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U MEÅ U NIVERSITY

M

ASTER

T

HESIS

Comparing Two Production Lines Using Simulation

Author:

Tim FORSBERG& Erik KARLSSON

Supervisor:

Markus ÅDHAL

A thesis submitted in fulfillment of the requirements for the degree of Master in Science

at

Umeå University

June 23, 2021

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iii

UMEÅ UNIVERSITY

Abstract

Department of Mathematics and Mathematical Statistics Umeå University

Master in Science

Comparing Two Production Lines Using Simulation by Tim FORSBERG& Erik KARLSSON

In order to reduce material shortage of doors in production, the current production processes needs adjusting. Currently when the buffer between the Mainline and the Door area is full the production in the unit stops. This is a problem that should not happen.

To circumvent this a new concept was produced and tested with simulation in order to compare the current state with the new concept model. To achieve this, data has been gathered and analyzed to create a model that is a close approximation of reality. Using the same data input, an alternative solution was tested on two variations of the concept model. The alternative solution showed that the material shortage occurred less frequently in the concept models. The result showed that the material shortage can be drastically reduced if one implements the concept model.

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iv

Sammanfattning

För att minska materialbristen på dörrar i produktionen måste den nuvarande produktionsprocesserna justeras. För närvarande när bufferten mellan Mainline och dörrområdet är full stoppas produktionen i enheten. Detta är ett problem.

För att kringgå detta producerades och testades ett nytt koncept med simulering för att jämföra det nuvarande tillståndet med den nya konceptmodellen. För att up- pnå detta har data samlats in och analyserats för att på så sett skapa en modell som är en nära approximation av verkligheten. Med samma data testades en alternativ lösning på två varianter av konceptmodellen. Den alternativa lösningen visade att materialbristen inträffade mindre ofta i konceptmodellerna. Resultatet visade att materialbristen kan minskas drastiskt om man implementerar konceptmodellen.

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Contents

Abstract iii

Sammanfattning iv

1 Introduction 1

1.1 Volvo Group Trucks. . . 1

1.2 Background . . . 1

1.2.1 Volvo Group Trucks in Umeå . . . 1

1.2.2 BIW. . . 2

1.2.3 Mainline . . . 2

1.2.4 PPP . . . 3

1.2.5 Current production flow . . . 3

1.2.6 CKD . . . 3

1.2.7 The Door Area . . . 3

1.3 Purpose. . . 3

1.4 Objectives . . . 3

1.5 Delimitations . . . 4

2 Theory 5 2.1 Discrete-event Modelling . . . 5

2.2 Pros and Cons of Simulation. . . 5

2.3 Evoma AB & FACTS Analyser. . . 5

2.4 Bottleneck Analysis . . . 6

2.4.1 Bottleneck analysis using shifting bottleneck detection . . . 6

Shifting bottleneck algorithm . . . 7

2.5 Calculation of P-value . . . 7

2.6 Expected Shortfall. . . 8

2.7 Lognormal Distribution . . . 8

2.8 Exponential Distribution . . . 9

3 Method and Data 11 3.1 The Door Area . . . 11

3.1.1 As Is . . . 11

3.1.2 Concept model . . . 13

3.2 Simulation Comparison . . . 14

3.3 Method of Work . . . 14

3.4 The Modeling Process . . . 15

3.4.1 Problem Formulation . . . 15

3.4.2 System Definition. . . 16

3.4.3 Input Data Collection and Analysis . . . 16

3.4.4 Model Translation . . . 16

3.4.5 Verification . . . 16

3.4.6 Validation . . . 16

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vi

3.4.7 Analysis . . . 16

3.5 DUGA - General Manufacturing Monitoring . . . 17

3.6 Data Selection . . . 17

3.7 Specific Loss Analyses . . . 17

3.7.1 MTBF and MTTR . . . 18

3.7.2 Defining a disturbance . . . 18

3.7.3 Long and short disturbances . . . 19

3.8 Distribution identification using Minitab . . . 19

3.8.1 Probability, Histogram and CDF plot for V1 MTBF . . . 20

3.8.2 Probability, Histogram and CDF plot for V1 MTTR . . . 22

3.8.3 Probability, Histogram and CDF plot for V3 MTBF. . . 23

3.8.4 Probability, Histogram and CDF plot for V3 MTTR . . . 25

3.9 Issues Fitting The Distributions . . . 26

4 Result 29 4.1 As Is Model . . . 29

4.2 Concept Model . . . 30

4.3 Bottleneck . . . 30

4.4 Scenario Analysis . . . 31

4.5 Disturbance in Production . . . 32

4.5.1 Expected shortfall . . . 32

5 Analysis 33 5.1 Conclusion . . . 33

5.2 Implementation . . . 34

5.3 Continuations . . . 34

A Extended Reading 37 A.1 Presentation For Production Management . . . 37

Bibliography 45

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vii

List of Figures

1.1 Overview of factory. . . 2

1.2 Flow chart of BIW . . . 2

2.1 FACTS Model page . . . 6

2.2 Lognormal Distribution . . . 9

2.3 Exponential Distribution . . . 10

3.1 Door Concept . . . 11

3.2 Door Model . . . 12

3.3 Door Concept Model . . . 13

3.4 Trend analysis . . . 17

3.5 MTBF . . . 18

3.6 MTTR . . . 18

3.7 MTBF Distribution V1 . . . 20

3.8 MTBF Histogram V1 . . . 21

3.9 MTBF CDF V1 . . . 21

3.10 MTTR Distribution V1 . . . 22

3.11 MTTR Histogram V1 . . . 22

3.12 MTTR CDF V1. . . 23

3.13 MTBF Distribution V3 . . . 23

3.14 MTBF Histogram V3 . . . 24

3.15 MTBF CDF V3 . . . 24

3.16 MTTR Distribution V3 . . . 25

3.17 MTTR Histogram V3 . . . 25

3.18 MTTR CDF V3. . . 26

4.1 Door Model As Is . . . 29

4.2 Door Model Concept . . . 30

4.3 Bottleneck . . . 30

4.4 BottleneckAsIs. . . 31

4.5 Percentile Plot As Is. . . 32

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List of Abbreviations

BIW Body In White

CDF Cumulative Distribution

CKD Completely Knock-downed Down GTP Group Trucks Purchasing

GTO Group Trucks Operations GTT Group Trucks Technology ML MainLine

MOO Multi-Objective Optimization MTBF Mean Time Before Failure MTTR Mean Time To Repair OA Operational Area

PPP Pressing (and) Parts Production WIP Work In Progress Function

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1

Chapter 1

Introduction

1.1 Volvo Group Trucks

In 1927 Volvo Group Trucks was founded and is part of the Volvo Group. Volvo Group Trucks is one of the world’s largest truck manufacturers, with nine assem- bly plants worldwide. Volvo Group Trucks includes three division, Group Trucks Technology (GTT), Group Trucks Operations (GTO) and Group Trucks Purchasing (GTP). Volvo GTT is the organization responsible for global technology and product development related to truck operations. Volvo Trucks GTO covers all production of the group’s engines, transmissions and trucks, as well as parts supply and lo- gistics. The third department, Volvo Trucks GTP, is a functional department of the global group, covering the procurement of automatic products and parts (including aftermarket) of all truck brands in the Volvo Group.

The Volvo Trucks brand focuses on safety, quality and environmental sustainabil- ity, with ambitions to become the world’s leading manufacturers of trucks, buses, construction equipment and marine and industrial engines

1.2 Background

1.2.1 Volvo Group Trucks in Umeå

The Volvo Group’s plant in Umeå produces the cabs of Volvo heavy trucks, which consist of three main operational areas; OA2, OA3 and OA4. The first unit OA2, Pressing and Parts Production (PPP), is the production location of all parts of the cab body, including the entire mature process from sheet metal to complete parts. In OA3, Body In White (BIW), components from OA2 are matched and assembled to form a complete cab body. The OA3 production unit is designed as a central trunk line in the fishbone factory concept, with multiple substreams on both sides. The last production unit of the Umeå plant is the paint shop OA4, where surface treatment and final color coating are carried out. OA4 is the final process before the cab is transported to the factory in Tuve or Gent for assembly of the chassis and to finally be delivered to the customer, see Figure1.1.

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2 Chapter 1. Introduction

FIGURE 1.1: Overview of the factory including all the operational areas.

1.2.2 BIW

BIW is where the cab components are assembled to form the main body of the cab.

The main part of the unit is the Mainline, and the attached sideline is a fishbone structure, see Figure1.2. After passing through the main line, the cab passes through three sides, with doors, front covers and trunk covers installed respectively. The final part of the BIW unit is the Finishline. This is a straight flow, composed of four segments, in which the main body of the cab is completed and the quality is carefully guaranteed. The different parts of the finishline are often refered to as Segments, for example Finishline 3 is often refered to as Segment 3. In contrast to the Mainline and its almost fully automated sub-processes, the Finishline and the three side departments of the door and covers are manual processes.

FIGURE1.2: Flow chart of the automated part of the BIW area.

1.2.3 Mainline

The Mainline includes five subsequent areas: ML1, ML2, ML3, ML4, and ML5, which are divided into several different security units in turn, called the V area.

If one robot in the V area fails, the entire unit will be shut down before the operator can perform maintenance work. The Mainline is direct, all taxis pass through all stations, and there is no parallel process inside the station, see Figure1.2.

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1.3. Purpose 3

1.2.4 PPP

PPP is the production area where the metal coils are cut, stamped and where all parts of the cab body are produced. The PPP consists of the full maturing process from sheet metal to complete components. These components are used to produce the cab in the BIW area but also where individual parts are shipped through the so called Completly Knocked Down (CKD) market to different parts of the world for subassembly.

1.2.5 Current production flow

Volvo Group Trucks provides each customer with the opportunity to customize trucks to suit all possible needs. Considering all the different characteristics of the cab, the factory must be able to produce endless cab variants. When the order is received, the cab must be produced and delivered within the agreed ten days. The variant of the cab depends on the color, height, length, engine type, gear unit, design and other attributes. From a production point of view, the biggest variant difference is the difference between the old and new cab. FM and FH. In OA2, the parts are produced according to order sequence, but both OA3 and OA4 have pull systems and the production of cabs starts when orders are received. The production order of the BIW in OA3 is determined daily according to the priority order, where the priority order is the delivery date and the delivery order required by the customer.

1.2.6 CKD

On top of the standard production for the plant there is also a production of body kits called CKD. These parts are produced in the standard production lines and is a part of the production sequence. Before arriving at the mainline parts are taken out and placed in racks. These parts are then sent to other plants around the world for further assembly.

1.2.7 The Door Area

One of these subassemblys in the fishbone concept is the door area. All doors used in the production comes through this area where the inner and outer door from PPP are merged and then mounted on a cab or is sent to CKD. The door area consists of two sides where the left and right door is produced. The left side is split into two security units V1 and V3. The right side is split into V2 and V4.

1.3 Purpose

Using simulation in FACTS analyzer to test an alternative production setup for when the old model is no longer produced, and using Risk measures to analyze the risk of interruptions in production.

1.4 Objectives

Creating two separate simulations of the door area in collaboration with supervi- sors from Volvo and comparing these to find the benefits and drawbacks to both alternatives.

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4 Chapter 1. Introduction

• Is the new model a feasible alternative?

• Can a change in the buffer placement in the production reduce the backlog?

• How does the removal of production sequence affect the production?

• What are the risks in both models?

1.5 Delimitations

In the simulation model only the left door area will be simulated. The right door area is a slightly simpler mirrored production flow since the driver is on the left side in a majority of produced cabs. Since the goal is to compare two different models some assumptions are made regarding complex factors inside the models. There is enough materials coming into the model, trucks are available to transport racks between the areas instantly. The only factor stopping Finishline 3 is the lack of material from the door area, i.e. material shortage. The model will be focused on the cab models FM24b and FHP29, excluding the cab-models FM24a and FM curb window. This is because only a few of these are produced each month, and therefore they will have a small impact. The production of FM24a will reduce as time passes since it is an older model that will be going out of production.

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Chapter 2

Theory

2.1 Discrete-event Modelling

Discrete-event simulation modeling will be used when it is impossible or impractical to conduct experiments on an impractical system due to high cost, system sensitivity, or unrealistic time frame. Simulation can shorten the planning cycle and can be used during equipment planning, implementation and operation.

For this project FACTS analyzer will be used when creating a model of the logistic system It is a discrete event simulation program created by Evoma AB. The program simulates a given production system and allows the use of a wide range of analysis tools to evaluate different manufacturing scenarios (Evoma, 2021).

Both BIW and PPP have a production process composed of separate worksta- tions, so discrete event simulation is considered a suitable simulation method.

2.2 Pros and Cons of Simulation

As mentioned above, there are several advantages to using simulation. Complex systems can be simulated within a given time frame, and multiple scenarios of each simulation can be run to test systems with a large number of random changes. An- imation tools that help visualize the simulation model can also be used to easily demonstrate the system flow. It can also display several operations and interactions at the same time, which helps users to analyze the model and its credibility (Chung, 2003, s.177–196).

No matter how good the model is, if it does not have accurate input data, practi- tioners will not be able to reasonably obtain an accurate output. Unfortunately, data collection is considered as the most difficult and time consuming part. Despite this, too little time is usually allocated in this process. Many practitioners may prefer to develop a model instead of collecting mundane data. This induce many simula- tion practitioners to accept historical data of dubious quality in order to save time for data collection. Many belive that simulation is the ultimate solution for a given problem. However simulation alone does not really solve the problem. It provides the user with a potential solution to the problem that later kan be presented to man- agement. It is then up to them to decide whether or not to implement the proposed changes (Chung,2003, p.24).

2.3 Evoma AB & FACTS Analyser

Evoma AB is a Swedish company focusing on developing their flagship, FACTS Analyser which is a discrete-event simulator used for optimization in production

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6 Chapter 2. Theory

flows. Evoma AB also offer courses on how to use their software in adition to con- sulting services for production flow optimization (Evoma,2021).

FACTS Analyser is the software created by Evoma AB and stands for Factory Anal- yses in ConcepTual phase using Simulation. FACTS use different objects divided into two categories to create simulations. The two objects are location-based and information-based objects. The location-based objects include source, buffers and operations while the information-based include timetable, orders, MaxWIP and more.

The objects are used to create the simulation in the Model tab and once the simula- tion is functional there are two more tabs to analyse its performance. The Animation tab can be used to see a real time animation of the model and the Experiment tab is where you can run experiments and simulation optimizations. These experiments can calculate the throughput, lead time and more for the simulateion on top of the utilization and occupation of individual operations, see Figure2.1.

FIGURE2.1: The Animation page from FACTS Analyser.

2.4 Bottleneck Analysis

When evaulating the model a bottleneck analysis will be performed. This will make it easier to find specific workstations or buffers that might cause bottlenecks if one wants to implement the model in the real world.

Finding a bottleneck is not trivial, the easiest way of doing this is by simply go to the production floor and ask the employees. Since the Door area is almost fully automated this can be a bit tricky (Roser and Tanaka, 2001, p.949-953). Instead, bottlenecks will be identified by looking at the different workstations status and compare them to each other.

2.4.1 Bottleneck analysis using shifting bottleneck detection

Shifting bottleneck detection was developed by the Toyota Software Laboratory in early 2000 (Roser et al., 2002). It defines the machine with the longest average active

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2.5. Calculation of P-value 7

period as the bottleneck. During production, the machines in a production line alter state over time. The different states: working, failed, setup, waiting, and blocked are logged together with information about breaks and unplanned activities in or- der to perform the shifting bottleneck analysis. The different states are grouped into active and in-active periods, where the states working, failed, and setup are con- sidered active. The momentary bottleneck is the machine with the longest active period. If there is an overlap between two consecutive bottlenecks, the overlap pe- riod is marked as a shifting bottleneck period and both bottlenecks are considered momentary bottlenecks during the shifting period.

Shifting bottleneck detection is the proportion of time the operation has been considered being a bottleneck. The momentary bottleneck is measured for the op- erations and an active state is considered to be “Processing, “Setup” and “Failed”

(Roser and Tanaka,2001, p.152).

Shifting bottleneck algorithm

FACTS uses the following algorithm when looking for shifting bottlenecks.

1. Initialization

• M0= (scheduled machines)

• G = only conjuctive arcs (represent sequence of jobs on a machine)

• Cmax= critical path in G

2. (Choice of machine.) For each Mi ∈ M−M0,

• generate the 1|rj|Lmaxschedule

• compute L|max(i).

3. Scheduling the bottleneck machine

• Let k be the machine that maximizes Lmax(i)

• Schedule k by the 1|rj|Lmaxsolution

• Update G

• M0= M0∪ {k}

4. (Resequence already scheduled machines.) For each MiM0k

• Delete disjunctive arcs for Mi from G

• Form the 1|rj|Lmax

• Reschedule Miaccording to this schedule 5. If M= M0stop, else go to 2

2.5 Calculation of P-value

There are multiple different test statistics that can be utilized for testing hypothesis.

Given an observed test statistic t from a unkown distribution T then the P-value is:

p= P(|T| > |t||H0)

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8 Chapter 2. Theory

The P-value is the value that indicates probability of achiving an effect that is at least as extreme as the effect in the sample data under the assumption that the null-hypothesis can not be rejected (Rice,1989). The size of the P-value indicates the degree of compatibility between the observed data and the hypothetical distribution, which can be used to estimate the fit of observed data to a statistical distribution.

In this thesis the software Minitab will be used to perform a goodness of fit test for the observed data to try and fit distributions to the data. Minitab uses Anderson- Darling goodness-of-fit statistic to produce a P-value. This is done by squaring the difference between the observed data and the hypothesized distribution with addi- tional weight added to the tails (Anderson and Darling,1954, pp. 765–769).

2.6 Expected Shortfall

A popular risk measure is Value at Risk (VaR) which is defined as the worst loss for a given time period at a confidence level. VaR does not say anything about the losses that exceed this confidence level.

Expected Shortfall (ES) is a risk measure that is used to estimate the average worst outcomes of an event in a given quantile, it is mainly used to asses the financial risk of an investment. ES is the expected loss given that it is larger than VaR (Hull, 2015, p.1103) .

Let L denote the loss then

ES100α%(L) = E[L|L>VaR100α%(L)]=(1−α)1∗E[L∗l>VaR100α%(L) One problem with ES is that it is diffucult to back-test since it is defined as the average loss given that the loss is greater than the given VaR level. In back-testing, the prediction is generated from a distribution based on historical data (Hull,2015, p.1106). While VaR is not subaddative ES is, because the doorline is divided into workgroups, ES is appropriate to use for addition of different individual shortfalls.

2.7 Lognormal Distribution

A log normally distributed stochastic variable can be written as eX, where X is nor- mally distributed with expectation value µ and standard deviation σ. The variable (X−µ)/σ has a normal distribution with expectation value 0 and standard devia- tion 1, whose distribution function is usually writtenΦ(•). A lognormal distribution variable thus has the following distribution function

F(x) =P(eX≤x) = P(X≤ log(x)) =P(Xµ

σlog(x) −µ

σ ) =Φ(log(x) −µ

σ )

(2.1) The density function is

f(x) = (√ 1

2πσx)exp{log(x) −µσ2

2 )}, x>0 (2.2) See Figure2.2of the distribution plot.

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2.8. Exponential Distribution 9

FIGURE2.2: Distribution plot of the lognormal distribution .

(Johansson,2014, pp. 32–33)

2.8 Exponential Distribution

The exponential distribution is a strictly positive and continuous distribution. The exponenital distribution is often used to describe waiting time between events.

f(y) =βeβy, y≥0 (2.3)

Also denoted as:

Y∼Exp(β) (2.4)

(Alm and Britton,2008, p.98) See Figure2.3for the distribution plot of the exponential distribution.

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10 Chapter 2. Theory

FIGURE2.3: Distribution plot of the exponential distribution .

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Chapter 3

Method and Data

3.1 The Door Area

In this section the work process of the Door area is described. First, a visualisation of the current flow is shown, Every step, from start to finish, will be shown and from this a model in FACTS will be created. The second part of this section will show an illustration of the new concept for the workflow. Through meeting with stakeholders involved a desired concept has been developed. This is based on identifying current problems with the Door area and adapting the model to eliminate these.

A recurring problem is that there is a risk of material shortages for Segment 3, this is due to the doors being produced in sequence and placed in a conveyor. Once the door is in it, it is not possible to pick it out. This means that a defective door must be mounted on the cab and then go into a repair department, taking both money and time.

For simplification we will reference the current model concept as "As Is" even though there is a small difference.

3.1.1 As Is

The door area is divided into two halves of mirrored parts, with one door for the right side and the other door for the left side. Each side is divided into two work zones V1 and V3, where each consist of a specified number of workstations (K- stations), see Figure3.1for concept illustration.

FIGURE3.1: The concept of the door area as is.

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12 Chapter 3. Method and Data

All doors are produced by an order sequence that is trying to maximize the throughput. The product flow in the door area starts at the source and exits via one of the two red sinks. One is connected to the buffer zone to the Mainline while the other is to the CKD- market (see Figure3.2).

FIGURE3.2: The door area.

There are two different loading tables in the door area, in Figure 3.2 they are grouped together and is called FH. One table is allocated to FM and the other is for FH. By looking at a tv-screen, the operator knows which model of the cab that will be produced. Before the operator loads the material a robot places the specific fixture on the workbench and the operator will then load it manually. The loaded fixture will then continue to the next station (K24). The parts will be installed on the fixing device until the operation of previous station is completed, then the part is taken to the next station (K14), and the fixing device returns to the turntable. The loading station cannot issue new parts until the fixture returns to its starting position. If the next deformation is not of the same design (FM/FH), the operator can start loading the next part before the fixture returns to the turntable. Each side has two zones V1 and V3, V1 ends where the buffer of both FM and FH is located, see Figure3.2. The next zone V3 is where the inner and outer parts of the door are glued together. A source named Outer will provide the outer part to workstation V3K24 and assemble the outer with the inner part that comes from one of the two buffers BufferFM and BufferFH. The last step in V3 is to mount the hinges, after this the door is either placed in a conveyor to Segment 3 or in a rack that goes to the CKD-market. Both the left and right section consist of a total of 52 workstation (i.e. 26 stations for each section ).

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3.1. The Door Area 13

3.1.2 Concept model

The concept model is similar to the current Door area. It is divided into two saftey zones, V1 and V3. It starts with a operator loads a fixture with material, the same operations as in the current model will be performed. The difference in V1 is that there is no sequence in buffer, also the buffers are only for FM24b och FH i.e., the newest models. In V3 the inner and outer parts are glued together, the last step is that a operator mounts the hinges before they are placed in a rack that holds 8 doors.

Each rack is then transported to Segment 3 or to a CKD with a truck, in total there are two racks of each variant both at the Door area and Segment 3.

FIGURE3.3: The concept of a alternative door area.

From Figure3.3a concept is illustrated for the left Door area. Door inner repre- sent V1 and Door Outer V3, the yellow square boxes are a so called 2-bin system, this means that two racks of each variant exist. Which minimizes the risk of material shortage. For a 2-bin system one would need four racks, however but at Volvo’s request, one will study whether it is possible to use fewer racks. Using too many racks requires lot of surface and ties up capital. Therefore, 3 and 4 racks was chosen to study and compare the material shortage.

Below are the outlined differences between As Is and the concept model.

• V1

Focus on filling the buffers.

No sequence.

• V3

Produces in batches.

The doors are loaded in racks, 2-bin.

• Segment 3

No conveyor.

2-bin for door mounting.

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14 Chapter 3. Method and Data

• CKD

If there is no demand for Segment 3, a CKD order is triggered.

Reserve buffer if needed.

3.2 Simulation Comparison

To be able to compare the two different models and how they handle different situ- ations. A scenario analysis is carried out, here three different scenarios will be tested.

For all scenarios the following assumptions have been made:

• A simulations horizon of six days, with one day warm-up

• 3-shifts, a day is divided into three shifts, Production starts at night and ends in the following morning

And for each individual scenario the following:

Scenario 1

• After four days there will be a stop in production lasting eight hours

• Analyse how long until material shortages Scenario 2

• After two days there will be a stop in production lasting 2 hours

• Analyse how long until material shortages Scenario 3

• After one days there will be a stop in production lasting one hours

• Analyse how long until material shortages

In addition to this, the two models and the Concept models variants will be sim- ulated 5000 times (without the predetermined disturbances from the scenarios anal- ysis) to create a percentile plot using MATLAB. These plots will describe the material shortage based on the 5000 replicants of each model. By compiling these plot the re- sult can be studied and compared, where the idea behind these percentile plot is to be able to conclude that one of the models is better than the other.

3.3 Method of Work

Below is a summary of the general method for how the practical work has been structured.

Data analysis

• Find individual cycle times for robots in each station and fit a distribution

• Find individual Mean Time to Repair (MTTR) and availability for robots in each station and fit a distribution

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3.4. The Modeling Process 15

• Determine cycle time, MTTR and availability for the station

• Determine cycle time, MTTR and availability for the restructured station

• Create flow charts for both scenarios Modeling

• Create an initial "As is" model using DUGA data

• Identify current bottlenecks and Work in Progress (WIP)

• Create a Concept model flow with guidance from the Volvo master plan Verification

• Compare "As Is" model to reality using existing data

• Compare variables from Concept model to "As Is" model

• Stable State analysis

• Bottleneck analysis Optimization

• Optimal buffer allocation

• Conduct scenario analysis

• Run experiments in FACTS Analyser

3.4 The Modeling Process

The simulation model will be created using the following steps that are outlined in Simulation Modeling Handbook (Chung,2003, p.20-210),

1. Problem Formulation 2. System Definition

3. Input Data Collection and Analysis 4. Model Translation

5. Verification 6. Validation 7. Analysis

3.4.1 Problem Formulation

The first step will be formulating the problem that will be under investigation. This problem will have a clear goal that can be meassured such as reducing waste, reduc- ing WIP, increasing customer satisfaction or increasing throughput.

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16 Chapter 3. Method and Data

3.4.2 System Definition

After, we need to determine what part of the system to model. Is the system discrete, continuous or a combination of both? How much of a complete system will we model and what components will be included? There also needs to be a decision on what input data is needed and the output data that the model will generate.

3.4.3 Input Data Collection and Analysis

The input data is what drives the simulation. This data needs to be collected and analyzed to see what the reality looks like to then translate it into a simulation. The data will also be fitted into a theoretical distribution to avoid only looking at histor- ical data since the collected data is only a sample from the actual distribution.

3.4.4 Model Translation

The model translation phase is where you take the collected data together with the system definition and make a simulation model in your selected computer program.

3.4.5 Verification

During the model translation phase, the focus is on making the simulation run, dur- ing the verification phase the focus is on making it run the way you want it too. Us- ing animation is a great tool to ensure the simulation runs smoothly since it makes it easy to follow entities path through the model.

3.4.6 Validation

In the validation phase the work is focused on making sure that the created model is a reasonable representation of the real system and is not to be confused with veri- fication.

3.4.7 Analysis

The analysis section in the modeling process gives the practitioner the necessary in- formation to make decision recommendations with the project objectives in mind.

Since manufacturing systems belong to the category of nonterminating systems, where the system is not completely emptied of entities at a regular interwall. The nonterminating system either runs continuously or stops and continues when the next shift or period begins with the entities remaining in place during the break. In the Simulation Modeling Handbook, an outline on how to approach the analysis of a nonterminating system is presented(Chung,2003, p.210):

1. Starting conditions - How the simulation is initialized

2. Determining steady state - Eliminate the nonrepresentative data that is present at the beginning of a simulation

3. Addressing autocorrelation - Analysis of the correlation between successive observation to see the variance

4. Length of replication - How long to run the replication

5. Batching method - Splitting long runs into sections for analysis

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3.5. DUGA - General Manufacturing Monitoring 17

3.5 DUGA - General Manufacturing Monitoring

DUGA is a system used by Volvo Group Trucks for measuring and showing losses in production. The system also shows a view of the line with the current status of machines and buffers, when stopped, alarms can be sent to selected operators. This program collects statistical data of the production line, which makes it easier to an- alyze the production, for example cycle trends, bottlenecks and system losses. This tool let you find historical data for each workgroup, including cycle times, variant descriptions, error codes. Information like mentioned above can easily be exported to an Excel file. When conducting the analysis the cycle time of robot inactivity where studied.

3.6 Data Selection

In a period of 11 weeks, data was collected from DUGA. In order to create the model, the cycle time, MTBF, MTTR, and availability had to be calculated, The data was extracted from the analytic part of DUGA, this data was exported to an Excel file for creation of distributions, cycle time calculations and variability of the robot activity.

FIGURE3.4: Data trend analysis between week 1 and 11, 2021.

In Figure3.4a deviations in week 8 can be seen in the trend analysis (the y-axis represent the cumulative stop time for one week), during all the other weeks the weekly stop time were almost equivalent or under 40 minutes of accumulated stop time. Later, when defining a disturbance the MTBF and MTTR is calculated by filter out the worst cases of failures. However, in order to simulate long-term and rare interference, the entire data set needs to be considered.

3.7 Specific Loss Analyses

There is a section called "Specific Loss Analysis" in DUGA. By using this option, you can select the work area, time period, workstation, etc. from which you want to extract data. The data from this is used to calculate MTBF, MTTR and to define the distributions.

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18 Chapter 3. Method and Data

3.7.1 MTBF and MTTR

MTBF is defined as the mean interval between failures for the separate workstations.

To calculate this, the tool DUGA was used to export the data, based on a time pe- riod of 11 weeks, of each workstation. The mean of all stations was calculated and compiled into a diagram, see Figure3.5.

FIGURE3.5: The mean time before failure for each workstation on the floor line between week 1 and 11 of 2021.

MTTR is defined as the mean duration of the failures. Likewise MTBF, DUGA was used to extract the data for the same time period as MTBF. The mean of all stations was calculated, see Figure3.6

FIGURE3.6: The average time to repair each workstation on the floor line between the 1st and 11th weeks of 2021.

By compiling the two diagrams Figure3.5and Figure3.6, MTBF and MTTR can be obtained and inserted when modeling the two models.

3.7.2 Defining a disturbance

In FACTS you can choose to add a disturbance, and there are three ways of defining it:

• Percent: Define a disturbance by specifying an availablility and a MTTR.

• Distributions: Define a disturbance by specifying separate distributions for the time to repair a machine and the time between failures.

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3.8. Distribution identification using Minitab 19

• Cycles: Define a disturbance by specifying separate distributions for the time to repair a machine and the number of entities that are processed between failures.

In our model we chose to have Percent, Distribution and Cycles as disturbances.

For Percent the MTBF and MTTR was added for each workstation and the separate distributions was assign to two failure zones to simulate the worst cases of distur- bances. For the scenario analysis a predetermined disturbances was set were each stop lasted a certain time to simulate how longer stoptimes affects the models.

3.7.3 Long and short disturbances

When simulating the model in FACTS two types of disurbances were used. For all 26 workstations the MTBF and MTTR were calculated, but also since in each workgroup V1 and V3, the workstations are connected to eachother. So if one robot is down the whole workgroup comes to a stop. So in order to get a more accurate model that represents reality, a failure zone was implemented. This failure zone has a disturbance that is generated from a given distribution. Each distrubution has a duration and an interval between failures, see section 3.8 Distribution identification using Minitab.

3.8 Distribution identification using Minitab

Using identification tools in Minitab on samples provides the user with an esstima- tion of how well the sample data fit a distribution and its parameters for a variety of different distributions.

However, in the data exported from DUGA there is only positive values and some zeros. In that case Minitab uses the following distributions to model the data, Minitab choose these automatic:

• 2-parameter lognormal

• 1-parameter exponential

• 2-parameter Weibull

• 2-parameter gamma

• 2-parameter loglogistic

Our data contains zeros (every event that is shorter than 18 seconds will be rounded down to zero, this is due to a coding error from the original DUGA pro- gram), then Minitab does not report results for these specific distributions. In that case, you must use the results for the higher-parameter version of each distribution.

For example, if your data contains zero values, Minitab does not show the results for the 2-parameter distribution. Instead, it will include a third parameter and test the results for the 3-parameter distribution to see if it gives a better fit. The 3-parameter distribution includes the threshold as the third parameter and provides an estimate of the minimum value of the random variable (Minitab,2021).

Generally, you want a high P-value so the null-hypothesis do not get rejected.

It is usually effective to compare the p-values between distributions and choose the highest of them all. A low P-value (for example, <0.05) indicates that the data does

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20 Chapter 3. Method and Data

not follow the distribution. For some 3-parameter distributions, the P-value cannot be calculated, if this is the case the P-value is indicated by an asterisk, this is because the model do not enough degrees of freedom for error. (Minitab,2021). When testing the data sets in minitab the hypothesis will be as follows:

H0µ=thedata f itthedistributionH1µ6=thedatadonot f ollowthetesteddistribution (3.1) The section below summarize the best-fit distrubutions for the given data. There is no correct answer for which distrubution each workgroup has, the variance/Covariance matrix of estimated parameters did not exist. And the threshold parameter is as- sumed fixed when calculating confidence intervals. Therefore, the result is arbitrary, and we choose the best-fit distribution for our data.

For further investigation of the achieved distributions, a cumulative distribution function (CDF) will be fitted.

3.8.1 Probability, Histogram and CDF plot for V1 MTBF

FIGURE3.7: Probability plot for workgroup V1 for MTBF.

Given, Figure 3.7, the highest P-value, we can choose the 3-parameter lognormal distribution as the most suitable distribution for us. By looking at the four graphs that provide the P-value for each distribution, as well as the probability plots. The 3-parameter lognormal is the best fit.

Probability plots are a way to visually identify the distribution of data. If the data follow the red line, the distribution fits. By looking at Figure 3.7 the 3-Parameter Lognormal in the graph above is the most suitable distributions.

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3.8. Distribution identification using Minitab 21

FIGURE3.8: Histogram plot for workgroup V1 for MTBF.

Figure3.8 represents a Histogram that is used to evalute the spread and shape of the data. By dividing the values into intervals where each interval represents the frequency of each value, each group is plotted as a bar to get the shape of the distribution. In Figure 3.8 the most frequent value for MTBF for V1 is at around 0.7 hours. A uprising followed by a downhill trend might indicate a lognormal distribution.

FIGURE 3.9: CDF for workgroup V1 compared to CDF of a 3- Parameter Lognormal distrubution.

In Figure 3.9 a empirical CDF (Derived from equation 2.1) plot is perfomed to evalute the distribution of the data. The following CDF shows the amount of time that goes by between failures in V1 and its distribution with corresponding per- centiles of the data. In the x-axis the MTBF is shown while the y-axis has the corre- sponding percentiles

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22 Chapter 3. Method and Data

3.8.2 Probability, Histogram and CDF plot for V1 MTTR

FIGURE3.10: Probability plot for workgroup V1 for MTTR.

By looking at Figure 3.10all the graphs data points do not follow the red line so well. But by choosing the highest p-value, the 2-Parameter exponential is the most suitable distributions.

FIGURE3.11: Histogram for workgroup V1 for MTTR.

In Figure3.11the most frequent value for MTTR for V1 is at around 0.020 hours using a Histogram. A downhill trend might indicate an exponential distribution.

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3.8. Distribution identification using Minitab 23

FIGURE3.12: CDF plot of workgroup V1 for MTTR compared to ex- ponential distribution.

In Figure 3.12a empirical CDF plot is perfomed to evalute the distribution of the data. The following CDF shows the mean time to repair a workstation in V1.

The distribution with corresponding percentiles of the data is showned in the y-axis while MTTR is in the x-axis.

3.8.3 Probability, Histogram and CDF plot for V3 MTBF

FIGURE3.13: Probability plot for workgroup V3 for MTBF.

Figure3.13, the highest p-value is given in the 3-parameter lognormal distribution.

The data points follow the line and therefore is the most suitable distribution.

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24 Chapter 3. Method and Data

FIGURE3.14: Histogram for workgroup V3 for MTBF.

In Figure3.14the most frequent value for MTTR for V3 is at around 0.760 hours using a Histogram. A uprising followed by a downhill trend might indicate a log- normal distribution.

FIGURE3.15: CDF for workgroup V3 for MTBF.

In Figure 3.15 a empirical CDF plot (Derived from equation 2.1) is perfomed to evalute the distribution of the data. The following CDF shows the amount of time that goes by between failures in V3 and its distribution with corresponding percentiles of the data. In the x-axis the MTBF is showned while the y-axis has the corresponding percentiles

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3.8. Distribution identification using Minitab 25

3.8.4 Probability, Histogram and CDF plot for V3 MTTR

FIGURE3.16: Probability plot for workgroup V3 for MTTR.

By looking at Figure3.16all the graphs data points do not follow the red line so well.

By choosing the highest p-value, the 2-Parameter exponential is the most suitable distributions.

FIGURE3.17: Histogram for workgroup V3 for MTTR.

In Figure3.17the most frequent value for MTTR for V3 is at around 0.030 hours using a Histogram. A downhill trend might indicate an exponential distribution.

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26 Chapter 3. Method and Data

FIGURE3.18: CDF plot for workgroup V3 for MTTR.

In Figure3.18a empirical CDF plot is perfomed to evalute the distribution of the data. The following CDF shows the mean time to repair a workstation in V1. The distribution with corresponding percentiles of the data is shown in the y-axis while MTTR is in the x-axis.

3.9 Issues Fitting The Distributions

Using Minitab one can see the goodness of fit for multiple distribution but it can be hard to get a appropriate fit. An issue arises when none of the distributions that are availabe in FACTS is a good fit for the given data sample. Then using historical data becomes an attractive option, taking a random value from the sample data and using that as a disturbance in the simulation. But once again this option is not available in FACTS. The option that is available in FACTS is creating multiple distributions for disturbances, for example different distributions for long and short disturbances.

So instead of trying to fit a distribution for the whole dataset V1 MTBF, V1 MTTR, V3 MTBF and V3 MTTR the 99th percentile is calculated. The value that represent this percentile will be the minimum value in our new distribution, the new interval will be based from the 99th percentile to the maximum value in the far right tail of the data set. With these new values a distribution is fitted, but only for the highest stop time and longest time between failures. See Table3.1for the achived 99th percentiles, the mean value for each set is also included.

TABLE3.1: The hourly duration and interval between failures for the two groups given the 99% quantile.

Workgroups .99% Quantile (Hours) Mean Value (Hours) Standard Deviation (Hours)

V1 MTBF 7.900 0.770 0.139

V1 MTTR 0.380 0.020 1.541

V3 MTBF 9.405 0.755 3.362

V3 MTTR 0.466 0.030 0.105

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3.9. Issues Fitting The Distributions 27

Test were also conducted on the 98th percentile. However, the data could not be fitted against a distribution even when the 99th and 98th percentiles where excluded from the data set in an attempt to make the distribution better when removing the extreme values. Fitting a distribution where the zero values in the sample was re- moved was also attempted. When conducting a new distribution identification on the new data sets the result made no significant difference. However the lognormal distribution was assumed the best-fit for MTTR, while for MTBF the exponential dis- tribution was the best-fit. Based on these results an assumption was made that these two were allowed to be the distributions describing time between failures and time to repair. The issues regarding fitting the distributions could possibly be explained by a mixed distribution that the long and short failures do not come from a single simple distribution.

Therefore, the best-fitted distributions that were available in FACTS were used in the model (the parameters was calculated using the mean value and the standard deviation of the sample set, see Table3.1) even though it underestimate the tails of the distributions, resulting in fewer long stop times and fewer long durations be- tween stops.

The best fitted distributions that also are available in FACTS are:

• V1

MTTR: Exponential distribution MTBF: Lognormal distribution

• V3

MTTR: Exponential distribution MTBF: Lognormal distribution

These distributions were used in the simulation model with the mean and stan- dard deviation of the sample.

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29

Chapter 4

Result

Using the collected data and the method outlined in Section3the following models were produced. The As Is FACTS model is shown in Figure4.1 and the concept model is shown in Figure4.2.

4.1 As Is Model

The model was verified using the Animation tab in FACTS showing the exact flow of entities throughout the model. Initially the simulation was tested without distur- bances in the production to see that the throughput of the simulation corresponds to the maximum hourly throughput which was used to validate the model. Finally the disturbances were added to see how the different models handles the stops in pro- duction, without the disturbances both models produced similar throughputs with no backlog in the demand of material to the Mainline.

FIGURE4.1: The door area as it will be with outgoing model being removed.

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30 Chapter 4. Result

4.2 Concept Model

To expand on the initial model the work focused on the processes before and after the door area. The operators input is instead decided by the buffers between the safety zones V1 and V3, instead of being produced in a predetermined sequence.

The output from the same buffers was changed to be ordered in batches depending on the demand from the mainline and CKD. When the demand arise an order is placed in an order queue where all the orders to the Mainline takes priority and skips ahead of the CKD orders in the queue.

FIGURE4.2: The door area concept model.

4.3 Bottleneck

FIGURE4.3: Graph of the bottlenecks in production from the concept model

In Figure 4.3 the bottleneck in the current production is shown. There is no change in the bottleneck between the two models, this is due to the similarities in the models at these points. Both stations are early in the V1 area where there is no difference between the models and limits the flow to the rest of the model. The two standout bottlenecks are the stations K24 and K10.

This clearly shows that K24 is the bottleneck operation. It is the sole bottleneck for 75 % of the time and a shifting bottleneck 20% of the time. While K10 is the

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4.4. Scenario Analysis 31

sole bottleneck 5% of the time and a shifting bottleneck 20 % of the time. Below the bottleneck analysis is presented, Figure4.4for the current production flow.

FIGURE4.4: Bottleneck analysis using shifting bottleneck detection for As Is model

4.4 Scenario Analysis

To clearly illustrate the differences in the two models some scenarios were tested with predetermined stopptimes on top of the MTTR and availability from a good week with no large stops and see the effect in material shortage (measured in pcs not delivered in time to Segment 3) in Segment 3. From testing we could see that the buffers in the three scenarios last for about 25 minutes in the "As Is", about 80 minutes in the concept model with three racks and 95 minutes with four racks.

Results from the scenarios with 500 replications:

• Scenario 1, one eight hour disturbance

Material shortage "As Is": 550, with standard deviation 38.8

Material shortage "Concept model, three racks": 545 with standard devi- ation 9.9

Material shortage "Concept model, four racks": 510, with standard devia- tion 7.5

• Scenario 2, two hour disturbance every two days

Material shortage "As Is": 221, with standard deviation 32.75

Material shortage "Concept model, three racks": 192, with standard devi- ation 6.5

Material shortage "Concept model, four racks": 130, with standard devia- tion 6.9

• Scenario 3, one hour disturbance every day

Material shortage "As Is": 179, with standard deviation 38.7

Material shortage "Concept model, three racks": 93, with standard devia- tion 18

Material shortage "Concept model, four racks": 0, with standard devia- tion 0

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32 Chapter 4. Result

4.5 Disturbance in Production

FIGURE4.5: Percentile plot of the two models and both scenarios of the concept model with 5000 simulations

From Figure4.5 the material shortage from 5000 simulation compiled into a per- centile plot is shown. From the graph the mean value of the As Is model is around 190 with a median at 167. Both scenarios of the concept model have a lower material shortage. The mean and median values of the concept model with 3 racks is 96 and 76 while the 4 racks scenario have mean and median values of 15 and 0.

4.5.1 Expected shortfall

The worst outcomes from a simulation of 5000 work weeks are presented down below in Table4.1

TABLE4.1: Expected shortfall of the 95th, 99th and 99.9th percentile measured in doors not delivered to Segment 3.

Models 95th 99th 99.9th

As Is 537 692 834

Concept model 3 racks 322 434 602 Concept model 4 racks 140 231 322

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33

Chapter 5

Analysis

5.1 Conclusion

The following things are the main differences between the As Is and Concept model:

• V1

Focus on filling the buffers No sequence

• V3

Produces in batches

The doors are loaded in racks, with a total of 3 racks or 4 racks (2-bin)

• Segment 3

No conveyor

2-bin for door assembly

• CKD

If there is no demand for Segment 3, a CKD order is triggered Reserve buffer if needed

From the scenario analysis we can see that the concept model perform similarly with the long disturbances, the large differnces can be seen when lowering the du- ration of the disturbance. For both Scenario 2 and 3 we can see a clear difference between the As Is model and the Concept model using three or four racks. In Sce- nario 3 we have a backlog of zero with standard deviation of zero for 500 replicants, meaning that there is never a material shortage towards Segment 3.

Simulating a long term projection for the concept model using three racks, we see From4.5that the median for the material shortage will be around 76 doors and the mean value 96 doors with time horizon of 5 days. If the mean value is much higher then the median one can say there is a tail of high values this we also can see in the same Figure.

From the bottleneck analysis no clear difference can be seen, therefore the issues remains independet of the buffer allocation. The large bottlenecks come from cycle times in station K24 and K10.

Furthermore, we can see from Table 4.1 that the As Is model has a higher risk of material shortage, compared to both the 3 and 4 racks models. At the 99.9th per- centile our 4 racks Concept model has a material shortage of 322 doors during a week. Compared to the current production at the 99.9th percentile with a shortage

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34 Chapter 5. Analysis

of 834 doors during a week we can say that our model is better at managing risk in terms of material shortages. This is logical because we have a larger buffer, hence more material in storage. However in terms of lean production one strives to re- duce inventory, and produce to order. Since the current production already uses this work method and a common stop in production is material shortage, Volvo should consider changing their current production method to perhaps our Concept model using 4 racks. It is important to remember this is only one model comparison that requieres a medium to high investment to make a reality. The best option is not guaranteed to be the optimal in other aspects. There is a trade off between spending more money and using up more surface area to getting a better result in the scenarios of the concept model.

5.2 Implementation

To be able to implement this concept an fairly large investment is required. First, the old model must be redone, no major difference takes place inside the cell, however all the buffers will need to be adapted, the sequence production must also be redone.

If V3 is to have an order in batches, this might need improvement, since this work was not about looking at how ordering from buffer takes place. In this case we put the size of the order so it did not cause any locking in the system (currently a batch is 8 pcs). Second, the conveyor must be removed and replaced with a 2-bin system. if this is to be done, it will most likely have to happen during a vacation so that production is not affected. This model clashes with the lean philosophy, which says that buffers and storage should be avoided as much as possible. If the sequence production is replaced by a 2-bin system, we get larger buffers that tie more capital and require more space. Also in the old model the last operations only has an occupancy rate of 30 %, but with our model an occupancy rate of 90 % is required, due to having to place every door in a rack. Below are the pros and cons of the two models listed.

• As Is

– Pros- Less buffer space (10-14 pcs)

– Cons- No possibility of reserve routine in case of material shortage

• Concept model

– Cons- Bigger buffers (8 * number of racks) – Pros- Less risk of material shortage to Segment 3 – Pros- CKD as emergency buffer

5.3 Continuations

To improve the model, one can expand it to include more details in the flow. You can go all the way back to PPP where parts are stamped or even further with coils being delivered. One could include all of the cab variants in the model and see if that has an effect on the outcome whereas currently it is assumed to have small or neglectable effect on the production.

One is limited when using FACTS, you cannot use historical data or advanced distributions, or even connect self-written code to the program. Also, the collected

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5.3. Continuations 35

data is a small sample, by using a larger time horizon you could potential get a better distribution fitted to the data. The issue is that there could be changes in the production that affect for example the distributions by changing the mean value or even the shape of the distribution.

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37

Appendix A

Extended Reading

A.1 Presentation For Production Management

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Simulering av

produktionsområde Dörr vänster

Med hjälp av FACTS Analyzer

Censurerad version

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Visualisation of flow

Door inner L

Door Outer L

BU P29 (FH, FM)

BU (FM 24 a)

As is

Seg 3

C K D

Operator gets order / trigger buffer location before Segment 1

C K D

Sequence queue all the way from charging

Door inner L

Door Outer L

BU (FH)

BU (FM)

Model concept

Adjust buffer FM 24a to FM24b

Seg 3

FH

FM

Operator gets order / trigger from buffer door interior

Release conv from tough 3 Set up 2 (rax 2-bin) per side No sequence on

the doorway

FM

FH FM

C K D

FH

Conveyor to Segment 3

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FH

Segment 3

FM

FM

FM FH

FH

Buffer/CKD

FH FM

FH

FM FH

FM

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Grund genomgång av nuvarande modell

Säkerhetsområde V1

• Operatör laddar fixtur

• X antal operationer genomförs

• Placeras i två buffrar, P29 (FM och FH), FM24

• Produceras i sekvens

Säkerhetsområde V3

• Automatisk hämtning ur buffer

• Yttre och inre del sammanfogas

• Y antal operationer genomförs

• Montör skruvar fast gångjärn

• Dörr placeras i conveyor eller racks för CKD

Segment 3

&

CKD

• Dörr transporteras med conveyor till Segment 3 eller körs med truck till CKD

• Anländer i sekvens mot Segment 3

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Grund genomgång av potentiell modell

Säkerhetsområde V1

• Operatör laddar fixtur

• X antal operationer genomförs

• Placeras i två buffrar, FM24b och FH

• Ingen sekvens i buffer

Säkerhetsområde V3

• Automatisk hämtning ur buffer

• Yttre och inre del sammanfogas

• Y antal operationer genomförs

• Montör skruvar fast gångjärn

• Dörr placeras alltid i racks (8st)

Segment 3

&

Buffert (CKD)

• Respektive racks transporteras till Segment 3 eller till buffer

• 2-bin Segment 3, dörrbanan

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Skillnader med den nya modellen

• Fokus på att fylla buffrarna

• Ingen sekvens

V1

• Producerar i batcher

• Dörrarna lastas i racks, 2-bin

V3

• Ingen conveyor

• 2-bin vid dörrmontering

Segment 3

• Finns inget behov mot Segment 3 triggas en CKD-order

• Reservbuffer vid behov

CKD

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Skillnader med den nya modellen

Nuläge

• Färre buffertplatser (10-14)

• Sekvenskö från laddoperatör

• Ingen möjlighet till reservrutin

Modell

• Fler buffertplatser (8*antal racks)

• Mindre risk för materialbrist hos Segment 3

• CKD som buffert

• Ingen sekvenskö (batchordrar)

• FM24 och curb window

exkluderad

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45

Bibliography

Evoma (2021). Evoma AB homepage.URL:https://www.evoma.se/.

Alm, Sven Erick and Tom Britton (2008). Stokastik - Sannolikhetsteori och statistikteori med tillämpningar. Liber.ISBN: 9789147053513.

Anderson, Theodore W and Donald A Darling (1954). A test of goodness of fit. Vol. 49.

268. Taylor & Francis.

Chung, Christopher A. (2003). Simulation Modeling Handbook. CRC Press.ISBN: 9781135513566.

Hull, John C. (2015). Risk Management and Financial Institutions. John Wiley Sons, Inc., Hoboken, New Jersey.ISBN: 9781118955949.

Johansson, Björn (2014). Matematiska modeller inom sakförsäkring. Matematisk statistik Stockholms universitet.

Minitab (2021). Individual Distribution Identification.URL:https://support.minitab.

com/en-us/minitab/19/help-and-how-to/quality-and-process-improvement/

quality-tools/how-to/individual-distribution-identification/before- you-start/example/.

Rice, William R. (1989). What is a p value and what does it mean? Vol. 43. 1. Society for the Study of Evolution, Wiley.URL:http://www.jstor.org/stable/2409177.

Roser C., Nakano M. and M Tanaka (2001). A Practical Bottleneck Detection Method.

Institute of Electrical and Electronics Engineers.

References

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