International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 2- February 2016
A Case Study on Modelling and Simulation to
know the Optimum no. of Service Points in
Sheet Metal Automotive Component of
Manufacturing Industry
Mohammad Javed#1, Dr. Vishal Saxena#2
#1
Assistant Professor Department of Mechanical Engineering, IFTM University Moradabad
#2
Professor Department of Mechanical Engineering, IFTM University Moradabad
Abstract This paper deals with the calculation of inter
arrival time and service time of dies in a sheet metal
working industry. Here we are talking about the sheet
metal working industry in which the different
components of a renowned automobile brand is to be
manufacture by the application of different processes.
These operations are the cutting, Forming, Punching,
blanking, pressing and lots more. In the whole process
of production total time is calculated by using a
particular tool and the main area at which there the
process is to complete is the press shop area. Press
shop area is the place where presses of different
tonnage and capacity is available for production work.
In the concern industry there is the lack of optimum no.
of service points. With this there is always a long
queue of dies around the press machines in the press
shop area.
Keywords - inter arrival time, Service time, tonnage,
press shop
service points is three and if we increase the number
of service points, the waiting cost and waiting time
will decrease, but service cost, on the other hand will
increase because they are inversely proportional to
each other. Also there is a possibility of losing the
customer in the long run because nobody likes to wait
for a long time. Therefore the company is interested in
knowing the suitable number of service point so that
waiting cost can be reduced which in turn will result
in the reduction of risk of losing the customers.
2. METHODOLOGY OF RESEARCH WORK
(a).Distribution of probability for inter-arrival
time of dies
Number of data points (inter-arrival time) = 493
Number of class-intervals = range / √ (number of data
points)
= (335-0) / √ 493
= 15.08 = 15
(approx)
1. INTRODUCTION
In this type of Industry different processes are used to
form a particular product. There is a lack of exact no.
of service points suitable to that industry. Here our
work is to know the no. of service points suitable to
that industry. For doing this firstly we have to
calculate the total no. of data points and after that
these data points is converted into particular format
and made a frequency table and then average inter
arrival time is calculated. In the last the data obtained
from the frequency table and average value is fed in to
the Minitab software and with the help of this software
we know the nature of probability distribution of the
data and then select the data best suited to that
industry on the basis of Anderson darling value. The
data obtained from this software is the required data
points and same procedure is follow for service time
of dies.
The concern Industry was facing the problem of high
waiting time of dies in the queue and they are paying
penalty as waiting cost. At present there are number of
ISSN: 2231-5381
Class Interval
Mid-point
Cummulative
Frequency
Frequency
0-25
12.5
440
440
25-50
37.5
470
30
50-75
62.5
474
4
75-100
87.5
480
6
100-125
112.5
483
3
125-150
137.5
486
3
150-175
162.5
488
2
175-200
187.5
488
0
200-225
212.5
490
2
225-250
237.5
491
1
250-275
262.5
492
1
275-300
287.5
492
0
300-325
312.5
492
0
325-350
337.5
492
0
350-375
362.5
493
1
Table 2.1 Frequency table for inter-arrival time
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International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 2- February 2016
Average value of inter-arrival time is:
= 440x12.5+ 30 x 37.5 + ………………+ 362.5 x 1
493
=
=
9762.5 / 493
19.80 min.
2.1 Histogram for Inter-arrival Time: The
histogram suggests the inter-arrival time distribution
should be Exponential or Weibull or Logistics or Loglogistic. This has further been strengthened by feeding
the inter-arrival time data to Minitab Software.
Graph 2.2.3 Logistic Probability Plot
2.2 Output of Minitab Software for Inter-arrival
Time Data
The probability plots obtained are shown below and
are self-explanatory. “ML Estimates” and “AD*”
stands for maximum likely estimates and AndersonDarling value respectively.
Graph 2.2.4 Log logistic Probability Plot
2.3 Comparison of the above four distribution
The comparison of the above probability plots shows
that the A-D value or error is minimum for Weibull
distribution whose Anderson darling value is 25.26.
So the Weibull distribution probability plot has been
selected for the distribution of inter-arrival time with
shape = 0.395 and scale =2.362
Graph 2.2.1 Weibull Probability Plot
(b).Distribution of probability for Service time of
dies
Number of data points (Service time)
= 64
Number of class-interval = range / √ (number of
data points)
= (53.1-3) / √ 64
= 6.6375 = 7 (approx)
ClassInterval
0-8
Graph 2.2.2 Exponential Probability Plot
MidPoint
4
Cumulative
Frequency
2
Frequency
2
8-16
12
11
9
16-24
20
29
18
24-32
28
47
18
32-40
36
59
12
40-48
44
62
3
48-56
52
64
2
Table 2.2 Frequency Table for Service time
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International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 2- February 2016
Average value of service time is:
= 2 x 4 + 9 x 12 + …………………………+ 2
x 52
64
= 1648 / 64
= 25.75 min.
2.4 Histogram for Service Time: The histogram
suggests that the service time distribution should
be Normal or Weibull or logistic or log logistic or
lognormal. This has further been strengthened by
feeding the service time data to Minitab Software.
2.4.1.Output of Minitab Software for Service Time
Data
Graph 2.4.1.3 Lognormal Probability Plot
The probability plots obtained are shown below and
are self-explanatory. “ML Estimates” and “AD*”
stands for maximum likely estimates and AndersonDarling value respectively.
Graph 2.4.1.4.Log logistic Probability Plot
Comparison of the above four distribution
Graph 2.4.1.1 Normal Probability Plot
This comparison represents that the A-D value or error
is minimum for Normal distribution whose A-D value
is 0.325. So the Normal distribution has been selected
for service time distribution. with Mean = 18.267 and
Standard Dev. = 7.272.
After finding out the waiting time for different number
of service points, the cost model was used to find out
the optimum number of service points. Here we have
calculated the waiting cost and service cost per die for
different service points and then finding the total cost
which have decided the required no. of service points
suitable to that industry and the service points
corresponding to the minimum total cost is the
optimum one.
3. Working Principle of Model
Graph 2.4.1.2 Weibull Probability Plot
The Generator icon named as source generates items
according to the distribution specified. We have
specified Weibull distribution because our data have
been fitted to this distribution.
The icon named as „program‟ generates items
according to the program set in it and feeds these
items to the icon name as service point. The service
point (actually press machine) has to receives the
information fed by the program. When the information
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International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 2- February 2016
is received by the service point, it performs
accordingly. If the information is fed by program
block to shut down, its„s‟ terminal outputs 1. This
signal in turn is fed to the shut down block. As the
shut down block receives signal „1‟, it does not allow
the items to pass through it. In this way shut down
becomes active.
count
f
Rand
d
V
In the queue block, the maximum number of items
(dies) can be fixed. When the number of items waiting
in the queue (dies) reaches the maximum number
specified, its F terminal outputs „1‟.This signal „1‟ is
fed to the shut concerned shut down block which stops
the items (dies) passing through it. In this way
maximum number of dies in the queue can be fixed. In
our case maximum 45 dies can wait in queue. So we
have specified maximum number of dies allowed as
45.
As dies arrive in the queue, they wait there for some
times and then they are allowed to go to the service
points according to the pre-specified conditions. After
unloading they are allowed to exit from the system.
3.1. Performance Measurement of the Existing
Model
For smooth running of the simulation model, the
inputs of the model are the characteristics of the
distribution i.e. outputs of the Minitab software. After
allowing the model i.e. system to run for 9 years, the
outputs of the simulation model obtained is as follows:
Average Queue length
= 45 dies
Average Waiting time
= 12.32 hour
Maximum Waiting time = 40.25 hour
3.2.MODEL WITH 5 SERVICE POINTS
The Simulation Model with 5 service points and its
performance measurement is shown below:
ISSN: 2231-5381
D down
service point
T U S
1 2 3
random no. input
F
L W
program
down
queue
STOP
down
f
A
shut down
down
D
STOP
Rand
down
A
f
f
d
D
down
d
plotter
T U S
down
a
f
1 2 3
STOP
L W
down
shut down
prioritiser
b
STOP
STOP
down
Exit
(4)
down
STOP
down
select
selection
f
#
D
T U S
F
d
STOP
A
1 2 3
? b
combine
down
T U S
Rand
b
STOP
1 2 3
STOP
down
source
f
Rand
f
prioritiser
V 1 2 3
down
d
STOP
start
a
STOP
down
a
Random number input block generates value
according to the distribution specified. Our service
time data follow the normal distribution, so we have
specified this distribution in random input block so
that different service time will be allowed for different
dies. The icon named as prioritizer prioritizes the item.
It first checks the machine for the availability
connected with the topmost terminal, then next one &
so on. If the topmost icon is available, item is fed to it
i.e. dies is allowed to got to this machine (service
point). If it is busy, then prioritizer checks the machine
(service point) connected to the next terminal. If it is
available, item is passed to it, otherwise checks the
other machine for availability & so on.
The icon named as „combine‟ combines the inputs and
transfers it to the exit icon. The two items here in the
combine block remains as separate items. They do not
get intermixed.
f
T U S
STOP
A
D
down
Rand
down
d
f
f
1 2 3
F
L W
queue
Fig. Model with 5 service points
3.3. Performance Measurement of the Model with 5
service points
For smooth running of the simulation model, the
inputs of the model are the characteristics of the
distribution i.e. outputs of the Minitab software. After
allowing the model i.e. system to run for 9 years, the
outputs of the simulation model obtained is as follows:
Average Queue length
Average Waiting time
Maximum Waiting time
= 4 dies
= 2.15 hour
= 11.52 hour
3.4. Summary of waiting time for different service
points
The summary of waiting time of dies obtained from
the simulation model corresponding to different
service points is shown below:
For 3 service points
= 12.32 hr.
For 4 service points
= 6.38 hr.
For 5 service points
= 2.15 hr.
For 6 service points
= 1.25 hr.
4. COST MODEL
After finding out the waiting time for different number
of service points, we then use the cost model to find
out the optimum number of service points. Strategy
here would be to calculate the waiting cost per dies
and service cost per dies corresponding to the different
service points. Then the total cost is determined which
in turn will decide the optimum number of service
points. The service points corresponding to the
minimum total cost would be the optimum one.
4.1. Waiting Cost Calculation
The waiting cost per dies as specified by the company
is shown below:
Waiting cost per dies = {Rs.10 per 10 dies if waiting
time is
more than 4 hour}
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International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 2- February 2016
= {Rs. 0 per die, otherwise}.
(80 dies in one day)
= Rs. 9,50,472
No. of Service
points
3
4
5
6
Waiting time
in hr.
Waiting cost per
dies (in Rs.)
6. CONCLUSIONS
12.32
6.38
2.15
1.25
432 (4.32*10*10)
238 (2.38*10*10)
0
0
The Sheet metal component manufacturing industry
which faces the problem of high waiting time and pay
penalty as waiting costs may be reduced by increasing
the number of service points. According to the results
obtained and analysis of data, it is concluded that the
optimum number of service points is five, which
means that there is a deficiency of two service points
in the existing system of the continuously operating
process industry (sheet metal manufacturing industry)
here.
To increase the service points, the selected industry
needs to install two new press machines. If the
industry installs two new press machines to make the
service points or loading and unloading points, there
can be a saving of Rs.09,50,472 per month and the
corresponding average waiting time of dies will be
2.15 (2 hour 15 min) hour which is lesser than the
average waiting time of the existing system.
The approach adopted in this work is of collecting the
data related to inter-arrival time of dies, service time
of arriving dies, finding the suitable probability
distribution of the data, developing a simulation model
of the existing system, waiting time, computation of
waiting cost per die and the resultant cost involved has
been found to be useful in modeling a proposed
system which enables to lower the costs involved due
to waiting time.
Table 4.1 Calculation of Waiting Cost
4.2.Summary of Service Cost for different Service
Points
The summary of service cost corresponding to
different service points is shown below:
Number of
service points
3
4
5
6
Service cost per dies (in Rs.)
95.54
103.04
118.04
133.04
Table 4.2 Summary of Service Cost
4.3 Total Cost
The total cost is the sum of waiting cost and service
cost. Total cost corresponding to different service
points is shown below:
Service point
Total cost per dies (in
Rs.)
527.51
341.04
131.47
148.66
3
4
5
6
Table 4.3 Total Cost
It is clear from the above analysis that the
optimum number of service points is 5.
4. RESULTS
The results based on the simulation model and cost
model are shown below:
The Optimum number of service points
= 5
Corresponding average waiting time of dies =
2.15
hr
(2 hr and
15 min)
If the company install a new service point,
Saving per dies
= Rs. (527.51 – 131.47)
= Rs. 396.03
Saving per month
= Rs. (396.03 x 80 x 30)
ISSN: 2231-5381
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