in the respective columns.

Relative importance of attributes (i.e. rij’s) is also assigned the values in the range0-10, based on Table II and is given in Table V. Information collected from literaturereview and based on data from present study, relative importance of attributes hasbeen assigned. For example, TMS is more important than the SI so a high value ofrelative importance is assigned to the TMS over the SI, and the low value of relativeimportance is assigned to the SI over the TMS. Similarly, the relative importanceamong the other attributes can be explained. It may be mentioned here that therelative values assigned are as per author’s perception of TQM implementationeffectiveness. The award committee or various national institute can have their ownperception to decide properly the relative importance among the performanceevaluation attributes.

The TQMpef for the matrix, expression (8), can be written on the lines of expression(4), and the value of TQMpei is calculated using Tables III and IV and the values of Ei’s

Attributes SPO TM EE SI CS

SPO – 5 5 5 5TM 5 – 6 4 4EE 5 4 – 5 3SI 5 6 5 – 5CS 5 6 7 5 –

Table IV.rij’s for various attributes

of the organization (fiveattribute model)

Organization SPO TM EE SI CS

1 27 36 28 30 302 29 26 31 25 293 26 34 37 29 354 24 20 24 27 285 32 36 34 37 36

Table III.Ei’s for various attributes

of the organization (fiveattribute model) (collected

as per questionnaire inannexure)

Organization SPO TM EE SI CS

1 4 10 3 4 32 6 4 5 0 13 3 9 10 3 94 0 0 0 2 05 10 10 8 10 10

Table V.TQMpea values (Ei’s) for

the organization (fiveattribute model)

(normalized in theinterval scale of 0-10 from

Table III)

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and rij’s for each organization. A computer program has been developed for calculationof the results to evaluate 5 £ 5 matrix. The TQMpei values of different organizationsare then arranged in descending order.

Conclusions

(1) The proposed graph theory and matrix approach model is applicable to anytype of industry.

(2) TQM performance evaluation function is proposed and is characteristic of anindustry. This helps to obtain the TQM performance evaluation index, whichevaluates and ranks industries for a given period.

(3) The proposed method strengthens the existing procedures by proposing alogical and rational method of performance evaluation of an industry with TQMprocesses.

Sample calculations for TQMPEI for a five attribute modelI. Attributes defined

E1 – strategic planning for TQM in organization (SPO);

E2 – top management support (TM);

E3 – employee empowerment (EE);

E4 – supplier involvement (SI); and

E5 – customer satisfaction (CS).

II. Diagraph for TQMpef (five attribute model) showing relationship of onenode with all the other four nodes (e.g. for node (1) – (r12r21), (r13r31), (r14r41),(r15r51), (r11)

III. Matrix-TQMpem for the diagraph (five attribute model)

A ¼

Attributes SPO TM EE SI CS

SPO Ei r12 r13 r14 r15

TM r21 E2 r23 r24 r25

EE r31 r32 E3 r34 r35

SI r41 r42 r43 E4 r45

CS r51 r52 r53 r54 E5

ð8Þ

IV. TQMpef for matrix expression (8) is written as

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PerðAÞ ¼Y5

i¼1

Ei þ SiSjSkSlSmðrijÞEjEkElEm þ SiSjSkSlSmðrijrjiÞEkElEm

{SiSjSkSlSmðrijrjkrkl þ rikrkjrjiÞElEm

þ {SiSjSkSlSmðrijrjiÞðrklrlmÞEm þ SiSjSkSlSmðrijrjkrklrliÞ þ ðrilrlkrkjrjiÞEm

þ {SiSjSkSlSmðrijrjiÞðrklrlmrmk þ rkmrmlrlkÞ

þ SSSSSðrijrjkrklrlmrmi þ rimrmlrlkrkjrjiÞ}

ð9Þ

V. Using the data from Tables III-V and the expression (9) the TQMpei can becalculated with the following method for organization (1).

First grouping ¼ E1 £ E2 £ E3 £ E4 £ E5 ¼ 4 £ 10 £ 3 £ 4 £ 3 ¼ 1; 440

Second grouping ¼ 0 ðself loopÞ

Third grouping ¼X5

i¼1

ðrijrjiÞElEmEn ¼ 20; 814:

Fourth grouping ¼ SiSjSkSlSmðrijrjkrki þ rikrkjrjiÞElEm ¼ 53; 490:

Fifth grouping Vaþ Vb

VðaÞ ¼ SiSjSkSlSmðrijrjiÞðrklrlkÞEm ¼ VðaÞ ¼ 42; 416:

VðbÞ ¼ SiSjSkSlSmðrijrjkrkirlm þ rilrlkrkjrjiÞEm ¼ 59; 400:

VðaÞ þ VðbÞ ¼ 42; 416 þ 59; 400 ¼ 101; 816:

GroupingOrg I II III IV Va Vb VIa VIb Total

1 1,440 0 20,814 53,430 42,416 59,400 10 125 277,6052 0 0 4,820 16,970 28,274 39,400 31,250 68,875 189,5893 7,290 0 64,985 103,710 60,154 84,550 100 125 421,5944 0 0 0 0 3,400 4,900 32,100 125 108,4755 89,000 0 83,400 218,560 84,890 118,500 100 125 795,475 Table VI.

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Sixth grouping

VIðaÞ SiSjSkSlSmðrijrjiÞðrklrlmrmk þ rkmrmlrlkÞ ¼ 31; 250:

VIðbÞ SiSjSkSlSmðrijrjkrklrlmrmi þ rimrmlrlkrkjrjiÞ ¼ 68; 875:

[Total of I þ II þ III þ IV þ VðaÞ þ VðbÞ þ VIðaÞ þ VIðbÞ

TQMpeiPerðAÞ ¼ 277; 685:

VI. Similarly for other organization calculations can be performed. The values of thegrouping are tabulated in Table VI.

VII. Therefore, the ranks of the organization as per their TQMpei are given indescending order.

(1) TQMpei (5)

(2) TQMpei (3)

(3) TQMpei (1)

(4) TQMpei (2)

(5) TQMpei (4)

Hence from the values of TQMpei, it is clear that the Fifth organization, i.e. TQMpei(5) isindicating the best TQM performance and TQM has been implemented in the best wayin that particular organization.

References

Hradesky, J.L. (1995), TQM Handbook, McGraw-Hill, New York, NY, pp. 2-3.

Ross, J.E. (1996), TQMText, Cases and Readings, Vanity Books International, New Delhi, pp. 1-2.

Bounds, G., Yorks, L., Meladams and Ranney, G. (1994), Beyond TQM towards the EmergingParadigm, McGraw-Hill International Edition, New York, NY, pp. 44-62.

Dale, B. and Cooper, C. (1997), Human Resource and Total Quality – An Executive’s Handbook,Beacon Books, A Blackwell Asia Imprint, New Delhi, pp. 19-21.

Juran Institute (1992), Total Quality Management – A Practical Guide, Qimpro Consultants PvtLtd, Mumbai, April.

Narsingh, D. (2001), Graph Theory with Applications to Engineering and Computer Science, 22nded., Prentice Hall of India private limited, New Delhi.

Venkate Rao, R. (2000), “Graph theory and matrix approach for the performance evaluation oftechnical institutions”, Indian Journal of Technical Education, Vol. 23.

Jurkat, W.B. and Ryser, H.J. (1966), “Matrix factorization of determinants and permanents”,Journal of Algebra, Vol. 3.

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