Simulation Modelling Practice and Theory 18 (2010) 471–482

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Simulation Modelling Practice and Theory

journal homepage: www.elsevier .com/ locate/s impat

Practical simulation application: Evaluation of process controlparameters in Twisted-Pair Cables manufacturing system

Amr Mahfouz a,*, Said Ali Hassan b, Amr Arisha a

a 3S Group, School of Management, Faculty of Business, Dublin Institute of Technology, Dublin 2, Irelandb Department of Decision Support, Faculty of Computers and Information, Cairo University, Giza, Egypt

a r t i c l e i n f o a b s t r a c t

Article history:Received 7 January 2009Received in revised form 22 October 2009Accepted 15 December 2009Available online 4 January 2010

Keywords:Twisted-Pair CablesIDEF modelling languageSimulation modellingDesign of experiment

1569-190X/$ - see front matter � 2009 Elsevier B.Vdoi:10.1016/j.simpat.2009.12.008

* Corresponding author. Tel.: +353 858490347.E-mail address: amr.mahfouz@dit.ie (A. Mahfouz

Intensive competition and rapid technology development of Twisted-Pair Cables (TPC)industry have left no room for competing manufacturers to harbour system inefficiencies.TPC are used in various communication and networks hardware applications; their manu-facturing facilities face many challenges including various product configurations with dif-ferent equipment settings, different product flows and Work in Process (WIP) spacelimitations. The quest for internal efficiency and external effectiveness forces companiesto align their internal settings and resources with external requirements/orders, or in dif-ferent words, significant factors must be set appropriately and identified prior to manufac-turing processes. Integrated definition models (IDEF0, IDEF3) in conjunction with asimulation model and a design of experiments (DOE) have been developed to characterizethe TPC production system, identify the significant process parameters and examine vari-ous production setting scenarios aiming to get the best product flow time.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Never have the pressures on TPC manufacturers been more severe to deliver on time in the context of volatile demandfrom telecommunication suppliers. Moreover, global competition and technology advancement impose further complexityinto the manufacturing processes of these products. TPCs have different characteristics including cable types, diameters,number of pairs and length. Each change in these characteristics influences product flow, equipment settings and productdispatching; hence creates complex interdependencies between manufacturing parameters. The manufacturing is performedin an environment of significant uncertainty both in dispatching rules used and process parameters.

Traditional analytical techniques and simple mathematical models are currently inadequate to analyse these complexmanufacturing environments [9]. Therefore, powerful modelling and simulation technique integrated with system analysisapproaches (IDEF0, IDEF3 and DOE) are needed to properly model the dynamics as well as variability of the system and thenoptimize the production variables.

Simulation has proved to be a useful tool in various manufacturing applications [1,6,10–12,20,24], as it is used to analysethe alternative system configurations. Many articles have been published about simulation approach in production systems,however few if any addressed TPC manufacturing issues. Therefore, this study is directed to analyse the influence of thechanges in dispatching rules and process parameters on system performance by conducting a simulation-based full factorialdesign.

. All rights reserved.

).

Fig. 1. Schematic diagram of TPC factory.

472 A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482

2. TPC process

TPC process consists of four main processes; Conductor Drawing, Twisting Operation, Cable Core Jacketing and finally thePacking Process; Fig. 1. The manufacturing process starts by producing the specified diameter for the conductor – the coreunit of cables manufacturing. The key features of the produced conductors include, profile, diameter and surface smoothness.The drawing process is operated with four identical parallel machines to produce solid copper conductor which is sur-rounded by an insulating material. Pre-twisting equipments are used to prepare conductors before the twinning operation.Ahead of the twisting operation, the conductors are divided into two groups according to the specifications of the requirednumber of pairs. Twisting operation consists of 13 machines in main five work-centres which are configured to twist anynumber of pairs. This process is critical as it directly affects the cable performance (transmission performance and high sig-nal immunity). Inspection is routinely done within each process as well as a main inspection is performed after finishingtwisting operation. One of three decisions is taken at the main inspection point; Accepted, Reworked or Scraped cable.

Jacketing cable core process is ultimately followed to shield the conductors providing insulating and protective layer.During jacketing process, the legend and other manufacturing data are stamped on the product. At the final stage of theTPC operation, the cables are cut from the master-reel into the required length and then rolled into plastic or wooden reelsas a finished product.

3. Problem definition

Given the economics of marketplace, TPC manufacturers face various challenges to meet the customised order at the righttime with the right quantity. Four attributes cause wide variety for manufactured cables; (i) cable type (TPC 154 and TPC450), (ii) cable diameter (0.4, 0.5, 0.6 and 0.9 cm), (iii) cable number of pairs (20 types varying from 2 pairs to 1500 pairs),and (iv) cable length (dependent upon customer demand). As the number of product variants is the Cartesian product of itsattribute configurations [17], the TPC industry has to deal with at least 160 different products for each cable length. Thishigh-mix of products places TPC manufacturing system under significant pressure to deliver the required orders on time.Thus high WIP in limited areas, low process performance, increased setup times and high throughput time are consequentialresults. To complicate things more, the TPC under study does not have an efficient pre-plan for resources availability. An-other source of complexity is the dispatching rules which need to be set prior to batch arrival [5,7,14].

In order to effectively manage the likes of TPC production systems, there is a need for a systematic methodology that pro-vides a better understanding of process dynamics and to determine the optimal operating conditions. The applied model suc-cessfully integrates four analytical techniques (i.e. IDEF0, IDEF3, simulation and DOE) to achieve the following objectives: (i)build an effective model to characterize TPC activities and decisions, (ii) develop a simulation model to examine TPC process

Fig. 2. Business process modelling methods classifications.

A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482 473

performance under different production scenarios, (iii) determine the main and interaction effects of process control param-eters, and (vi) find the optimal combination of process parameters in order to enhance system performance. Three key pro-cess control parameters have been the focus of the study; machine speed (MS), machine rule (MR) and preventivemaintenance policy (PM). The performance measure of interest is Average Flow Time (AFT) measured by days.

4. Business process model of TPC

4.1. Business process modelling background

Business process modelling is a presentation for the sequences of system’s processes, procedures and resources. It alsoshows the relationship between system’s objects (i.e. products, customers,. . .) and their status during system’s life cycle.Many modelling methods are studied in business process modelling literature [27]. According to the level of details, businessprocess modelling methods are classified into two categories – generic and specific methods (Fig. 2). The generic methodsare used to model the whole system life cycle (i.e. thinking macro scale) by integrating different modelling methodologies[e.g. IDEF family, Object Oriented (OO), . . . , etc.]. For instance, Open System Architecture for Computer Integrated Manufac-ture (CIMOSA) analyses the system so that using OO programming will be easier. Integrated Enterprise modelling (IEM)method uses block diagrams based on IDEF0 and OO for the modelling process. Structure System Analysis and Design Meth-odology (SSADM), Soft System Methodology (SSM) and Graph with Results and Activities Interrelated (GRAI) are additionalgeneric business process modelling methods consider respectively the analysis and design stages of system development,support and structure thinking about complex organisational problems and address production management decisions inmanufacturing systems [28].

On the other hand, Specific Modelling Methods (Fig. 2) contain approaches that ultimately used for modelling specificviews according to system requirements. Flow and Gantt charts are the main methods that use graphical presentation inorder to show sequence and duration of process’s activities and tasks. Although they are clear and flexible, applying themcreates a risk of ignoring important details of the studied processes. This is due to the absence of hierarchical structure intheir nature. For modelling information flow, Data Flow Diagram (DFD) is a common methodology that provides a cleardescription of information flow from the source to the destination. The lack of logic expression (e.g. and, or, . . . , etc.) andthe weak decomposition capability are the main deficiencies of DFD [29]. Rule Activity Diagram (RAD) and Rule InteractionDiagram (RID) are another two modelling methods aim to illustrate system’s rules and their interactions. RAD is based on agraphic representation for the business rules that can be applied on a specific system process. While RID shows all rules ap-plied in the system using a graphical combination of all RAD models. System’s cost is one more important perspective formodelling process. Given its ability to model system’s indirect costs, Activity Based Cost (ABC) is considered one of the mainmethods for modelling system costs [31]. It is used in several manufacturing studies particularly in job shop systems [32]. Inaddition, Petri-Nets (PN), IDEF2 and Structure Analysis for Real Time (SA/RT) are commonly used methods for modelling dy-namic system behaviour through representing the time variant behaviour of resources in manufacturing systems. PN anal-yses the concurrent processes performed with the use of shared resources (machines, equipment, operators, etc.) [33]. Onthe other hand IDEF2 decomposes the system to four main sub-models; (1) facility sub-model, (2) entity flow sub-model,(3) resource disposition sub-model, and (4) system control sub-model to completely describe the dynamic system behaviour[34]. SA/RT is developed by proposing a real time extension of Structure Analysis (SA) method [25,26]. This extension is

A0

Function Name(Inputs) (Outputs)

(Controls)

(Mechanisms)

Fig. 3. Basic IDEF0 construct.

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mainly using control flow diagram CFD (events) in order to describe the dynamics of the system along with data processingfrom DFD models. However, SA/RT limitations are; (i) the aforementioned deficiencies of DFD cause weakness of data rep-resentation, (ii) the representation of data and control flows at the same diagram yields a lot of information which requiresformation roles to prevent information confusion, and (iii) using of different types of diagrams, tables and transition statearrays for specifying control logic causes unstructured nature for modelling process [35]. For highly uncertain dynamic sys-tems, IDEF2 and Petri-Net methods can be more effective in modelling processes.

Due to the importance of the clear communication between end users and modellers, the existence of modelling languagethat is understandable by both parties is vital. This language can be found through the use of an intuitive but structured setof modelling techniques such as IDEF family. The existence of unified syntax and semantics for the language decreased theproblem of misunderstanding. IDEF family is a group of methods that provide the capability of modelling the business areafrom different perspectives (e.g. process, objects, information . . . , etc). IDEF methods have hierarchical structure capabilityand language simplicity that give them an advantage on other modelling approaches. They are initiated from a top-level dia-gram, and decomposed to several bottom-levels. IDEF0, IDEF1X, IDEF2 and IDEF3 are the most relative methods for businessprocess modelling.

For TPC system, IDEF0 and IDEF3 were found to be adequate for modelling the dynamic nature of the system. IDEF3 en-ables the modeller to consider the combination between activities and objects’ flows.

4.2. Modelling TPC functions using IDEF0

Taking into account the complexity of TPC manufacturing environment with such level of uncertainty due to multiplecontrols and mechanisms required, IDEF0 emerges as a powerful tool for modelling such intricate systems. A hierarchicalmodelling approach using IDEF0 allows users (e.g. strategic managers, operational engineers and system analysers) to com-prehensively understand the sequence of system’s functions. An activity block which is the main unit for IDEF0 describes themain function of the process. ICOMs (Input, Control, Output and Mechanism) are represented by horizontal and vertical ar-rows (Fig. 3). Process control (top arrow) can be company regulations, standards or legislation, whereas process mechanismsare usually the agents which facilitate the activity (e.g. People and automated tools). Further information about IDEF0 can befound in Refs. [8,22,23].

IDEF0 is used in conjunction with IDEF3 as a modelling approach to conceptualize TPC processes before developing thesimulation model. Fig. 4 shows the top level of the developed IDEF0 model which indicates the sequence of activities, theinputs such as sales orders and supplier list, the control such as Bill of Materials (BOMs), Due Dates and customer informa-tion, the mechanisms (several departments and computer applications) and the output (finished products). The followinglevel of the model (Fig. 5) shows more details of the manufacturing activities. All production steps and their controls are welldescribed in the diagram A3 Node (Fig. 5).

The main inputs of the manufacturing system are raw materials (i.e. copper reels) and production orders which containrequired cable specifications (e.g. cable length, diameter and number of pairs). These orders are categorized into four groupsaccording to the required cable diameter. Subsequently, the raw materials of each order group are transported to conductordrawing workstation where drawing and insulating operations are performed. Cables are then admitted to a pre-twistingworkstation for a cleaning process before they move to the twisting operation. Operators of twisting workstation clusterthe incoming cables into two groups in front of twisting workstations according to the required cables number of pairs. Eachgroup follows a several route for twining operation. Cables inspection is undertaking at the main inspection unit (A35) beforethe commencement of jacketing and packing processes. Since the factory under study has limited production capacity andspeed, cables which require the aforementioned processes may have to enter a queue, unless there is idle workstation capac-ity available at the moment they arrive. This means that cables which are waiting to be processed (i.e. WIP) may occupy asignificant floor space until the next station is ready to process them. Subsequently, this WIP usually causes an increase in

NODE: NO.:A0 TITLE: Main TPC Processes

A1

Order Arrival

A2

Logistics and Planning

A3

TPC Manufacturing

A4

TPC Delivery

Sales Order

Supplier List

Product Specification

Raw Material

Production Order

Finished Products

Arrival Time Product ListProcess Factors

Process Characteristics Due Dates Customer

Information

Sales & Marketing Department

Logistics Department

Product Specification

Tools and Machines Setting

Delivery Department

BOM

Computer ApplicationLabours

Fig. 4. Basic function blocks for TPC.

NODE: NO.:A3 TITLE:

TPC Manufacturing

A31

Loading

A32

Conductor Drawing

A34

Cables Twisting

A35

Inspection

A36

Jacketing Process

A37

Packing

Copper Reel

Production Order

Forklifts Machines Setting

EquipmentsUnscheduled Machine Breakdown

Scheduled Preventive maintenance

Copper Conductor

Single Cable Reel

Twisted Cable Reel

Insulated Cable Reel

Finished Products

Process Characteristics

Process Factors

BOM Due Dates Routing

A32

Pre-Twisting

Fig. 5. TPC manufacturing sub-function blocks.

A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482 475

product cycle time, which has a negative effect on system performance. The variety of TPC products and their operationscombined under one roof in the manufacturing system creates a very complex set of internal decisions. The establishmentof process characteristics for each workstation, the routing of items and job due date form necessary controls for TPC system.

Maintenance process represents another source of difficulty for managing production in the TPC factory. The challenge isnot only how to handle maintenance problems and the resulting loss of production arising from them, but how to provide arobust preventive maintenance program in order to reduce the probability of breakdowns.

Fig. 6. A detailed IDEF3 process model for cable twisting function.

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4.3. Modelling TPC processes and objects using IDEF3

IDEF3 is integrated with IDEF0 to model the behavioural aspects of the processes due to its ability to model both processand object flow. IDEF3 consists of two modelling modes:

(i) Process flow description (PFD) describes the events and activities in each process, their relationships and inter-rela-tionship logic (e.g. and, or, . . . , etc.).

(ii) Object State Transition Description (OSTD) summarises the information about objects status through the system, theirrelationship and transition states.

Fig. 7. A detailed IDEF3 object model for cable twisting function.

A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482 477

In contrast to IDEF0, IDEF3 has less strict syntax and semantic rules, while it still keeps process decomposition capability[30]. Integrating IDEF0 and IDEF3 using the hierarchical structure of IDEF language is shown in Fig. 6. Taken as an illustrativeexample, a detailed process and object flows for the fourth TPC function in IDEF0 model (cable twisting function (CTF)) areexhibited at Figs. 6 and 7.

Two alternative numbers of pairs – 2 pairs and 10 pairs – are used as a basic for any required TPC with any number ofpairs. The two alternatives are shown in two different routes (blocks 4.1.2 and 4.1.18) (Fig. 6). In each route, the twistingprocess takes place using various machines according to the product specification [i.e. required number of pairs (50, 100,500, 1000, etc.)]. Process flow modelling using IDEF3 provides a clear understating of the sequence of activities and the deci-sion points in CTF. For example, since the two pairs workstation (block 4.1.2) is the only station in CTF that have parallelidentical machines, the workstation supervisor always takes a decision of which operation rule (operate in parallel or in ser-ies) should be selected. As CTF progresses, there is an inspection unit after each operation. Inspection outcome can be one ofthose; TPC rework, transferred TPC to final inspection or TPC need more twisted pairs (e.g. blocks 4.1.9, 4.1.10 and 4.1.11).The numbering system of IDEF3 facilitates tracking the sequence of processes as well as the link between IDEF3 and IDEF0.

As process flow at Fig. 6 gives details about process sequence and operation rules, Fig. 7 provides the object’s flow andtransition state of CTF. Cable reels are the first object that arrives from the predecessor function (Pre-Twisting Function(IDEF0 model)). Using manufacturing blocks that are modelled at Fig. 6 (block 4.1.6, 4.1.7 and 4.1.21), cable reels are trans-formed to 2 and 10 pairs twisted cables objects. Both 2 pairs and 10 pairs cables obtain one of the following states; morepairs is needed, final inspection, or reworked. Modelling operation sequences, decision points and objects’ flows supportthe development process of simulation model.

5. Simulation model

In this study a probabilistic model is required in order to capture the randomness of demand patterns along with theirproduction route, the various possible cable configurations, the variability in the length of cycle time and the uncertaintyof unscheduled breakdown occurrence. The stochastic technique for discrete-event simulation is chosen as it is capable ofmanipulating the variability and uncertainty of this system. A computer simulation model based on the conceptual modelshown in Figs. 4–7 was developed. The model assumptions are (i) Product scrap and rework have been assumed as a fixedpercent of production output (ii) products are interrupted on unscheduled machine breakdown occurrence (iii) preventivemaintenance does not start until product processing is finished. This model uses entities to describe the cable movementthrough the production line, while resources represent the manufacturing tool (e.g. machines, workstations) which modifiesthe entities. Resources are characterized by their capacity, breakdown schedules, repair time and preventive maintenancescheme, whilst the attributes of the entities are arrival time, processing time and product configurations. Logical entitiessimulate the decisions for creating, joining, splitting, buffering and branching entities. Each product specification has itsown statistical arrival distribution, while product processing time is a function of product diameter and length. Machinebreakdown and repair time are set to have different statistical distributions for each machine. As previously mentioned,the original purpose of the model is to determine the main and interaction effect of process control parameters against threescheduling rules and to find the best combination of the process parameters to enhance system performance.

Growing applications of simulation modelling in manufacturing systems has resulted from the increasing number of bothgeneral purpose and specific simulation software packages. It is essential that an appropriate simulation package should beselected as it has a significant impact on the ultimate validity of the model and on the timeliness of the simulation projects[36]. There is a dilemma on which are the criteria that can be used for the selection process of simulation software [37].

Fig. 8. Model validation.

478 A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482

Having such diversity of systems’ characteristics and structures, leaves no single simulation package ranked as the best touse in modelling manufacturing systems [21]. The simulation model used to model TPC has used a generic package of sim-ulation and customised it using Java and XML technologies. This selection provides flexible and efficient simulation model ofTPC for three reasons; (1) it helps to provide object-oriented hierarchical and event-driven simulation capabilities for mod-elling such large-scale application, (2) It utilises breakthrough activity-based modelling paradigm (i.e. real world activitiessuch as assembly, batching and branching), and finally (3) it also used to customise objects in the package to mimic the real-life application characteristics.

In an effort to make the decisions taken based on simulation models more accurate, efficient methods of verification andvalidation are needed. For the verification process, in addition to decomposition model (i.e. to verify every group of blocks), asimulation software built-in debugger is used. A decomposition approach is effective in the detection of errors and insuringthat every block functions as expected. The studied model has been validated using two techniques. The first is ‘Face Vali-dation’ that was performed by interviewing managers and manufacturing teams in order to validate simulation model re-sults. The second approach is ‘Comparison Testing’ which done by comparing the model output with the system outputunder identical input conditions [16,18]. A chart of validation results using ‘Comparison Testing’ approach has showed thatonly 10% average percentage of the deviation between simulated and actual results based on a sample of 17 scenarios(Fig. 8).

6. Simulation experiments

TPC manufacturing system is quite complex which makes it difficult for managers to control the process parameterswhich have a significant effect on system performance [2,3]. In this case, a designed factorial experiment was used to deter-mine the relative significance of factors and their interactions in order to find the best possible combination [13,15]. Thestudied process parameters are:

(1) Machine speed (MS): low (level 1), normal (level 2) and high (level 3) speeds are three levels of MS that managersapply according to production conditions and factory’s power consumption. However, the logic thinking implies thatthe higher the speed the better the performance, TPC dynamic complex environment might dictate different outcomewith higher speed. Taking into account the work in progress (WIP) issues and different scheduling rules, the best speedoption might vary.

(2) Machine rules (MR): most of TPC factory workstations (e.g. conductor drawing workstation, cable twisting worksta-tion and cable jacketing workstation) contain several machines that can do same function. The operators of theseworkstations (WS) are normally in position to select the best operating rule for these machines based on productionconditions. Two MR are used in TPC factory; series (level 1) and parallel (level 2) rules. The first rule dictates that thesingle work order (might contain multiple TPC) should be operated on one single machine at the workstation. Whileparallel operating rule prescribes that work order can be operated on parallel machines. Although parallel machineoperating rule has the advantage of higher machine utilization, series machining rule minimizes the risk of reworkand high setup times. The debate between the rules and the optimum combination reflected the urge of effective tool(i.e. simulation modelling) to be applied to test production strategies.

(3) Preventive maintenance policy (PM): two alternative policies for maintenance are examined in this study. EntirePM policy (level 1) applies the maintenance on whole factory’s machines at one time. Production process isstopped and the entire factory is to shut down for maintenance. On the other hand, partial PM policy (level 2)provides schedules for maintenance activities to happen with minimum interruption to production. Single-machine workstations suffer the highest WIP. Another argumentative decision is to be made by the factory man-ager and needs simulation capabilities to examine the impact of each policy before committing into new produc-tion orders.

The main and interaction effect of the three process parameters will be tested under various dispatching rules (Rule 1,Rule 2 and Rule 3). For the model to reach its steady state condition, the warm-up was 4800 h. Every simulation run repre-sented a year of actual timing. Each experiment result (Table 1) is an average of five independent replications. Common Ran-dom Numbers (CRN) is used to reduce the variance between experiments’ outputs. Compared with other variance reductiontechniques, CRN is defined as one of the effective methods that can be used when a small number of experiment replicationsare done [4].

7. Results analysis

Analysis of Variance (ANOVA) models are used to assess main and interaction effect of system’s factors [19]. The principleof ANOVA model is testing null hypothesis – change of one or more factors’ levels does not cause variation for response’smeans – against the alternative hypothesis that has at least one variant response mean. One-way ANOVA model splitsthe total response variations into two parts; one due to random error and the other due to changes in factor levels (Eq. (1)).

Total SS ¼ SSTþ SSE ð1Þ

Table 1Design matrix for all factors combination under three different dispatching rules.

Experiment MS MR PM Response (AFT)

Rule 1 Rule 2 Rule 3

1 1 1 1 231.64 156.76 167.472 1 1 2 238.45 151.06 167.583 1 2 1 171.72 119.57 106.524 1 2 2 173.72 120.12 109.635 2 1 1 184.92 134.12 153.526 2 1 2 186.33 134.98 154.97 2 2 1 142.22 115.68 103.438 2 2 2 143.22 115.62 104.169 3 1 1 139.02 117.75 97.510 3 1 2 142.16 118 95.1411 3 2 1 108.15 99.52 94.7312 3 2 2 109.25 98.75 92.7

A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482 479

where Total SS is the total sum square (the total response’s variation), SST is the sum of square of treatments (factor levels),and SSE is the sum of square of errors.

Terms in Eq. (1) are calculated using the following formulas:

Total SS ¼Xm

j¼1

Xnj

i¼1

ðXij � XÞ2 ð2Þ

SST ¼Xm

j¼1

njðXjÞ � XÞ2 ð3Þ

SSE ¼Xm

j¼1

Xnj

i¼1

ðXij � XÞ2 ð4Þ

where nj is the number of observations for treatment j (i.e. factor level J), m is the number of treatments, X is the overall meanfor all observations, Xij is the ith observation in treatment j, and Xj is the sample mean of treatment j.

In order to test ANOA hypothesis, variance measures (i.e. mean squares) for both treatments and errors need to be cal-culated. When null hypothesis is true, the two mean squares should have approximately equal magnitude; their ratio shouldbe close to 1. On the other hand, if null hypothesis is false, the mean square of treatments (MST) should be larger than meansquare of error (MSE). The mean squares are formed by dividing the sum squares by the associated degree of freedom asfollows:

MST ¼ SSTm� 1

ð5Þ

MSE ¼ SSEn�m

ð6Þ

where n is the total observations for all treatments ðPm

j¼1njÞ, (m � 1) is the degree of freedom for SST, and (n�m) is the de-gree of freedom for SSE.

Because the mean squares are variances, F-test can be used to test the equality of variances using F-statistics [38]

F ¼MSTMSE

ð7Þ

F value follows F-distribution with (m � 1) and (n �m) degrees of freedom. The null hypothesis is rejected if F is larger thanspecific value of F-distribution indicating that mean square of treatments is significantly larger than mean square of error.This result provides statistical evidence that any change in the factors’ level will have a significant effect on system response.

The principle of higher degree ANOVA models (i.e. 2-way, 3-way, . . . , etc.) is similar to the one-way ANOVA. While theone-way ANOVA investigates the main effect of one factor on system’s response, 2-way and 3-way models assess the inter-action effect of more than one factor. For example in 2-way ANOVA, the total variation can be partitioned into componentparts corresponding to the variation in each factor, interaction and random error as follows:

Total SS ¼ SSAþ SSBþ SSABþ SSE ð8Þ

where Total SS is the total sum of squares, SSA is the sum of square due to factor A, SSB is the sum of square due to factor B,SSAB is the sum of square due to interaction, and SSE is the sum square due to error.

For ‘r’ treatment levels of factor A and ‘c’ treatment levels of factor B and ‘k’ the number of replications of each treatmentcombination, the mean squares for the factors and their interactions are as follows:

Table 2Main ef

Disp

Rule

Rule

Rule

Table 3Interact

Disp

Rule

Rule

Rule

480 A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482

MSA ¼ SSAðr � 1Þ ð9Þ

MSB ¼ SSBðc � 1Þ ð10Þ

MSAB ¼ SSABðr � 1Þðc � 1Þ ð11Þ

MSE ¼ SSErcðk� 1Þ ð12Þ

Similar to one-way ANOVA, F-statistics is calculated by dividing each mean square of the factors and their interactions by themean square of the error (MSE). Based on F-distribution, one can identify the significance of the factors and theirinteractions.

For this study the main and interaction effects of the chosen process parameters (MS, MR and PM) were analysed using95% confidence interval (Tables 2 and 3).

It is worth noting that the main effect analysis (Table 2) is conducted by changing one single factor at a time while allother parameters are fixed. Using dispatching Rule 1, MS and MR show significant effects on the response function withMS holding the highest F value. Looking at (Table 1) results, it is clear that changes in MS impinge on AFT (44% decreases),however changes in MR and PM decrease AFT by 24% and 1%, respectively.

Using the other two dispatching rules, MR has the greater deduction on AFT since it has the highest F value in both rules.Table 1 results reflect the positive effect of changing MR levels on system performance by 18% and 27% respectively. When-ever ‘P’ value is greater than 0.05, the parameter is not significant. PM has not shown any significant effect on system per-formance under the three selected dispatching rules. Surprisingly, MS was not influential when dispatching Rules 2 and 3were used.

On the other hand, interaction effect analysis is based on changing two or more factors at the same experiment to exam-ine the impact of the changes on the response function. Table 3 shows the results of the Two-Way ANOVA model. MS and MRinteractions are significant under the three dispatching rules especially on dispatching Rule 3 which has the largest F value. Itis clear that other interactions have low significant effect.

As shown in Fig. 9, changes in MS level have a cogent effect on decreasing AFT. The best deduction of the response func-tion is witnessed at level 3 of MS (Fig. 9c). There is also a significant difference between the uses of the two levels of MRfactor with AFT being shorter when using the second level of MR as opposed to the first one. Matching the aforementionedANOVA results MR factor has shown a stronger effect on AFT then does MS factor, especially at the last two dispatching rules.

For the three speed levels of MS, the AFT value using the second level of MR is much better than using the first level; how-ever, the difference in performance using the two levels of MR is less pronounced the third rule with MS at level 3 (Fig. 9c).

fect of process parameters for three dispatching rules.

atching policy Source Sum of square Df Mean square F P

1 MS 12557.185 2 6278.593 8.341 0.009MR 6267.298 1 6267.298 4.797 0.043PM 19.918 1 19.918 0.01 0.921

2 MS 1625.47 2 812.735 3.879 0.061MR 1713.869 1 1713.869 9.535 0.011PM 1.679 1 1.679 0.006 0.942

3 MS 4083.728 2 2041.864 3.016 0.09MR 4216.388 1 4216.388 7.073 0.024PM 0.074 1 0.074 0 0.993

ion effect of process parameters using three dispatching rules.

atching policy Source Sum of square Df Mean square F P

1 MS �MR 474.919 2 237.459 44.224 0.000MS � PM 5.433 2 2.716 0.002 0.998MR � PM 4.392 1 4.392 0.003 0.960

2 MS �MR 154.953 2 77.476 27.192 0.001MS � PM 4.882 2 2.441 0.008 0.992MR � PM 1.548 1 1.548 0.007 0.936

3 MS �MR 1866.195 2 933.097 512.91 0.000MS � PM 8.454 2 4.227 0.004 0.996MR � PM 0.6 1 0.6 0.001 0.978

Dispatching Rule1 Dispatching Rule2

(b) MS

321

Est

imat

ed M

argi

nal

Mea

ns

225.00

200.00

175.00

150.00

125.00

100.00

21

MR

MS321

Est

imat

ed M

argi

nal

Mea

ns

160.00

140.00

120.00

100.00

21

MR

MS321

Est

imat

ed M

argi

nal

Mea

ns

180.00

160.00

140.00

120.00

100.00

80.00

21

MR

(c)

(a) Dispatching Rule3

Fig. 9. Average flow time versus the interaction between MS and MR under Rules 1, 2, and 3.

A. Mahfouz et al. / Simulation Modelling Practice and Theory 18 (2010) 471–482 481

Based on the previous analysis, the optimal factors combination at any dispatching rule is the level three of MS with the sec-ond level of MR with an AFT 108.15. Changing PM policy has a minor impact on performance function.

8. Conclusions

The large range of products in various configurations along with the objective of on-time delivery create a challengingmanufacturing environment for TPC. As process analysis is considered a critical task in such complex systems, it becomesnecessary to choose effective approaches to model them.

IDEF0 and IDEF3 have been integrated to develop the conceptual model applying standard formats to define the se-quences, relationships and interdependences between TPC activities and objects. They prove to be efficient system descrip-tion tools which offer a structured modelling approach. IDEF0 and IDEF3 have enabled the system analysis phase by breakingthe processes into stages which describe each manufacturing activity as well as envisage the overall system view.

Simulation modelling often provides a robust tool to evaluate the impact of different manufacturing policies and strate-gies with a minimum cost and risk. Hence, it has been employed to imitate the shop floor activities of TPC production. Thesignificance of process parameters on system performance was analysed using factorial design of experiments. Results showthat in contrast to preventive maintenance policy, machine speed levels, machine operation rules and their interactions havesignificant effects on AFT regardless of dispatching rules applied.

This paper presents an integrated model of IDEF0, IDEF3, simulation modelling and simulation optimization (DOE) thatsupports decision making in TPC industry. The model has been verified and validated against real data and showed satisfac-tory results. The best combination of process control parameters (e.g. machine speed level, machine operation rules, and pre-ventive maintenance policies) and the significance of their impact on system performance can easily be obtained as modeloutputs.

Due to the flexibility of IDEF language, simulation modelling and DOE in modelling different manufacturing characteris-tics, the represented model can be customised to support decision making process for other industrial systems (e.g. automo-tive, semiconductor, furniture industries, etc.).

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