Simulation of a Manufacturing Cell for
Silicon Nitride Balls
Submitted to: Prof. Ernesto Gutierrez-Miravete
By Roman Czarniecki
Class: DES. 6460
Date: December 21, 2000
Table of Contents
Page 3
Abstract
Page 3
Introduction
Page 4
Objective
Page 5
Scope
Page 5
Requirements
Page 6
Arrivals of Orders
Page 7
Cycle Times and Set-Up Times
Page 8
Locations
Page 8
Resources
Page 9
Assumptions Used in the Model
Page 10
Verification & Validation of Model
Page 11
Performance Metrics
Page 12
Results/ Discussion
Page 13
Conclusion
Page 14
References.
Exhibits 1 to 5
Text view of Program
Program output
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ABSTRACT:
This project is a model of a manufacturing cell that produces balls made of silicon nitride
material. These balls are used as rolling elements in ballbearings. The model includes two
operations, a rough lapping step and a finishing step. Each operation has two types of machines,
small and large capacity. There are a total of 48 machines modeled. A cleaning process between
the two operations and a final cleaning process are also included.
The Project explores the effect that changing the number of employees operating the cell
has on the cost per unit produced, and overall profitability of the cell. Fixed over head, labor, raw
material, and variable operating expenses are figured into the calculation for cost per unit. Profit
calculation takes into account the cost per unit and also the production rate for the various
scenarios.
INTRODUCTION:
As the General Manager of a ballbearing plant in Winsted CT, I am concerned with the
costs of parts produced and the overall profitability of the plant. Some times it is not intuitive
that the lowest cost scenario will produce the most profits. This is because you have to balance
cost with volume of production. To illustrate this, if particular items sells for $100 and under one
scenario the cost is $50 per unit to produce it at a production rate of 10 units per day. Profit
would be $500 per day. Under another scenario, the cost is higher, $60 per unit, but the
production per day is 15. Here the profit would be is $800 per day.
Changing the number of employees working in a cell has a big effect on production and
production costs. Experimenting on the floor is costly and time consuming. It takes time and
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money to recruit and train employees. This model allows experimentation with relatively little
expense or time.
The area explored is a manufacturing cell that produces silicon nitride balls for use as
rolling elements. Ballbearings using this type of balls are primarily used in high-speed spindles
in machine tools. The lightweight, durability, and ability to machine them to supercritical
tolerances make them ideal for those demanding applications. The result is a spindle that can
operate at higher RPM’s, with less vibration, and for longer mean time to failure than bearings
with steel balls. The sphericity specification for these balls is less than 0.000005” and the
maximum diameter difference between any 2 balls in a batch is 0.000010”. The process involves
the rough machining of blanks and the final polishing operation. Both processes are batch
processes where a quantity of balls are processed at the same time. Because of the toughness of
the material and the tolerances involved, the cycle time is extremely long. Average cycle time is
over 106 hours per process per batch. There is a cleaning operation after the rough machining
and a final cleaning operation after finish lap. The inspection and packing operations afterwards
are not considered in the model since they are not a major expense and the model was to be as
simple as possible. See exhibit #1 for a process diagram.
OBJECTIVES:
1) To determine the number of machine operators needed to run the cell so that it
produces silicon nitride balls with the lowest cost per unit.
2) To determine the number of machine operators needed to run the cell so that it
produces the most amount of profit.
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SCOPE:
Scope was limited to the manufacturing cell. In the cell, 2 operations are performed.
rough lapping, and finish lapping. Modeling included the set up time, load/unload time, cycle
time, and machine attendance time required by the operator. Cleaning in-between operations, and
final cleaning was also included in the model. The arrivals of orders were not modeled nor were
the inspection and packaging operations that occur after the manufacturing operations.
REQUIREMENTS:
The set up times and cycle times for each operation had to be gathered from the
production cell. The information regarding cycle times was available in the production control
software used in the plant. The software keeps track of all operation times. The times for the
subject operations were downloaded into a spreadsheet and the distribution type and descriptive
statistics were determined. See exhibits 2 and 3.
Times for setup were obtained from log sheets. While the load, unload, and machine
attendance times were estimated by asking and observing the operators.
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ARRIVALS of ORDERS:
The entities involved in this model are the silicon nitride balls. The different types are all
similar except for the diameters. Since the balls are processed as a batch. The entity for the
model was chosen to be a batch of balls. For each diameter, the quantity of balls per batch varies
in order to keep the volume the same. The larger the diameter, the fewer balls in the batch. Since
the volumes are similar, the process times for the different diameters turns out to be the same.
This led to the ability to simplify the model and use two entity types, one for the large machines
and one the small type of machines. Batch quantities for this model were chosen to be constant at
2,500 for the small machines and 7,500 for the large ones.
The production orders are scheduled by the production control department. They use a 6week window for planning. The result is a level schedule for each size. There are enough
machines in the cell to dedicate machines to certain sizes. Hence set-up for change over to
different diameters are not common in the cell. For this reason, it was decided not to model
random arrivals. Instead the arrivals will be scheduled deterministically. A model of the
incoming sales orders is beyond the scope of this model.
The arrivals consist of an entity called blanks. These are then split into two types of
entities that simulate the small machines and the large machines running at the same time. The
arrivals will be scheduled so that work will always be available for the first operation. This is a
true representation of the cell since they are working off a backlog of orders.
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Cycle Times and Set-Up Times:
The two maching operations are; rough machining the blank, and finish lapping. Both are
similar operations. Both use the same type of machines but the difference is in the abrasives
used. The cycle times have been engineered to be the same so that the rougher feeds the finisher
without a bottleneck situation. The process times are engineered to be 100 hours each.
Examination of actual process records showed that the actual times varied according to a normal
distribution with a mean of 106 hrs and a sample standard deviation of 12.8 hrs. The machines
have to be loaded and unloaded by the operator. Once loaded, the machine runs continuously
until the process is complete, but, the operator has to check the machine once per hour to visually
inspect and gauge 5 pieces from the batch. One minute per machine per hour is allotted to do
this. This was modeled by using the resource down time function in Promodel. The operator is
also responsible for changing the tooling. The tooling is changed after eight batches are
completed on the rough lap operation and after 12 on the finish lap. It is also changed if a
different diameter size is to be run. The later is a rare case and therefor not included in this
simplified model. Changing the tooling, was modeled using the machine downtime function of
Promodel.
The cleaning operations are manual operations performed by the operators. No records
are maintained nor are there any engineered standards. By talking with the operators and
observing the operations the times indicated in exhibit 4 were estimated.
The load and unload times were also estimated by the operators since no log was
maintained that kept track of this part of the operation. See exhibit 4
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LOCATIONS:
It was desirable to keep the model simple enough to be able to model on the student version of
Promodel. The locations were limited to an incoming queue, two sizes of roughing machines, a
rough cleaning area, a finish lap queue, two sizes of finish machines, a final clean area, and an
exit area called packing. The number of units for each of the machine sizes was set to 12. This
configuration had a total of 48 processing machines.
RESOURCES:
The operator is the only resource considered in the model. The Operator is responsible
for all functions in the cell. The list of tasked performed is; move work from location to location,
load machines, unload machines, perform cleaning operations, perform setups and preventative
maintenance, and monitor each of the machines running. The number of operators was varied
from one to three to study the effect on cost and profit
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ASSUMPTIONS MADE:
1)
Each machine is dedicated to a particular diameter ball. No change over times are
modeled. In reality, change-overs are done in response to the changing demands
of the various diameters of balls produced. Since change overs are not frequent,
and they are normally scheduled for a machine that is due for a set-up due to
tooling wear, this assumption does not significantly effect the accuracy of the
model.
2)
The correct number and size of raw material blanks are always available for the
first operation. The validity of this assumption depends on a correct forecast, and
the rate of change from the forecasted amounts. This area could also be a topic for
a simulation model. It is not included in the scope of this simulation model.
3)
No scrap or rework activity is modeled. Actual data shows scrap and rework to be
less than one percent of the total output. For the objective stated, this simplifying
assumption has little impact on the results.
4)
All operators are fully trained, and the system is operating in a steady state.
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VERIFICATION:
The Model was verified by watching the animation to make sure the model was doing
what was intended. Deterministic values were entered first and compared to hand calculations for
what the outputs should be. Once this was done then the deterministic values were replaced by
appropriate distributions such as normal and exponential, and triangular.
VALIDATION:
The outputs from the model were compared to the actual results from the manufacturing
cell. The cell modeled is ½ the size of the actual cell in terms of number of machines. The cell
operates with three operators per shift. Three shifts run per day on a five day week. The cost per
unit is $0.53, this compares to the model cost of $0.55. The actual cell production rate is one
batch per week. The model with two operators, produced 53.7 batches in the one year simulation
time frame. These figures support the validation of the model.
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PERFORMANCE METRICS:
Units Produced:
The total number of explicit exits reported by Promodel for each entity was multiplied by the
batch quantity for each type. Small batches were 2,500 and the large ones were 7,500.
Operator Cost:
The total number of scheduled hours multiplied by the hourly rate plus 30% for fringe benefits
multiplied by the number of operators per shift.
5760 * 14.69 * 1.30 * # of operators
Machine Cost:
Reported by Promodel is the hourly rate multiplied by the hours that it was actually running.
Fixed Cost:
This includes such items as Rent, property taxes, selling and supervisory expenses. The figure of
$625,000 was obtained from the accounting department.
Raw Material Cost:
Price per unit that the blanks cost.
Cost Per unit:
Total cost divided by the Units Produced
Gross Profit:
The (selling price per unit minus the cost per unit) multiplied by the # of units produced.
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RESULTS/DISCUSSION:
The simulations were run for a 1-year period (5,760 hrs), and a warm up period of 3
months. The long period was chosen due to the long cycle times and long times between tool
changes. The long warm up period allowed the system to reach steady state operation. A few
warm-up periods were tried starting from 100 hours and growing until there was no significant
effect on the total quantities produced.
Total cost per unit, number of units produced and total profit for the year was calculated.
The simulation was run with one, two, and three operators to see the effect on cost and profit.
See exhibit 5
The results indicate that the best configuration is to have two operators run the cell. This
results in the lowest cost per unit, and also the most profit for the cell. Using one operator is not
good because the operator is not able to keep of with all of the tasks and therefore Machines are
idle waiting for service from the operator. For the case of one operator, the machine utilization
for the various types of machines ranges from 58% to 75% and the Operator utilization is 96%.
While the case where two operators are used, the machine utilization is greater than 99% and the
operator utilization is 54%. For the case where 3 operators were used, the machine utilization
remained about the same so the added cost of another operator was not absorbed by any
significant increase in productivity. This resulted in a higher unit cost and a lower profit than the
case of using 2 operators. See exhibit 5 for detail comparison.
The actual cell has twice the machines that the model had and uses three operators. The
results suggest this may be the correct mix because the in the model with two operators, the
operator utilization was low 54%. The next step would be to grow the model to include the entire
system.
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CONCLUSION:
Two operators are needed to run the cell in a manor that produces the balls at the lowest
cost. It is also the configuration that produces the most profit. The utilization of the machining
equipment is over 99% and the utilization of the 2 operators is 54%. See exhibit 5 for details
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References
1
Simulation Modeling and Analysis, third edition-Averill M. Law & W. David Kelton
2
Simulation using promodel, third edition-Dr. Chales Harrell, Dr. Biman K. Ghosh, Dr.
Royce Bowden
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