A Novel Model to Analyse the Effect of Deterioration on Machine Parts

in the Line Throughput

E. Garcia

1 a

, N. Montes

2 b

, N. Rosillo

2 c

, J. Llopis

1 d

and A. Lacasa

1 e

Ford Spain, Poligono Industrial Ford S/N, CP 46440, Almussafes, Valencia, Spain

Department of Mathematics, Physics and Technological Sciences, University CEU Cardenal Herrera,

C/ San Bartolome 55, Alfara del Patriarca, Valencia, Spain

Keywords:

Manufacturing Systems, Machine Variability, Bowl Phenomenon, Line Throughput.

Abstract:

This paper presents evidence on how the variability of machine parts can affect the throughput of an assembly

line. For this purpose, a novel model based on mini-terms and micro-terms has been introduced as a machine

subdivision. A mini-term is a cycle time subdivision that can be selected by the user for several reasons: the

replacement of a machine part or simply to analyse the machine more adequately. A micro-term is a mini-

term subdivision and it can be as small as the user wishes. Therefore, the cycle time of a machine is the sum

of mini-terms or the sum of the micro-terms. This paper focuses its attention on a welding line in a Ford

Factory located in Almussafes (Valencia) where a welding unit was isolated and tested for some particular

pathologies. This unit is divided in three mini-terms: the robot motion, the welding motion and the welding

task. The cycle time of each mini-term is measured by changing the deteriorated components for others in the

time. The deterioration of a proportional valve, a cylinder, an electrical transformer, the robot speed and the

loss of pressure are tested within a range that cannot be detected by alarms and maintenance workers, that is,

the range of normal production. The real welding line is modelled and a novel simulation algorithm is created

based on mini-terms. The experimental measurements are introduced in the simulation model and the effect

of the pathologies in the production rate is computed. As a result, the pathologies with greater variability

have a deeper impact in the production rate mainly due to the bowl phenomenon effect. On the contrary, the

pathologies with low variability have a low effect in the production rate. In fact, this paper demonstrates that

the maximum rate capacity can be achieved if the machine variability is near zero.

1 INTRODUCTION

A production line is a set of sequential operations

established in a factory whereby materials are put

through a reﬁning process to produce an end prod-

uct that will be suitable for onward consumption; or

where components are assembled to make a ﬁnished

item. Because of the high investment and running

costs involved, the design of such lines is of consid-

erable importance, (O.Battaia and A.Dolgui, 2013).

There are a large number of crucial decisions to be

made in ﬂow line design such as, product design,

process selection, line layout conﬁguration, line bal-

ancing, machine selection, available technology, etc.

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Usually, these problems are considered one at a time

because of their complexity, (O.Battaia and A.Dolgui,

2013).

The last and crucial step in the process design is

line balancing, (O.Battaia and A.Dolgui, 2013). It’s

here where tasks will be assigned to the workstations

and resources will be used in the line (this is a com-

plex combinatorial problem and the solution mostly

determines the efﬁciency of the line designed). Due

to the relevance of this task, a large number of re-

searchers have been working on this topic ((O.Battaia

and A.Dolgui, 2013) represent a state-of-the-art un-

derstanding in the matter). Depending on industrial

environments, there are solutions to a number of prod-

uct models, line layout, tasks and their attributes,

workstations and their attributes, etc, see (O.Battaia

and A.Dolgui, 2013). Currently, one of the impor-

tant topics under assembly line design and balancing

is the task processing time variability engendered by

the following factors, (E.Gurevsky et al., 2012): in-

Garcia, E., Montes, N., Rosillo, N., Llopis, J. and Lacasa, A.

A Novel Model to Analyse the Effect of Deterioration on Machine Parts in the Line Throughput.

DOI: 10.5220/0009594100260034

In Proceedings of the 17th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2020), pages 26-34

ISBN: 978-989-758-442-8

Figure 1: Jobs Per Hour produced in a real line production VS idealized production rate. Note: ECR (engineering running

capacity). ERR (engineering running rate).

stability of operators performing tasks with respect to

work rate, skill and motivation; materials of differ-

ent composition of product items; changes in products

and workstation characteristics; as well as failure sen-

sitivity, (E.Gurevsky et al., 2012). In particular, more

papers were published in the last years about learning

and ageing effect, see (Janiak et al., 2011), where the

mean value and standard deviation are often used for

model task times.

At the beginning of modern production systems,

as well as in most research papers about line balanc-

ing problems, (O.Battaia and A.Dolgui, 2013), it was

thought that a ‘perfectly balanced’ line was the most

efﬁcient line design. However in practice, the perfect

balanced line seldom exists, because some degree of

imbalance is inevitable. When the line is designed

by an expert team, a maximum production rate is de-

ﬁned, mainly in jobs per hour (JPH). It is known as

“Engineering Running Capacity” (ERC). The factory

employees will concentrate on the task of achieving

this maximum production rate, see Fig.1, deﬁning the

throughput of the line. Reality shows that the ERC

is extremely difﬁcult to achieve so the factory deﬁnes

a new maximum production rate that is more realis-

tic and is known as the “Engineering Running Rate”

(ERR).

Recent studies have shown that unbalanced lines

with a bowl shape workload conﬁguration can yield

performance in throughput as good as, or even better

than perfectly balanced lines. It is known as a “bowl

phenomenon”. This phenomenon has been studied in

literature during the last decades. It determines that if

we introduce a higher load to the beginning and end

workstation, the throughput can be increased. More

recently a study of the bowl phenomenon was pre-

sented in large unpaced assembly lines under stochas-

tic processing times. The results of this study suggest

that unbalancing a large assembly line in a bowl shape

workload conﬁguration could provide statistical sig-

niﬁcant improvements in throughput. In this study,

single bowl conﬁguration and multiple bowl conﬁgu-

rations are tested, see (C.E.Lopez, 2014).

The present paper develops a novel simulation

tool that will allow us to know in real-time the

throughput of the production line. This novel tool

uses two new data classiﬁcations, the mini-term and

the micro-term, (E.Garcia, 2016), (E.Garcia et al.,

2018), (E.Garcia and N.Montes, 2019). The literature

classiﬁed the data used in the analysis into long-term

and short-term. The difference between both terms

has been addressed by (Chang, 2005). Long-term

is the cycle time mainly used for process planning,

while short-term is the cycle time focused primarily

on process control. A mini-term is a short term subcy-

cle time subdivision and a micro-term is a mini-term

subcycle time subdivision.

A Novel Model to Analyse the Effect of Deterioration on Machine Parts in the Line Throughput

The goal of the present study is to determine how

the production rate and bottleneck location are af-

fected by the mini-term variability and with some de-

terioration machine parts that are not detectable by

the control system of the machine and also by main-

tenance workers. For instance, the stiffness of a pro-

portional valve, the pneumatic cylinder wear, galling

or communication inside the stem, the loss of the wire

insulation in a transformer, the loss of pressure in a

pneumatic circuit (below the alarm value) and the loss

of the robot speed. All of these pathologies are mea-

sured in a real welding unit. In order to test the ef-

fect of the measured pathologies, a real welding line

is modelled. In particular, a real welding line in Ford

S.A. located in the factory in Almussafes. This line

has 35 welding units distributed in 8 workstations.

The simulation results provide jobs per hour (JPH)

due to the analysed pathologies. The paper is orga-

nized as follows. Section 2 presents a mathemati-

cal model to compute the long-term and short-term

by means of the mini-terms and micro-terms. Sec-

tion 3 presents a real case study, which is a welding

unit where mini-terms are measured experimentally

for particular pathologies. Section 4 presents a model

of a real welding line and the simulation results for

each of the pathologies. Section 5 presents a discus-

sion on the results and Section 6 concludes the paper

with an emphasis on future research challenges.

2 FROM THE MICRO-TERM TO

THE LONG-TERM

The literature classiﬁes the data used in the anal- ysis

into long-term and short-term cycle time. Long- term

is mainly used for process planning while short- term

focuses primarily on process control. There is abun-

dant literature for long-term analysis in com- parison

with the literature that studies short-term data.

Therefore, following the deﬁnition by (L.Li et al.,

2009), the short-term is referred to an operational pe-

riod not large enough for a machine’s failure period to

be described by a statistic distribution. The machine’s

cycle time is considered short-term. The present study

redeﬁnes short-term cycle time into two new terms,

mini-term and micro-term. A mini-term could be

deﬁned as the cycle time of a machine part that, in

a preventive maintenance policy or in a breakdown,

could be replaced in an easier and faster manner than

another machine part subdivision. Also a mini-term

could be deﬁned as a subdivision that allows us to un-

derstand and study the machine behaviour, see ﬁgure

Each mini-term is modelled statistically by the

Figure 2: From Micro-term to Long-term.

mean value µ and standard deviation σ of the mini-

term cycle time, T m

(µ

T m

, σ

T m

). Then, the mean

value of the short-term machine cycle time for a ma-

chine i(µ

) can be computed as;

∑

j=1

T m

(1)

where µ

T m

is the j mean value of each mini-term

cycle time. The standard deviation of the short-term

machine cycle time for a machine i(σ

) can be com-

puted as;

∑

j=1

T m

(2)

where σi

is the j standard deviation of the short-

term machine cycle time. In the same way, a micro-

term is deﬁned as each mini-term part in which could

be divided itself. Each micro-term is also modelled

statistically by the mean value and standard deviation

of the micro-term cycle time, T

(µ

T µ

, σ

T µ

). Then,

each mini-term is deﬁned as:

T m

∑

k=1

T µ

, σ

T m

∑

k=1

T µ

(3)

Now, the next step to move upward in the pyramid

of ﬁgure 2, is to simulate the workstation joined with

the other ones. The common way is using a simpli-

ﬁed machine state, see Figure 3 . There are three pos-

sible workstation states, “Working”, “Starving” and

“Blocking”. If the current station is in “Working”

state and the work is ﬁnished, it checks the follow-

ing station, if it is in “Starving” state, the ﬁnished

part of product is delivered to it and the state of the

current station is free to receive another job. If the

next station is in “Working” state when the current

one ﬁnishes its work, the current station changes its

state to “Blocking”, that is, blocking itself until the

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

next station is free. If the current station is free to re-

ceive another part, it checks the previous station. If

the previous station is in “Working” state, the current

state changes to “Starving” state waiting itself until

the previous station has a part to work on. If the pre-

vious station is in “Blocking” state, the current sta-

tion receives the part and the current state changes to

“Working”. There is always work available for the

ﬁrst station and there is always a ﬁnal product to be

taken from the last one. When the simulation starts,

every station state is set to “Starving”, but the ﬁrst

one whose state is set to “Working” state. The sim-

ulation loop runs at predeﬁned step time (4t). For

each step time, the cycle time of each workstation de-

creases until the cycle time is zero, meaning that the

work is ﬁnished and the events are triggered. The cy-

cle time of a workstation has a probabilistic distribu-

tion TC

(µ

, σ

) that depends on mini-terms and

micro-terms, see equations (1) to (4). Then, when a

new job is started in a workstation, a new cycle time

is generated based on the probabilistic distribution. It

also means that the Starving and Blocking states have

a probabilistic time distribution that is, T S

(µ

T S

, σ

T S

T B

(µ

T B

, µ

T B

), respectively. At this point the latency

time is also deﬁned, which determines the rate with

which a ﬁnished part is extracted from the worksta-

tion, LA(µ

, σ

). The jobs per hour produced by

the line, JPH(µ

JPH

, σ

JPH

), are computed using long

time simulation. If we increase the time simulation

for the lifetime of the factory, the total production can

be computed, see ﬁgure 2, the upper part of the pyra-

mid.

3 CHARACTERIZATION OF

MINI-TERM DETERIORATION

IN A REAL WELDING STATION

The goal of the present study is to demonstrate the

effect of deterioration of some micro-terms on the

throughput of the line. For this purpose, a welding

line is taken as an example. The welding lines are one

of the most relevant because there are 4.500 weld-

ing points in a car. The welding line is composed

by welding workstations which have welding stations

working in parallel, see section 4. A welding station

is composed of a robot arm and a welding clamp, see

Figure 4. In the present study, a welding station was

isolated for the welding line in order to analyse, un-

derstand and measure the results presented in this sec-

tion.

The behaviour of the welding unit is simple. First,

the robot arm moves the welding clamp to the point to

weld. Then, a pneumatic cylinder moves the welding

clamp in two phases: one to approximate the clamp

and the second one to weld. The pressure applied by

the clamp is controlled by a control system. Each of

these devices needs a certain time to develop their task

and within each of these devices, there are also com-

ponents that need a certain time to develop their own

tasks. In order to analyse the deterioration effect of

some micro-terms, the welding unit is divided in three

mini-terms, the robot arm, the welding clamp motion

and the welding task.

Figure 5 shows the experimental setup to measure

the cycle time of each mini-term in the welding sta-

tion where the PLC and the PC are used to measure

the time. The experimental test is quite simple. The

robot arm, starting from a predeﬁned initial point,

moves the clamp to a predeﬁned welding point; the

clamp is closed and develops the welding task. Due

to the welding motion and the welding task that are

low time consuming, the task is repeated 6 times.

3.1 Pathologies Analysed

The welding station, as well as other stations in the

industry, could suffer an amount of pathologies that

produce an effect on the cycle time. Based on the op-

erator’s experience, we selected some pathologies for

a welding clamp station. These pathologies produce

a cycle time modiﬁcation but fail to produce the rup-

ture of the component, going unnoticed for mainte-

nance workers and also for the control system that has

some alarms to trigger fails. The pathologies for the

welding clamp mini-term are: the proportional valve,

the cylinder stiffness, welding failure produced by the

transformer and the pressure loss, and the pathology

for the robot arm mini-term is: the robot arm speed.

A brief description of each one are hereby explained:

- Pathology 1 (Proportional valve): This valve

transmits the pressure to the cylinder and the con-

troller controls it. It is responsible for maintaining the

proper pressure in the cylinder. During its lifetime,

its components suffer deteriorations that produce the

stiffness of some of them. This condition creates a

time delay. When the deterioration is big enough, the

valve cannot transmit enough pressure to the cylinder

and the welding task cannot be carried out.

- Pathology 2 (Cylinder stiffness): A critical term

in welding resistance is the pressure force on the met-

als together. This force is necessary to ensure good

electrical contact between the parts to be welded, and

to maintain the ﬁxed parts until the metal forming the

solid board has time to solidify. The elements re-

sponsible for transmitting the proper pressure to these

plates are cylinder clamps. In this case, one of the

A Novel Model to Analyse the Effect of Deterioration on Machine Parts in the Line Throughput

Figure 3: Simpliﬁed machine state for the workstation.

Figure 4: Welding station.

Figure 5: Experimental setup for the welding station.

cylinders could have a wear, galling or communica-

tion inside the stem. This condition creates a time de-

lay. Maintenance workers detect this pathology when

the cylinder cannot transmit enough pressure on the

metals and the welding task cannot be performed.

- Pathology 3 (Welding failure): The welding pro-

cess between parts consists of passing an electric cur-

rent through intensive metals to be joined. The de-

vice generally used for this task is a transformer. The

power goes through a transformer in which the ten-

sion is reduced and the current is increased substan-

tially. The fatigue of this component is mainly pro-

duced due to the loss of wire insulation. A modiﬁ-

cation is carried out in the value of the insulated re-

sistance and therefore a current reduction is produced

affecting the welding time. Maintenance workers de-

tect this pathology when the failure is so big that the

welding task cannot be performed.

- Pathology 4 (Pressure loss): One of the most

common delays is produced by pressure losses in a

pneumatic circuit. The pressure drop causes a delay

or malfunction in the pneumatic devices to be oper-

ated. This pathology could be produced by many facts

such as a simple pore that produces a failure in the

compressor. Maintenance workers detect this failure

when the low pressure alarm is triggered.

- Pathology 5 (Robot speed): The common indus-

trial robots have 6 axes. All these axes (motors) are

synchronized to achieve the points that have been de-

ﬁned by the program to perform its function or task. If

we have a failure in the operation, it causes an engine

speed reduction that directly affects the process cycle

time. There is an amount of reasons that produce this

pathology. In these industrial robot arms, high speed

and high accurate operation are required. However, in

the case of high speed operation, it often causes high

jerk, i.e., rapid change of acceleration. Jerk causes de-

terioration of control performance such as vibration of

a tip of a robot arm. Jerk forces are not equally dis-

tributed and as the robot arm does the same movement

again and again, the deterioration is located in some

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

particular joints. Mechanical structure deterioration

or the deterioration of electrical parts also affects the

speed. This pathology is very difﬁcult to detect by the

maintenance workers because it does not produce the

breakdown of the machine and, as the robot moves

at high speed, it is nearly impossible to be detected

without a speciﬁc procedure.

3.2 Experimental Test

The experimental methodology is as follows. The

clamping task is to weld the same point 6 times in

order to obtain enough time precision. The robot arm

trajectory is the same in all the movements. Then,

the clamping task is repeated 40 times in order to ob-

tain a sufﬁcient number of samples to measure the

mean value and the standard deviation for each mini-

term. First, the welding clamp station is tested with-

out any of the pathologies hereinbefore explained.

Afterwards, a particular component with each pathol-

ogy is replaced in the station and the test is repeated.

It is important to remark that the components are in

the normal production rate. Table 1 shows the ex-

perimental result measurements of all pathologies for

each mini-term. (x, S).

4 WELDING LINE. MODELLING

AND SIMULATION

A previous section shows how the welding unit and,

machines in general, have a probabilistic behaviour.

In addition, the deterioration of the machines pro-

duces a delay in the intermediate task and/or in the

standard deviation. In this section we will analyse

how many jobs are lost in a real line due to these

pathologies. For this purpose, a real welding line in

Ford S.A. located at the Almussafes factory has been

selected. The welding line was installed in 1980. The

staff group that designed the line deﬁned the maxi-

mum running capacity, ECR (engineering running ca-

pacity), 60 JPH. However, the plant engineers have

another maximum running capacity, that is the ERR

(engineering running rate), in this case deﬁned in 51

JPH. And our daily production to reach is GRR (Get

Ready Requirement) our (28,9 JPH). The GRR means

market requirements, i.e. customers’ orders. Figure 6

shows the production rate of the welding line.

In a real welding line like this, there are welding

workstations where, each one of them has welding

stations working in parallel and sometimes in serial.

Each welding station makes some welding points in

the same cycle time. We can ﬁnd 1, 2, 4 or at least 6

welding stations in the same workstation, where each

one of them makes up to 19 welding points, see ta-

ble 3. In our particular case, our welding line has 8

workstations where 3 are for 6 welding units, 4 with

4 welding units, and 1 for 1 welding unit. Each weld-

ing unit is modelled with robot motion, welding mo-

tion, welding task as well as the offset. Robot mo-

tion means how many seconds the robot is moved,

the welding motion and welding task mean how many

welding points the welding clamp has to perform. The

offset means how many seconds the welding station

must wait for another station to do the job.

5 WELDING LINE SIMULATION

In order to simulate the welding line, a state ma-

chine simulator is developed. There are three pos-

sible workstation states: “Working”, “Starving” and

“Blocking”, see ﬁgure 3 and ﬁgure 7. The loop is up-

dated with an incremental time of 0.01 seconds. In

the simulated welding line, there is always a job in

the ﬁrst workstation, so that the blocking state can-

not happen in the ﬁrst station. In addition, all the

jobs ﬁnished in the last workstation are removed, so

that the “Starving” state in the last workstation can-

not happen. The loop starts with all the stations in the

“Blocking” state.

The cycle time for each workstation is the maxi-

mum cycle time of each welding station that works in

parallel, indicating the slowest welding unit and the

bottleneck for a particular workstation. The transfer

time is added to the cycle time. This time is the time

required to transport the car from one workstation to

the next one (12 seconds), see ﬁgure 8.

The cycle time of each welding unit is computed

as shown in ﬁgure 9. A pseudo-random number based

on mean and variance is computed for each mini-

term using the experimental values of table 2. The

algorithm repeats the creation of a number as many

times as the mini-term is repeated (i.e. for 10 weld-

ing points, the algorithm will produce 10 numbers).

The offset is also added if necessary. The simula-

tion is computed with two time bases, one hour (JPH)

and one day (JPD) with an incremental time of 0.01

seconds. This simulation is repeated 50 times and

the mean and variance of the jobs produced are com-

puted. First, the simulation with any pathology is

performed. The results are for one-hour time base,

(51,1.05) JPH, similar than the ERR, and for one-day

time base, (1252, 3.09) JPD. Table 2 shows the sim-

ulation results where a particular pathology is located

in a particular welding station. Obviously, the rest of

welding units are considered without pathology.

A Novel Model to Analyse the Effect of Deterioration on Machine Parts in the Line Throughput

Table 1: Mean and standard deviation values for the robot motion miniterm, (x, S) respectively.Units (ms).

C P

(35549.7, 21.4) (35547.1, 33.6) (35549.6, 25.7) (35549.2, 36.1) (35548.5, 30.1) (463314, 31.4)

(1, 604 · 10

−6

) (1, 945 · 10

−6

) (1, 72 · 10

−5

) (1, 101 · 10

−5

) (1, 848 · 10

−6

) (1, 67 · 10

−5

)

Figure 6: Jobs Per Hour produced in a real welding line VS idealized production rate. Note: ECR (engineering running

capacity). ERR (engineering running rate). GRR (get ready requirement.

Figure 7: State machine workstation simulation.

5.1 Discussion

Through the simulation results obtained we can see

how sensitive the production rate is to some small cy-

cle time variations, in particular, mini-terms. Table 2

shows the maximum and minimum Jobs produced for

each base time. If we compare the results with the

simulated ERR, (51,1.05) JPH, there is a lot of jobs

per hour lost.

The least impact is from pathology 3 and 5, just

only a few jobs in a day. By contrast the greatest im-

pact is for pathologies 1 and 2, where in the worst

case more than 50 % of production can be lost. It

is important to remark the dispersion of the results.

In the worst case of pathology 2, the variance is 9.5,

in JPH and 171 in JPD. These results are due to the

Bowl Phenomenon effect that propagates the variabil-

ity starting from the bottleneck and producing a mul-

tiplied effect, see (C.E.Lopez, 2014). The bowl phe-

nomenon is the main responsible for the results, be-

cause, when the pathology has a similar variance than

the ERR, the difference only depends on the mean

value. For instance, Pathology 5 has a 30 % of mean

time in the mini-term robot motion, compared with

the mean value of ERR. However, if it has similar

variance, it means that only the mean value affects

the production rate. However, the results are very dif-

ferent when the variance is greater than the ERR. In

this case, the welding line is completely unbalanced

and the production rate turns unpredictable. The sim-

ICINCO 2020 - 17th International Conference on Informatics in Control, Automation and Robotics

Figure 8: Cycle time computation for each robot/Welding unit.

Figure 9: Cycle time computation for each Workstation.

ulation result demonstrates that the reason for the loss

of jobs is the machine variability, and ERC cannot be

achieved due to the mini-term and micro-term time

deviation of each machine. For instance, if we replace

the deviation of each mini-term in the case of “with-

out pathology” for 0.01 sec, the simulation gives (57,

0.47) JPH, 4 Jobs below the ERC.

6 CONCLUSIONS AND FUTURE

WORKS

This paper presents how the variability of a machine

part can affect the production rate in a line. For this

Table 2: Simulation results when a single pathology occurs

in a single welding station (µ, σ) JPH.

Pathology Production Rate Location (WS,Wu)

Max (35,3.39) (1,4)

Min (26,6.28) (8,6)

Max (39,0.98) (1,1)

Min (24,9.53) (7,5)

Max (51,1.06) (1,1)

Min (50,1.44) (1,5)

Max (40,3.25) (1,4)

Min (34,7.01) (7,5)

Max (51,1.11) (1,4)

Min (50,1.17) (8,4)

purpose, mini-term and micro-term cycle time sub-

division is introduced. The present paper focuses its

attention on a welding line located in a Ford Factory

in Almussafes (Valencia). A welding station is iso-

lated and tested for some particular pathology. The

deterioration of a proportional valve, the cylinder, the

transformer, the robot speed and the loss of pressure

are tested in the range that the alarms and the main-

tenance workers cannot detect. The welding line is

modelled and a simulation algorithm based on ma-

chine states is constructed. The experimental mea-

surements are introduced in the algorithm and the

effect in the production rate is tested. As a result,

the pathologies with greater variability have a deep

impact in the production rate mainly because of the

bowl phenomenon effect. On the contrary, patholo-

gies with low variability have a low effect in the pro-

duction rate. The simulation algorithm allows us to

demonstrate the reason for which the ERC cannot be

achieved in a real production line, which is the ma-

A Novel Model to Analyse the Effect of Deterioration on Machine Parts in the Line Throughput

chine time variability. If we replace the deviation

of the mini-terms in the case of “without pathology”

near to zero, the JPH are near to the ERC. The re-

sults presented in this study open new challenges and

research work for the future. On the one hand, the

watchdog agent that detects these anomalies in the

production rate will be our immediate future work.

Early detection of these pathologies will produce an

increase in the throughput. On the other hand, a deep

characterization of the machine part deterioration is

required. Although manufactures have a threshold for

the lifespan of the parts, however, for maintenance

workers the evolution of the deterioration during the

lifespan time could be crucial in the throughput of

the line, as well as for the detection of pathologies

with great variability, evidence is given on how the

variability of machine parts can affect the through-

put of an assembly line. It is important to state that

the present study only takes into account one pathol-

ogy in one welding unit and the others are without

pathologies. It is likely that in a real welding line all

the welding units have a percentage of deterioration.

ACKNOWLEDGEMENTS

The authors wish to thank Ford Espa

na S.L. and in

particular the factory in Almussafes for the support in

the present research. The authors also wish to thank

Joan Camps Soria for his support in the present work.

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