International Journal on Emerging Technologies 6(2): 87-94(2015)

ISSN No. (Print) : 0975-8364ISSN No. (Online) : 2249-3255

Quantifying the Various Factors for Automation of FoundryTechnology in Indian Casting Industry

Shweta Bisht*, Anurag Jha**, Samar Sultan*** and Dinesh Kumar*****Assistant Professor, Department of Mechanical Engineering,

Faculty of Engineering & Technology, Manav Rachna International University, Faridabad, (HR), INDIA**Full Time M. Tech. Student, Maintenance Engineering & Management, Mechanical Engineering, Maulana Azad

National Institute of Technology, Bhopal, (MP), INDIA***Assistant Professor, Department of Mechanical Engineering, Noida Institute of Engineering & Technology,

Knowledge Park- II, Gautam Buddha Nagar, Greater Noida,(UP), INDIA****Full Time M. Tech. Student, Mechanical Engineering, Inderprastha Engineering College, Sahibabad Industrial

Area, Ghaziabad, (UP), INDIA

(Corresponding author: Shweta Bisht)(Received 04 June, 2015 Accepted 04 August, 2015)

(Published by Research Trend, Website: www.researchtrend.net)

ABSTRACT: Foundry plays an important part in the manufacturing industry, where metal is casted into adefinite shape and in the required quantities as per the customer schedule received. So the manufacturer hasto supply the products on time and of correct quantity and in sufficient amounts to retain the customers. TheIndian Foundries are developing in a progressive manner where a lot many manufacturers are aiming foradvanced manufacturing systems in their foundries which will enable them to satisfy the customers whilemore increasingly gaining market shares. The objective here is to determine a single numerical index whichtakes into account different factors of foundry by considering their inheritances and interactions, and accesstheir effect on the automation of foundry in the Indian environment. This can be done by developing amathematical model using graphs theoretic approach, which studies the interactions among the variousfactors that affect the automation for a foundry. These factors have their own influencing sub-factors whichinteract with each other and have an overall affect on the automation. To signify the automation factors atsystem and sub-system level, an index has been characterized which shows the extent of automation factorsfor the foundry. This procedure may yield fruitful results in the self-analysis and standardizing among theorganisations. The paper takes into account various general factors, which may change depending upondifferent organisation views (mission & vision). Hence the variation in the factors can be studied upon andused through the useful methodology for the organisation to assess the factors & improve on. Themethodology for the step-wise application of the proposed model is shown with example.

Keywords: Foundry, Casting, Numerical index, Graph theoretic approach

I. INTRODUCTION

The scope of this project is to identify the requirementsfor automation in an Indian casting industry andunderstand the benefits from the reconfiguredproduction system. A production system has a directimpact on the productivity and quality, which helps thecasting manufacturer to determine the cost of theproduct along with the retention of customersatisfaction. This also helps them to maintain acompetitive approach in the market among the numberof other manufacturers. And for the improvement of theproductivity (on volume & quality) the foundry has toinvest in upgraded technology for faster qualityproduction in the equivalent time. Here has theexploitation of an automated manufacturing system asthe foundry has varied processes and different kinds ofproducts lie under its manufacturing line.

Also the foundry manufacturing process is time-consuming operation and tedious task due to the highvolume and reoccurrence of all the processes that has tobe performed on the product.Traditional operation involves the mould preparation(hand moulding) in a vast area and getting the melt (inCupola furnace) ready in the mean time. Once the meltprepared, its transferred to the pouring ladle and pouredrespectively in the prepared moulds. After the completeextraction and pouring of the metal from the furnaceinto the moulds, the moulds are broken (knock-out),after solidification/cooling time and sent for thecleaning and grinding (fettling operations) of theprepared castings. This process doesn’t yield in highproductivity under the case of diverse productrequirement in a short period of notice.

et

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This limits the manufacturer into the manufacturing ofonly one or similar products only and to a solecustomer, thus reducing the market share. Hence aninitiative for implementation of an automated system isprepared by the casting manufacturer for gaining acompetitive edge in the market for gaining more marketshare to increase their reach in different product rangerather than being retained in the production of just asingle component.Mostly study were being conducted based on theReturns on Investment or Internal Rate of Returns thatare supposed to be receiving but this method doesn’tusually yield into a good profiteering company as thislacks in encapsulating the other variables which affecttheir customers directly. The automation for thefoundries in India is a new area of research and thereferences had been taken based on the implementationof the (FMS) flexible manufacturing systems as thereare different processes that are being performed insidethe casting industry which can be automated.An automated manufacturing system (FMS) is designedto combine the efficiency of a mass-production line andthe flexibility of a job shop to produce a variety of workpieces on group of machines. In FMS - automatedsystems, the manufacturing of different products ispossible since the machines are promptly flexible inmanufacturing, to the required changes along with thecompetence of varying level of production volumes.Lately, many foundries are opting for an investment inautomation. But, it’s has also been seen that manyautomated foundries had to be closed because of thevarious factors that weren’t considered at the time ofimplementation. Hence it’s sometimes suggested for theimplementation of automation as a gradualdevelopment of an existing foundry, considering thecost factors in the Indian foundry industry. Spendingfor an automated foundry is a multi-attribute decisionand includes various quantitative and qualitativeattributes. Some of the attributes include skilledemployment requirement with expertise, work inprocess, varied production in flexibility and volumes,quality requirements, lead times, floor spacerequirements, etc.

II. LITERATURE REVIEW

Various researches had been conducted on FMSselection based on the financial analysis methods likeNet Present Value (NPV) method, Return OnInvestment (ROI) method, Internal Rate of Return(IRR). The insufficiency of the traditional financialanalysis and measures lies on their non-stochasticnature. Nelson introduced a scoring model for FMSproject selection by complementing the traditionalcapital budgeting procedures with the treatment ofproject interdependence and non-economic criteria.Wabalickis developed a justified methodology based onthe AHP to evaluate many tangible and intangible

benefits of an investment on FMS. In addition, Bayazitpresented an AHP approach for selecting a FMS. Stamand Kuula developed a two-phase decision procedurethat uses the AHP method and multi-objectivemathematical programming to select an FMS. Boucheret al. argued that AHP is often criticized for the way thecriteria weights are elicited, rank reversal problem,inappropriateness of the crisp ratio representation, andproblems faced in the comparison process when thenumber of criteria and/or the number of alternativesincrease. In addition, Karsak and Kuzgunkayapresented a fuzzy approach with multi-objectiveprogramming for selection of a flexible manufacturingsystem. Data envelopment analysis (DEA) has beenused severally as a tool for evaluation of manufacturingtechnologies and FMSs. Shang and Sueyoshi proposeda selection framework of a FMS using AHP,simulation, and data envelopment analysis. Theyintegrated AHP and simulation to generate "input" dataand used computing techniques to provide "output" datafor analysis using DEA. Sarkis applied DEA techniquefor evaluating FMSs. He presented a number of DEAmodels to aid in the investment and adoption decisionprocess. Shiang integrated Fuzzy Data Envelopmentanalysis (FDEA) and Assurance Region (AR) approachfor selection of FMSs when the input and output data isrepresented as crisp and fuzzy data. He comparedtwelve FMS alternatives (DMUs) by considering twoinputs and four outputs. Capital and operating costswere considered, and floor space requirement as inputfactors and improvements in qualitative factor, work-in-process (WIP), numbers of tardy jobs, and yield asoutput factors.

III. PROBLEM FORMULATION

In this paper, the interdependences and the overallimpact of the automation factors are discussed using amathematical model by applying graphs theoreticapproach. Graph theory which is a logical andsystematic approach and moreover graph/digraphmodel representations have proved to be useful formodelling and analyzing various kinds of systems andproblems in numerous fields of science and technology.An equivalent matrix of the graph/digraph model can bedefined. Graph theory and the matrix approach help inidentifying attributes, and offer a better visual appraisalof the attributes and their interrelations. This approachis capable of handling the inherent errors, and can dealwith any number of qualitative and quantitativeattributes simultaneously. The method has axiomaticfoundation, involves less computation, provides greatemphasis on decision-making methodology, and offersa more objective, simple and consistent decision-making approach. In addition, identification andcomparison of alternatives in terms of their similarity/dissimilarity can be carried out.

Bisht, Jha, Sultan and Kumar 89

The application of graph theory and the matrixapproach as a decision-making tool in manufacturingsituations is relatively new. The method ofquantification looks at the factors that affect theautomation from an aspect of Indian manufacturingindustry such that an improvement can be practisedover the present situation. The main advantage of thismethod is that it gives a better view of the interdependencies between the factors that account for theautomation factors, which is very efficient in ourscenario as there is an interactive complexity that leadsto the Automation for a foundry. All the factors havebeen studied by representing them in numerical indices.

A. Automation Attributes DigraphAutomation in simple words can be defined as the useof different systems which leads into the change in theexisting working procedures such that the newprocedure yields into a higher productivity and betterquality products in a manufacturing unit. To incorporatethe automation in a foundry, there can be two methods:one in a totally new plant& the other in existingfunctioning plant. The first situation is highly risky aslot of funds are to be contributed and the results of theplant are yet far to be seen. But in case, the contributionfor the automation can be diverted from the returnsfrom the existing run-up of the plant. Also theimprovements are to be seen in the regular practise asthe automated section is to be directly linked up in theproduction system, which gives the manufacturer asurety for the goodwill on returns. So majority of thecasting manufacturers prefer this scenario forimplementing automation in the plant.Factors affecting the automation vary for each foundryaccording to their mission, vision & goals. This yieldsthe input to understand the competitiveness aimed bythe manufacturer, the aim of organisation aboutglobalisation, target of market share aimed and thevalue given to the customer.For a foundry to be competitive in market, the companyshould offer the best price for the product to thecustomer which should also incorporate the operatingcosts involved for the casting manufacturer. Theseoperating costs vary from the traditional castingmethodology and from that incurred in the automated oradvanced casting manufacturing methodology. Themanufacturer can also bargain with the customer on theproduct price based on the volume of productionreceived since this has a direct impact on the operatingcost for that particular customer’s product. Theachieved rated capacity of the manufacturing system ofthe foundry is also a stimulant for undertaking thevolume of production, work in process to be kept. Forbetter competition, every manufacturer aims for acontinuous production which is not possible to be seenwithout having any down-time for the machinery repair

& maintenance; which has a direct impact on theimplementation of automation. These factors lead to thepoint of increasing the productivity which is of no gainif quality is not drawn off the system. By having anautomated plant, target is to have a better control onprocess parameters, which increases the quality ofproducts. This is greatly acceptable by the customers asthey ask for the manufacturing system to be SystemOriented rather than Person Oriented. To gaincustomers confidence, it is also required to have goodoperating skills personals and proper trainings to beimparted to the operators of all levels as this helps inbetter production lead times, better equipment &service support for the machinery. The goal of gettingglobalized for the company gets affected by its productquality & reliability, company’s flexibility overchangeovers of the production items with least possiblesetup times required, company’s aim towards the directonline delivery system. These, award the company in itsimage and technological leadership in the market. Withincrease in globalisation, competition and customerexpectation, to sustain & improve in the market share isa great deal of pressure. This has a direct impact fromthe rejection levels maintained, their returns oninvestment, skilled labour requirements, floor spaceavailability, services provided & ease in by-producthandling.To achieve the desired goals of the organisation throughautomation, it is necessary to understand, analyse andevaluate the contribution of critical factors & sub-factors. This is achieved through quantification of effectand interdependency among these factors discussed inthe next section.

B. Development of Graph Theoretic ModelGraph theoretic and matrix model consists of digraphrepresentation, matrix representation and permanentrepresentation. Digraph representation is useful forvisual analysis. Matrix model is useful for computerprocessing. Permanent multinomial functioncharacterizes abstract Automation uniquely. Permanentvalue of multinomial represents the effect of differentfactors on environment uniquely by a singlenumber/index, which is useful for comparison, rankingand optimum selection.

C. Behavioural DigraphA Behavioural digraph is prepared to represent thebehavioural factors of the Automation environment interms of nodes and edges. Let nodes representbehavioural factors and edges represent theirinteractions. The four behavioural factors:competitiveness (B1), globalisation (B2), market sharesustainability (B3), customer expectation (B4) andinteractions amongst them are shown in Fig. 1.

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Fig. 1. Behavioural Digraph.

D. Behavioural MatrixSince, digraph is a visual representation; it helps inanalysis to a limited extent only. To establish anexpression for behavioural effect, the digraph isrepresented in matrix form, which is convenient incomputer processing also. The behavioural matrixrepresenting the digraph shown in Fig. 1 is written as:

Off diagonal elements with value 0 or 1 represent theinterdependency of behavioural factors. The diagonalelements are 0 since effect of behavioural factors is nottaken into consideration. To consider this, anothermatrix, behavioural characteristic matrix is defined.

E. Behavioural Characteristic Matrix (CM-B)The characteristic matrix already used in mathematicsis used to characterize behavioural factors affectingAutomation. Considering I as an identity matrix and Bas the variable representing behavioural factors,behavioural characteristic matrix is written as C = [BI -A]

In the above matrix the value of all diagonal elements issame, i.e. behavioural factors have been assigned samevalue which is not true practically, since all behaviouralfactors have different values (effects) depending onvarious parameters affecting them. Moreover,interdependencies have been assigned value depending

on it is there or not. To consider the effect ofbehavioural factors and their interdependencies, anothermatrix, behavioural variable characteristic matrix(VCM) is considered.

F. Behavioural Variable Characteristic Matrix (VCM-B)It is proposed to characterize the Automation by variousbehavioural factors and their effects through VCM. Forthis let us consider digraph in Figure 2 for definingVCM-B. Consider a matrix D with off-diagonalelements ’s representing interactions betweenbehavioural factors, i.e. instead of 1 (as in matrix 1).Consider another matrix E with diagonal elements Bi, i= 1, 2, . . . 6, where Bi represent behavioural effect ofvarious factor, i.e. instead of B only (as in matrix 2).Considering matrices D and E, the VCM-B is written asH = [E - D]

The matrix provides a powerful tool through itsdeterminant called variable characteristic behaviouralmultinomial (VCBM). This is a characteristic of thesystem and represents the behavioural effect of thesystem consisting of behavioural effect of factors andtheir interactions. Determinant of matrix equation (3),i.e. VCBM carries positive and negative signs withsome of its co-efficient. Hence, complete informationon behavioural effect will not be obtained as some willbe lost due to addition and subtraction of numericalvalues of diagonal and off diagonal elements (i.e. Bi’sand ’s).

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Fig. 1. Behavioural Digraph.

D. Behavioural MatrixSince, digraph is a visual representation; it helps inanalysis to a limited extent only. To establish anexpression for behavioural effect, the digraph isrepresented in matrix form, which is convenient incomputer processing also. The behavioural matrixrepresenting the digraph shown in Fig. 1 is written as:

Off diagonal elements with value 0 or 1 represent theinterdependency of behavioural factors. The diagonalelements are 0 since effect of behavioural factors is nottaken into consideration. To consider this, anothermatrix, behavioural characteristic matrix is defined.

E. Behavioural Characteristic Matrix (CM-B)The characteristic matrix already used in mathematicsis used to characterize behavioural factors affectingAutomation. Considering I as an identity matrix and Bas the variable representing behavioural factors,behavioural characteristic matrix is written as C = [BI -A]

In the above matrix the value of all diagonal elements issame, i.e. behavioural factors have been assigned samevalue which is not true practically, since all behaviouralfactors have different values (effects) depending onvarious parameters affecting them. Moreover,interdependencies have been assigned value depending

on it is there or not. To consider the effect ofbehavioural factors and their interdependencies, anothermatrix, behavioural variable characteristic matrix(VCM) is considered.

F. Behavioural Variable Characteristic Matrix (VCM-B)It is proposed to characterize the Automation by variousbehavioural factors and their effects through VCM. Forthis let us consider digraph in Figure 2 for definingVCM-B. Consider a matrix D with off-diagonalelements ’s representing interactions betweenbehavioural factors, i.e. instead of 1 (as in matrix 1).Consider another matrix E with diagonal elements Bi, i= 1, 2, . . . 6, where Bi represent behavioural effect ofvarious factor, i.e. instead of B only (as in matrix 2).Considering matrices D and E, the VCM-B is written asH = [E - D]

The matrix provides a powerful tool through itsdeterminant called variable characteristic behaviouralmultinomial (VCBM). This is a characteristic of thesystem and represents the behavioural effect of thesystem consisting of behavioural effect of factors andtheir interactions. Determinant of matrix equation (3),i.e. VCBM carries positive and negative signs withsome of its co-efficient. Hence, complete informationon behavioural effect will not be obtained as some willbe lost due to addition and subtraction of numericalvalues of diagonal and off diagonal elements (i.e. Bi’sand ’s).

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Fig. 1. Behavioural Digraph.

D. Behavioural MatrixSince, digraph is a visual representation; it helps inanalysis to a limited extent only. To establish anexpression for behavioural effect, the digraph isrepresented in matrix form, which is convenient incomputer processing also. The behavioural matrixrepresenting the digraph shown in Fig. 1 is written as:

Off diagonal elements with value 0 or 1 represent theinterdependency of behavioural factors. The diagonalelements are 0 since effect of behavioural factors is nottaken into consideration. To consider this, anothermatrix, behavioural characteristic matrix is defined.

E. Behavioural Characteristic Matrix (CM-B)The characteristic matrix already used in mathematicsis used to characterize behavioural factors affectingAutomation. Considering I as an identity matrix and Bas the variable representing behavioural factors,behavioural characteristic matrix is written as C = [BI -A]

In the above matrix the value of all diagonal elements issame, i.e. behavioural factors have been assigned samevalue which is not true practically, since all behaviouralfactors have different values (effects) depending onvarious parameters affecting them. Moreover,interdependencies have been assigned value depending

on it is there or not. To consider the effect ofbehavioural factors and their interdependencies, anothermatrix, behavioural variable characteristic matrix(VCM) is considered.

F. Behavioural Variable Characteristic Matrix (VCM-B)It is proposed to characterize the Automation by variousbehavioural factors and their effects through VCM. Forthis let us consider digraph in Figure 2 for definingVCM-B. Consider a matrix D with off-diagonalelements ’s representing interactions betweenbehavioural factors, i.e. instead of 1 (as in matrix 1).Consider another matrix E with diagonal elements Bi, i= 1, 2, . . . 6, where Bi represent behavioural effect ofvarious factor, i.e. instead of B only (as in matrix 2).Considering matrices D and E, the VCM-B is written asH = [E - D]

The matrix provides a powerful tool through itsdeterminant called variable characteristic behaviouralmultinomial (VCBM). This is a characteristic of thesystem and represents the behavioural effect of thesystem consisting of behavioural effect of factors andtheir interactions. Determinant of matrix equation (3),i.e. VCBM carries positive and negative signs withsome of its co-efficient. Hence, complete informationon behavioural effect will not be obtained as some willbe lost due to addition and subtraction of numericalvalues of diagonal and off diagonal elements (i.e. Bi’sand ’s).

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Thus, the determinant of VCM – behavioural, i.e.matrix equation (3) does not provide completeinformation concerning behavioural effect. For this,another matrix, behavioural variable permanent matrix(VPM-B) is introduced.

G. Behavioural Variable Permanent MatrixOverall behavioural effect is max when the behaviouraleffect of all the factors is max. Since, total quantitativeinformation is not obtained in VCM-B, VPM-B isdefined for the system in general (assuming interactionsamong all factors) as B = [E + D]

Where E and D have meaning as in matrix equation (3).The permanent of matrix equation (4) is multinomialand is called variable permanent behavioural function(VPF-B), also known as permanent of B (per B). Thepermanent for matrix equation (4) in general form iswritten as:Per B = B1.B2.B3.B4 –b12.b21.B3.B4 –b34.b43.B1.B2+b12.b21.b34.b43 + b12.b23.b31.B4 – b13.b31.B2.B4 -b12.b23.b34.b41 + b13.b34.b41.B2 + b13.b2.b31.b42 –b14.b23.b31.b42 – b13.b24.b32.b41 + b13.b21.b32.B4– b23.b32.B1.B4 – b13.b21.b34.b42 – b23.b42.B1.B2 +b14.b21.b42.B3 + b14.b31.b43.B2 – b12.b24.b31.b43 –b14.b41.B2.B3 + b12.b24.b41.B3 …(5)

The permanent function defined above, i.e. equation (5)is the complete expression for behavioural effect as itconsiders presence of all attributes and theirinterdependencies.

Quantification of Bi’s and ’s

Quantification of human factors (i.e. Bi’s) is carried outon the lines of per B (equation (5)). Each factor isidentified as a subsystem and graph theoretic approachis applied in each subsystem. Behavioural subsystempermanent characteristic matrix (similar to equation (5))is evaluated for permanent function considering variousfactors affecting the subsystem. The various factorsaffecting subsystems are identified in Figure 1. Thedependencies of factors at subsystem level arevisualized through digraphs. These digraphs lead to theinheritance of factors at system level through matrixand measures. The corresponding variable permanentmatrices are then derived for each subsystem (ss) andpermanent function of each VPM (ss) is evaluated. Thepermanent functions of these matrices (similar toequation (5)) will lead to inheritance of behaviouralfactors. Thus, graph theoretic approach may be appliedat every level. In order to avoid complexity, suitablescale may be used to assign value at subsystem level orsub subsystem. If all the factors are not equallyimportant to an organization, suitable weights may beassigned. Table I suggests assignment of numericalvalues to factors. To get the complete value ofmultinomial (equation (5)), the off diagonal elements inVPM-B (equation (4)) are to be assigned numericalvalues. As already discussed, these off diagonalelements represent interdependencies among the factorsfor Automation. However, this dependence amongfactors at system level (or subsystem level) cannot bemeasured directly and values can be assigned only afterproper interpretation through a team of experts. It issuggested to use Table II for value ofinterdependencies.The index is a means for the manufacturing unit to seeupon the impact of the various factors on theimplementation of Automation. The higher the indexvalue more beneficial is the environment for theAutomation. This index value can also be used for self-analyses of the organisation and any improvements canbe judged for.

Table 1: Quantification of Factors.

S. No.Qulitative Measure of Automation

FactorsAssigned Value of Factors

1 EXCEPTIONALLY LOW 12 VERY LOW 23 LOW 34 BELOW AVERAGE 45 AVERAGE 56 ABOVE AVERAGE 67 HIGH 78 VERY HIGH 89 EXCEPTIONALLY HIGH 9

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Table 2: Quantification of factor interdependencies.

IV. METHODOLOGY USED TO EVALUATETHE AUTOMATION INDEX

(i) The various factors affecting the automation of afoundry in Indian environment have been identified inFigure 1.(ii) The sub-factors affecting the automation are listedin Table III.

(iii) The dependencies of factors at subsystem level areunderstood by the digraphs shown in Figures 3-8.Superscript denotes the subsystem and subscriptindicates the factors affecting the subsystem.(iv) Variable permanent matrix for digraph for eachsubsystem is written. At subsystem level, variablepermanent matrix for digraph for subsystem 1 (Figure3) in general form is considered. VPM-B1 is given by

Similar to equation (6) variable permanent matrix foreach subsystem are written.(v) At the sub subsystem level Tables I and II are usedto determine numerical values for inheritance of

attributes and their interactions. The variable permanentmatrices for different subsystems (based on theirdigraphs) are written through equations (7.1)-(7.6).

Similarly, variable permanent matrices for other subsystems are written as,

1 2 3 4 5 6 SUB-FACTOR7 0 3 0 0 4 14 8 3 0 0 5 2

VPM B2 = 3 5 6 4 0 4 3 (7.2)3 4 3 5 0 4 43 4 3 3 5 3 50 0 3 0 0 7 6

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1 2 3 4 5 6 SUB-FACTOR9 3 3 0 5 0 13 5 3 0 0 0 2

VPM B3 = 3 3 7 3 5 4 3 (7.3)4 0 3 5 0 0 40 3 3 0 8 4 53 3 4 3 0 5 6

1 2 3 4 5 6 SUB-FACTOR6 3 0 3 3 0 13 7 4 3 0 5 2

VPM B4 = 4 0 6 3 0 0 3 (7.4)0 0 3 8 0 4 43 0 4 3 5 4 54 4 3 4 0 9 6

(vi) The permanent of matrix (6) – Per Bss1, which willlead to inheritance of behavioral factor 1, is evaluatedon the lines of equation (5). The complete expressionfor the Per Bss1 is given as:

The value of permanent function for ss1 leadsto the inheritance of behavioral factor B1.Substituting the values from equation (7.1)

Per Bss1 = 286312(vii) Similarly the value of permanent functions ofdifferent subsystems are evaluated from the variablepermanent matrices in equations (7.1)-(7.6) and arewritten as under:

Per Bss1 = 286312Per Bss2 = 226920Per Bss3 = 427833Per Bss4 = 485322

(viii) Behavioral factor digraph is shown in Figure 2and behavioral matrix at system level is developedthrough equations (1)-(4). Variable permanent matrixfor this example is written in symbolic form as:

The values of the diagonals are to be taken from step 7and the values of off diagonal elements are taken fromTable II.

(ix) After substituting the values in step 8, the variablepermanent matrix behavioral becomes:

(x) Value of permanent function for the system isevaluated as per equation (5).The value of permanent of above matrix (equation (10))is 1.34901 X 1022, which indicates the index for thecase considered. By carrying out similar analysisindices for different foundries can be obtained. Assuggested, this will help an organization to assess itselfand improve. It is also suggested to find hypotheticalbest and hypothetical worst value of index. Automationindex is at its best when the inheritance of all its factorsis at its best. Since, inheritance of factors is evaluatedconsidering sub factors and applying graph theoreticapproach at the subsystem level, it is evident that indexis at its best when inheritance of sub factors is at itsbest. Since, Table I is used at subsystem level,maximum value of Per B1 is obtained when inheritanceof all the sub factors is maximum, i.e. value taken fromTable I is 9. Thus, equation (7.1) may be rewritten forthe maximum value of Per B1 as

1 2 3 4 5 6 SUB-FACTOR9 4 3 4 2 5 10 9 2 4 4 4 2

VPM B1 = 0 0 9 3 4 4 3 (11)2 4 4 9 3 5 40 0 0 0 9 4 50 0 0 4 0 9 6

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The value of the permanent of the above function is1.20532 X 106, i.e. max. Per Bss1 = 1.20532 X 106.Similarly index is at its worst when the inheritance ofall its factors and sub factors is at its worst.

This is the case when inheritance of all the sub factorsis minimum, i.e. value taken from Table I is 1. Thus,equation (7.1) may be rewritten for the minimum valueof Per B1 as

1 2 3 4 5 6 SUB-FACTOR1 4 3 4 2 5 10 1 2 4 4 4 2

VPM B1 = 0 0 1 3 4 4 3 (12)2 4 4 1 3 5 40 0 0 0 1 4 50 0 0 4 0 1 6

The value of the permanent of the above function is4011, i.e. min. Per Bss1 = 4011.Similarly maximum and minimum values for eachsubsystem are evaluated and different values ofpermanent of subsystem matrices are summarized inTable IV. Maximum value of index at system level isevaluated by considering maximum values of all

subsystems and minimum value of index at systemlevel is evaluated by considering minimum values of allsubsystems. The value of per B indicates the value ofindex. Thus, the maximum and minimum value ofautomation index indicates the range with in which itcan vary. Experts can use this range to decide athreshold value for a given set of similar industries.

Table 4: Values For Maximum/Minimum Automation Index.

System/Subsystem Current Value Maximum Value Minimum Value

Per B1 286312 1.20532 X 106 4011Per B2 226920 1.14026 X 106 1936Per B3 427833 1.65243 X 106 29035Per B4 485322 1.50899 X 106 28114Per B 1.34901 X 1022 3.42701 X 1024 6.33874 X 1015

V. CONCLUSION

A casting industry is a combination of differentprocesses through which the manufacturer aims forhigher benefits and implementing automation inside theplant is of much interest in the present day scenario.This project proposes a model for the implementationfor the automation inside a foundry in Indian industry,which is based on the study of different attributes ofgoals and targets of the industry affected by externaland internal parameters.The case study gave an outline on some of the factorsthat affect the automation implementation which mayvary for different casting industries.

VI. FUTURE SCOPE

The project is the framework for the identification ofthe attributes that affect the implementation of theautomation in the foundry in Indian casting industry.Further study can be improved upon for the calculationof the efficiency of the implemented automation of thefoundry. Also the timeline for the implementation of

the automation can be dealt in detail for the futurework.

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