Workers and Machine Performance Modeling in Manufacturing

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Volume 8(4) 185-190 (2015) - 185J Comput Sci Syst BiolISSN: 0974-7230 JCSB, an open access journal

Research Article Open Access

Jilcha et al., J Comput Sci Syst Biol 2015, 8:4

http://dx.doi.org/10.4172/jcsb.1000187

Research Article Open Access

Computer Science

Systems BiologyJournal

of

Comput

er

Science&

Sy

stem

s

Biolo

gy

ISSN: 0974-7230

Keywords: PVC pipe product; Arena simulation; Waiting time;Troughputs; Capacity utilization

Introduction

Industry Perormance improvements arising rom increasedmanuacturing integration continues to be one o the primarycompetitive issues in current days. Faced with ever-increasingchallenges such as the globalization, increased world competition, andincreased customer expectations, companies are pursuing strategies

to improve their perormance and reduce their costs. Discrete-eventmodeling and simulation (DES) is a popular tool in widely varying fieldsor identiying and answering questions about the effects o changeson processes. Recent research into manuacturing systems integrationhas identified the need or effective positioning o business objectivesdown through the organization and the subsequent measurement operormance in critical areas as key elements o sustainable competitiveadvantage [1-7]. One o the best tools that can indicate the perormanceo any company is simulation sofware. Te simulation sofware can bedivided in to bigger group Simulation Language and Simulators. Tesimulation language is programming based using simulation sofware.Te simulator allows one to build a model o the desired system byusing beore- made modeling constructs [8]. In Simulation, languagesofware the model is developed creating a program syntacticallyor graphically using languages modeling constructs. Tese typeso simulation sofware are very flexible tools but the user needs toknow programming concepts and longer modeling times [8,9]. Tus,simulation can be either discrete event or continuous simulation. Incontinuous model, the state o the system can change continuously overtime. In discrete model, though changes can occur only at separatedpoints in time [10].

During the past decade, the manuacturing industry has undergonea dynamic transormation. Recently, traditional manuacturers areinherently subject to high-mix, low volume manuacturing as abusiness model [11]. In this paper, discrete event simulation is used tomodel workers and machine perormance in Ethiopia Plastics Industry.Highly industries rely on workers and machine perormance since

productivity depends on workers and machine availability. A companywill not be able to participate and will not survive in a long-termperspective i employees do not attribute a high significance to such

organization goals. However, poor workers and machine and machineperormance can be recognized some o the actors are o high loado work, financial stress, and illness. Tereore, workers and machineperormance, as this unction is essential required or huge value to theorganization in maintaining and strengthening its business and revenuegrowth [12-16].

Multi-skilling o workers can be achieved by cross-training. Cross-training is a process in which workers are trained on the tasks, duties,and responsibilities o multiple tasks in a specific work cell or work area

[14]. Worker assignment and involvement within a labor-intensive cellis a major role in the perormance o the cell [17]. Te first model assignsmulti-skilled workers to existing cells while the second model finds theoptimal operator assignment within a cell [15]. Te perormance othe workers can be determined rom the arena simulation tools to takean action in line with the other techniques and tools presented in theprevious researches.

Te problem observed in this case company is the lack o expertsand variation on processing the PVC pipe in adjusting the heattreatment and low capacity utilization o the workshop which causes

variation to the specified product. During this, the number o recycledproducts is higher per days. Te industry can ail to achieve the goalor efficient and economical production. Capacity includes all resources

such as machineries, workers etc. o the actory.Tereore, the objective o this paper is to provide industry with a

complete set o tools, techniques and procedures to allow examining oexisting workers and machine perormance systems. Tese techniques

*Corresponding author: Kassu Jilcha, Addis Ababa University, Addis Ababa

Institute of Technology, Addis Ababa, Ethiopia, Tel: +251 913 01774; E-mail:

[email protected]

ReceivedMay 05, 2015; AcceptedMay 18, 2015; PublishedMay 20, 2015

Citation:Jilcha K, Berhan E, Sherif H (2015) Workers and Machine Performance

Modeling in Manufacturing System Using Arena Simulation. J Comput Sci Syst Biol

8: 185-190. doi:10.4172/jcsb.1000187

Copyright: 2015 Jilcha K, et al. This is an open-access article distributed underthe terms of the Creative Commons Attribution License, which permits unrestricted

use, distribution, and reproduction in any medium, provided the original author and

source are credited.

Abstract

This paper deals with the workers and machine performance measurements in manufacturing system. In

simulating the manufacturing system, discrete event simulation involves the modeling of the system as it improves

throughput time and is particularly useful for modeling queuing systems. In modeling this system, an ARENA simulation

model was developed, veried, and validated to determine the daily production and potential problem areas for the

various request levels in the case company (Ethiopia Plastic Factory). The results obtained show that throughput

time in the existing system is low because of occurrence of bottlenecks, and waiting time identied. Therefore,

some basic proposals have been drawn from the result to raise awareness of the importance of considering human

and machine performance variation in such simulation models. It presents some conceptual ideas for developing a

worker manager for representing worker and machine performance in manufacturing systems simulation models.The company workers and machine performance level is raised by identifying the bottle neck area. They were

recommended to amend the main basic bottle necks identied.

Workers and Machine Performance Modeling in Manufacturing System

Using Arena SimulationKassu Jilcha*, Esheitie Berhan and Hannan Sherif

Addis Ababa University, Addis Ababa Institute of Technology, Addis Ababa, Ethiopia
http://dx.doi.org/10.4172/jcsb.1000187http://dx.doi.org/10.4172/jcsb.1000187


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Citation: Jilcha K, Berhan E, Sherif H (2015) Workers and Machine Performance Modeling in Manufacturing System Using Arena Simulation. J

Comput Sci Syst Biol 8: 185-190. doi:10.4172/jcsb.1000187


helps in applying simulation system model which could be used asbeore an existing system is altered or a new system built, to reducethe chances o ailure to meet specifications, to eliminate unoreseen

bottlenecks, to prevent under or over-utilization o resources, and tooptimize system perormance.

Material and Methods

Te study was conducted by considering different materials

and methods to achieve the goal o this study. Te literature reviews

and arena sofware applications were utilized to come up with good

solution. Simulation, in particular discrete event simulation, has

still not gain industries wide acceptance as decision support tool or

perormance evaluation. Te researchers have provided the example o

the application o discrete event simulation in evaluating perormance

o a production line in the case company. Te data was collected rom

an Ethiopian Plastic industry production line and the simulation model

is built using arena sofware simulation. A simulation model providesa visual animation o the line to see how product will flow through

the line. An ARENA simulation model was developed, verified, and

validated to determine the daily production and potential problem

areas or the various production levels in the plastic industry.

Discussion and Results

Production process flow

In general, there are 5 main workshops in Ethiopia plastic industry.Raw materials in the orm o garden hose and master batch are supplied byoreign countries like Asia and in domestic like Elsewady Cables Ethiopiaand directed to raw material store or storing and quality checking.

Tey will be sent to two operating process continuous and injectionsection and turn on heat treatment and take the melted plastic withscrew thread then orced into mold. Te bundle will be prepared byhauloo. Afer the product is finished it will be inspected and thenpackaging will be done. Finally; the product will be kept in finishingstorage as shown in Figure 1. Te other process is continues (extrusion)process flow which begins at raw material receiving, and balling unitmachine as indicated by Figure 2.

Data analysisTe collected data through the means o interviews, direct

observation and company document review were analyzed. FittingInput Distribution through the input analyzer is used to identiy fittedstatistical distribution [18]. It is used to evaluate the distributions

Receiving

production

orders

Raw material

RequisitionProperly

mounting mold

Machine

setup

parameters

Full hopper with

raw materialTurn on

heater

Turn on motor

granule plasticmelted and move

screw thread

Open molted and

product take off

Meltedplastic

Finished

product

Packing,

labeling,

stamping

ShippingQuarterly

checked

yes

No

Recycle

Reject

Take corrective action

Figure 1:Injection process ow.

Raw material (garden

hose & master batch

receiving from store)

Mini storeFilter and

stablizerMixer

Spine

conveyor

HopperExtruder

machine

Vacuum

tank

Cooling

tankNumbering stamp

machine tank

Take off

Balling unit

machine

Figure 2:Continuous (extrusion) process ow diagram.


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Model formulation

In modeling design the type o analysis is perormed on workers

and machine perormance. Te products that are selected are the one

those most ofen produced. Tey are considered as one o the main

products o Ethiopia Plastic Industry in this case company. Te working

period in Ethiopia Plastic Industry is five days and a hal day withineight working hour consideration. Tis means the working days rom

Monday to Friday 8:00 working hours and on Saturday 4:00 working

hours are utilized in the company. Te three models or the arena

simulations are workers distribution models, continuous extrusion

models, and injection models as shown in Figures 4-6.

Model verification

Verification assesses the correctness o the ormal representation

o the intended model, by inspecting computer code and test runs, and

perorming consistency checks on their statistics [20]. More specifically,

verification consists in the main o the ollowing activities:

Inspecting simulation program logic.

Perorming simulation test runs and inspecting sample path

trajectories. In particular, in a visual simulation environment

(like Arena), the analyst inspects both code printouts as well as

graphics to veriy (as best one can) that the underlying program

logic is correct.

Perorming simple consistency checks, including sanity checks

as well as more sophisticated checks o theoretical relations hips

among predicted statistics.

In simulation modeling, each part o model run with different

set o inputs and the obtained outputs were compared by using

throughputs and littles ormula with real outputs.

Model validation

Validation activities are critical to the construction o crediblemodels. Te standard approach to model validation is to collectdata (parameter values, perormance metrics, etc.) rom the systemunder study, and compare them to their model counter parts. Teseparameters will prove the validity o the data and simulation.

Number of replication estimation

A good design o simulation replications allows the analyst toobtain the most statistical inormation rom simulation runs or theleast computational cost. In particular, minimizing the number oreplications and their length is necessary to obtain reliable statistics.In order to decide the number o replication the model must run some

initial set o replication so that sample average, standard deviation andconfidence interval are computed. Tis initial set o replication is shownin able 4.

parameter and calculates a number o measures o the data. o selectwhich type o distribution to use, the authors have compared thesquare error o each distribution. Te larger the square error value, the

urther away the fitted distribution is rom the actual data. Te data wasanalyzed by using real recorded time rom the operation areas o theselected product in the case company section. Tese data supported theanalysis o validation, verification and number o replication estimationas discussed in the next sections [7].

Model assumption

In Ethiopia Plastics Industry, there are three shifs per day. Workersdistribution through the specified time per shifs can be delayed bydifferent kind o incidents. Te actual working time or whole systemis 8:00 working hours per day. Since it is not expected that a personwill work without some interruptions, the operators may take time ortheir personal needs. Assumptions are taken or modeling the variation

o workers perormance at time to rest, machine ailure, and poweroff. Te model or one shifs are modeled and analyzed. In the studyonly polyvinyl chloride (PVC) pipe line is selected. Raw material isassumed as a constant input, no interruption o operation is occurred incontinuous and random or injection. Te manuacturer working timeis 8:00 working hours per day. Distribution is fitted to input analyzer;it evaluates the distributions parameter and calculates a number omeasures o the data. In order to select which type o distribution isused, the author has compared the square error o each distribution.Te larger the square error value, the urther away the fitted distributionis rom the actual data (19). Tereore the ollowing fit all summaryorders in worker perormance distribution rom smallest to largestsquare error. From the table it can be seen that triangular is the onewith smallest square error and thus it is selected. Line indicates that the

data normal distribution and the blocks are the actual datas situationhistogram expression when compared to the normal distribution. Tenormal distribution is skewed to the right (ables 1-3, Figure 3 [18,19]).

s/n Process Distribution Square error

1 Raw material requisition 3.5+3 BETA (0.3847, 0.648) 0.023693

2 Machine set up 4.5+3 BETA (0.896, 0.979) 0.004202

3 Hopper 3.5+3 BETA (1.05, 0.7336) 0.012719

4 Turn on heater 5.5+3 BETA (11.76, 2.47) 0.000290

5Turn on motor granular plastic

melted move to screw thread22.5+3 BETA (11.16, 1.52) 0.001000

6 Melted plastic forced into mold 5.5+GAMM (0.663, 22.87) 0.011748

7 Takeoff 4.5+5 BETA (0.928, 11.35) 0.019469

8 Package 6.5+4 BETA (0.996, 1.44) 0.002769

Table 1:PVC pipe process time distribution in injection.

S/n Continuous (extrusion) Distribution Square

1 Workers distribution TRIA (5.5, 6.8, 7.5) 0.00473

Table 2:Workers distribution in continuous (extrusion).

S/n Process Distribution Square error

1 Mixer 9.5+11 BETA (0.789, 0.848) 0.000365

2 Hopper 4.5+6 BETA (1.37, 0.815) 0.000534

3 Extruder 1.5+2 BETA (1.33, 1.42) 0.000121

4 Vacuum 4.5+WEIB (0.873, 1.9) 0.003243

5 Cooling 3.5+4 BETA (1.52, 0.678) 0.001297

6 Number of stamps TRIA (1.5, 3.2, 4.5) 0.00112

7 Takeoff 2.5+4 BETA (0.934, 0.903) 0.0001232

8 Balling 9.5+6 BETA (0.935, 0.836) 0.001245

Table 3:PVC pipe process time distribution in continuous (extrusion).

Figure 3:Input analyzer distribution histogram.


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Figure 4: Workers distribution model.

Figure 5:Continuous extrusion model.

Figure 6: Injection model.


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For PVC pipe continuous extrusion production line initialreplication (no) is 6 and the initial hal width (ho) is 21.40. Assumingthat the h= 0.25, taking 95% Confidence Level.

DF= n-1= 6-1= 52

2

21,1 / 2

sn t n a

h

2

2

2

3.97n 6 1,1 0.05 / 2

0.25t

2 22

2 2

3.97 3.97n 0.025, 5 (2571)2 * 1, 666

0.22 0.25t =

By considering this equation the number o replications is 1,666

Conclusion

In this study worker and machine perormance in manuacturingsystem using simulation has been used. Te simulation is done by usingArena sofware. Te perormance measure used is throughput and it isdirectly related to waiting time; work in process, resource or capacityutilization. Simulation models were built or the continuous (extrusion)and injection workshops separately and finally a model is preparedor the purpose o conducting the computer based simulation. Teproblems identified are the throughput time rom the existing system islow because o occurrence o bottlenecks, and waiting time identified.Workers agent should be assigned on the machinery and workersperormance to ocus on each operating system due that the numbero recycle products can be reduced. Otherwise, the company continues

like this or a long time and it will be difficult or them to compete intodays market. Tereore, to improve the existing perormance o thecompany, resource utilization improvement is a mandatory.

References

1. Suer GA (1996) Optimal Operator Assignment and Cell Loading in Labor-

Intensive Manufacturing Cells. Computers & Industrial Engineering 31: 155-

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137-147.

Workshop Replication Number out (hr) Total time (hr) WIP per (hr)

Continues (extrusion )

1 1.903 0.4014 0.7691

2 1.909 0.4484 0.8588

3 1.904 0.4697 0.8977

4 1898 0.4014 0.6691

5 1899 0.7484 0.8588

6 1.904 0.5497 0.9977

Mean 1,902.83

Half width 21.40

Standard deviation 3.970

Injection mold

1 2.424 9.5589 26.134

2 2.453 7.3193 19.4321

3 2.447 8.2891 23.0371

4 2.460 6.5589 22.897

5 2.452 7.2165 15.465

6 2.448 8.4356 25.786

Mean 2,447.33

Half width 34.84


Workers shift time

1 150 2.9167 0.4404

2 151 2.9167 0.4413

3 151 2.196 0.4420

4 151 2.134 0.4303

5 151.40 2.5674 0.4405

6 151.33 2.214 0.412

Mean 150.95

Half width 1.08


Table 4:Number of replication.
http://dx.doi.org/10.4172/jcsb.1000187http://www.sciencedirect.com/science/article/pii/0360835296001015http://www.sciencedirect.com/science/article/pii/0360835296001015http://www.sciencedirect.com/science/article/pii/0360835296001015http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117837&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117837http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117837&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117837http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117837&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117837http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fwww.researchgate.net%2Fprofile%2FJuhani_Heilala%2Fpublication%2F228359022_Use_of_simulation_in_manufacturing_and_logistics_systems_planning%2Flinks%2F0c96051d19c9d95231000000.pdf&ei=gE5bVcneBceWuASzl4KQDQ&usg=AFQjCNGtn9gd5w4ephzBnA8L7KVHRIsW4A&bvm=bv.93756505,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fwww.researchgate.net%2Fprofile%2FJuhani_Heilala%2Fpublication%2F228359022_Use_of_simulation_in_manufacturing_and_logistics_systems_planning%2Flinks%2F0c96051d19c9d95231000000.pdf&ei=gE5bVcneBceWuASzl4KQDQ&usg=AFQjCNGtn9gd5w4ephzBnA8L7KVHRIsW4A&bvm=bv.93756505,bs.1,d.c2E&cad=rjahttp://www.springer.com/in/book/9780387964676http://www.springer.com/in/book/9780387964676http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fprt2.uprm.edu%2Fdde%2F2001%2Ffinalreports02%2Ffrancisco_final_report_may02.pdf&ei=6lFbVdCPNdWOuAT8rIHABw&usg=AFQjCNHay1pR7iu0zPLd6NE0ae4UqUncSA&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fprt2.uprm.edu%2Fdde%2F2001%2Ffinalreports02%2Ffrancisco_final_report_may02.pdf&ei=6lFbVdCPNdWOuAT8rIHABw&usg=AFQjCNHay1pR7iu0zPLd6NE0ae4UqUncSA&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fprt2.uprm.edu%2Fdde%2F2001%2Ffinalreports02%2Ffrancisco_final_report_may02.pdf&ei=6lFbVdCPNdWOuAT8rIHABw&usg=AFQjCNHay1pR7iu0zPLd6NE0ae4UqUncSA&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.gsb.stanford.edu/faculty-research/working-papers/evolutionary-model-organizational-performancehttp://www.gsb.stanford.edu/faculty-research/working-papers/evolutionary-model-organizational-performancehttp://www.sciencedirect.com/science/book/9780123705235http://www.sciencedirect.com/science/book/9780123705235http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117833&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117833http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117833&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117833http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117833&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117833http://www.sciencedirect.com/science/article/pii/0925527395001727http://www.sciencedirect.com/science/article/pii/0925527395001727http://www.sciencedirect.com/science/article/pii/0925527395001727http://www.sciencedirect.com/science/article/pii/0925527395001727http://www.sciencedirect.com/science/article/pii/0925527395001727http://www.sciencedirect.com/science/article/pii/0925527395001727http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117833&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117833http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117833&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117833http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4117833&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4117833http://www.sciencedirect.com/science/book/9780123705235http://www.sciencedirect.com/science/book/9780123705235http://www.gsb.stanford.edu/faculty-research/working-papers/evolutionary-model-organizational-performancehttp://www.gsb.stanford.edu/faculty-research/working-papers/evolutionary-model-organizational-performancehttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fprt2.uprm.edu%2Fdde%2F2001%2Ffinalreports02%2Ffrancisco_final_report_may02.pdf&ei=6lFbVdCPNdWOuAT8rIHABw&usg=AFQjCNHay1pR7iu0zPLd6NE0ae4UqUncSA&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fprt2.uprm.edu%2Fdde%2F2001%2Ffinalreports02%2Ffrancisco_final_report_may02.pdf&ei=6lFbVdCPNdWOuAT8rIHABw&usg=AFQjCNHay1pR7iu0zPLd6NE0ae4UqUncSA&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fprt2.uprm.edu%2Fdde%2F2001%2Ffinalreports02%2Ffrancisco_final_report_may02.pdf&ei=6lFbVdCPNdWOuAT8rIHABw&usg=AFQjCNHay1pR7iu0zPLd6NE0ae4UqUncSA&bvm=bv.93564037,bs.1,d.c2E&ca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Citation: Jilcha K, Berhan E, Sherif H (2015) Workers and MachinePerformance Modeling in Manufacturing System Using Arena Simulation. J

http://dx.doi.org/10.4172/jcsb.1000187http://www.springer.com/in/book/9780857291387http://www.springer.com/in/book/9780857291387https://rucore.libraries.rutgers.edu/rutgers-lib/21312/https://rucore.libraries.rutgers.edu/rutgers-lib/21312/http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fijme.us%2Fcd_11%2FPDF%2FPaper%2520188%2520INT%2520301.pdf&ei=cFVbVYOeIsGiugTA2ICQCQ&usg=AFQjCNEFf3zQAWkrv5MyWZRv-_G_7dshVg&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fijme.us%2Fcd_11%2FPDF%2FPaper%2520188%2520INT%2520301.pdf&ei=cFVbVYOeIsGiugTA2ICQCQ&usg=AFQjCNEFf3zQAWkrv5MyWZRv-_G_7dshVg&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fijme.us%2Fcd_11%2FPDF%2FPaper%2520188%2520INT%2520301.pdf&ei=cFVbVYOeIsGiugTA2ICQCQ&usg=AFQjCNEFf3zQAWkrv5MyWZRv-_G_7dshVg&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttps://vtechworks.lib.vt.edu/handle/10919/26386https://vtechworks.lib.vt.edu/handle/10919/26386https://vtechworks.lib.vt.edu/handle/10919/26386https://vtechworks.lib.vt.edu/handle/10919/26386http://www.sciencedirect.com/science/article/pii/S1367578803000300http://www.sciencedirect.com/science/article/pii/S1367578803000300http://www.sciencedirect.com/science/article/pii/S1367578803000300http://dl.acm.org/citation.cfm?id=27111http://dl.acm.org/citation.cfm?id=27111http://iiesl.utk.edu/Courses/IE406%20S07/Slides/Statistical%20Distributions.pdfhttp://dx.doi.org/10.4172/jcsb.1000187http://dx.doi.org/10.4172/jcsb.1000187http://iiesl.utk.edu/Courses/IE406%20S07/Slides/Statistical%20Distributions.pdfhttp://dl.acm.org/citation.cfm?id=27111http://dl.acm.org/citation.cfm?id=27111http://www.sciencedirect.com/science/article/pii/S1367578803000300http://www.sciencedirect.com/science/article/pii/S1367578803000300http://www.sciencedirect.com/science/article/pii/S1367578803000300https://vtechworks.lib.vt.edu/handle/10919/26386https://vtechworks.lib.vt.edu/handle/10919/26386https://vtechworks.lib.vt.edu/handle/10919/26386https://vtechworks.lib.vt.edu/handle/10919/26386http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fijme.us%2Fcd_11%2FPDF%2FPaper%2520188%2520INT%2520301.pdf&ei=cFVbVYOeIsGiugTA2ICQCQ&usg=AFQjCNEFf3zQAWkrv5MyWZRv-_G_7dshVg&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fijme.us%2Fcd_11%2FPDF%2FPaper%2520188%2520INT%2520301.pdf&ei=cFVbVYOeIsGiugTA2ICQCQ&usg=AFQjCNEFf3zQAWkrv5MyWZRv-_G_7dshVg&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttp://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB0QFjAA&url=http%3A%2F%2Fijme.us%2Fcd_11%2FPDF%2FPaper%2520188%2520INT%2520301.pdf&ei=cFVbVYOeIsGiugTA2ICQCQ&usg=AFQjCNEFf3zQAWkrv5MyWZRv-_G_7dshVg&bvm=bv.93564037,bs.1,d.c2E&cad=rjahttps://rucore.libraries.rutgers.edu/rutgers-lib/21312/https://rucore.libraries.rutgers.edu/rutgers-lib/21312/http://www.springer.com/in/book/9780857291387http://www.springer.com/in/book/9780857291387http://dx.doi.org/10.4172/jcsb.1000187

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Workers and Machine Performance Modeling in Manufacturing