Transcript Introduction to Assembly Lines Active Learning – Module

Unpaced Lines - Module 4
Dr. Cesar Malave
Texas A & M University
Background Material
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Any Manufacturing systems book has a
chapter that covers the introduction about the
transfer lines and general serial systems.
Suggested Books:
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Chapter 3(Section 3.5) of Modeling and Analysis of
Manufacturing Systems, by Ronald G.Askin and Charles
R.Stanridge, John Wiley & Sons, Inc, 1993.
Chapter 3 of Manufacturing Systems Engineering, by
Stanley B.Gershwin, Prentice Hall, 1994.
Lecture Objectives
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At the end of the lecture, each student should be
able to
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Estimate the throughput of a line in all the cases listed
below
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Identical workstations, random service, no buffers and no failures
Identical workstations, random service, equal buffers and no
failures
Constant processing time, random failures and random repair times
Determine the optimal location of the buffer in a transfer
line.
Time Management
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Readiness Assessment Test (RAT) - 5 minutes
Lecture on Unpaced Lines - 10 minutes
Spot Exercise on Unpaced Lines - 5 minutes
Lecture on Unpaced Lines (contd..) - 15 minutes
Team Exercise on Unpaced Lines - 5 minutes
Homework Discussion - 5 minutes
Conclusion - 5 minutes
Total Lecture Time - 50 minutes
Readiness Assessment Test (RAT)
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Differentiate between Paced and Unpaced Lines
Paced Lines
Unpaced Lines
Also referred to as a synchronous
line
Also referred to as an
asynchronous line
Limit on time available to
complete each task
No fixed time to complete a task
Cycle time determines the
production rate
Buffers between workstations
are necessary
Each workstation is given the
same amount of time to perform a
job, and as such they start and
stop at the same time
The unpaced line moves the job
either to the next workstation or
buffer immediately upon
completion
Unpaced Lines

Introduction
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Each workstation acts independently
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Random processing times are involved
Each job has its own requirements at each workstation
Upon completion of the task, each workstation attempts to
pass its part on to the next workstation or the buffer
 If the next workstation is idle or buffer space exists part is passed
 Else, the station becomes blocked
Upon passing the part, the workstation checks its input
buffer
 If a part is available, the station is active and begins
working
 Else, the station becomes starved
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Unpaced Lines (contd..)
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Identical Workstations, Random Processing Times,
No Buffers, No Failures - Case 1
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Consider a line with M stages and all workstations have
the same processing time distribution
Processing times for each stage of each job are assumed to
be independent and identically distributed
Workstations do not break down
No Buffer space exists
Workstations will be starved until the upstream station
finishes its operation
Workstations will be blocked until the downstream station
finishes its operation and is able to pass on its job
Unpaced Lines (contd..)
Coefficient of Variation of processing time (CV)
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CV determines the throughput
CV = standard deviation / mean
Effect of random processing time in balanced, unbuffered lines
1.0
0.9
Relative output
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CV = 0.1
0.8
CV = 0.3
0.7
CV = 0.5
0.6
0.5
CV = 1.0
0.4
1
2
3
4
5
6
Number of stages
7
8
9
Unpaced Lines (contd..)
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Analysis of Conway’s findings - Case 1
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Throughput decreases as the number of stages increases,
but levels off immediately.
A two-stage line with CV of 0.5 has only 80% of the
throughput of a single-stage line
But a eight or higher stage line with the same CV will
have 65% of the throughput of the single-stage line
After a certain number of stages, a further increase in the
number of stages will only lead to a minor reduction in
the throughput as compared to a single-stage line
For CV = 1, throughput levels off at 45% of the singlestage output and for CV = 0.5, throughput levels off at
65% of the single-stage output
Spot Exercise
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Suppose a serial processing unit has 3 stages and
each station requires a mean service time of about
10 minutes with an exponential distribution.
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Find the production rate for the line if there are no buffers.
Suppose service time variability could be reduced to a
standard deviation of one minute (non-exponential), find
the production rate.
Solution
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Case (i):
CV for an exponential distribution = 1.0
From Conway’s findings, we find that for 4 stages,
the relative output value is 0.55.
Therefore, instead of 1 unit being produced every 10 minutes
i.e. a production rate of 0.1/min, we have a production rate
equal to 0.55*0.1 = 0.055/min = 3/hr
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Case (ii):
New coefficient of variation (CV) = 1/10 = 0.1
From Conway’s findings, we find that for 4 stages,
the relative output value is 0.91.
Therefore, instead of 1 unit being produced every 10
minutes i.e. a production rate of 0.1/min, we have a
production rate equal to 0.91*0.1 = 0.091/min = 5.5/hr
Thus, there is a significant increase in the production rate
from Case 1 to Case 2.
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Identical Workstations, Random Processing Times,
Equal Buffers, No Failures - Case 2
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Buffers of same capacity are placed between each pair of
workstations
The first buffer will always be full since the first
workstation is never starved
The last buffer will always be empty since the last
workstation is never starved
The middle buffer will be half full or half empty on the
average
Overall, the buffer utilization decreases from the front to
the rear of the line
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Case 2 (contd..)
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Since buffers are involved in this case, throughput
depends on the ratio of buffer capacity (Z for each buffer)
to the processing time CV
1.0
0.8
0.6
0.4
0.2
0
10
20
30
40
50
60
Z = Size of each buffer
70
80
Z
CV
Proportion of lost output recovered by buffering in balanced lines
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Case 2 (contd..)
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In this case, some percentage of the capacity lost can
be recovered by the addition of buffers
This is marginally dependent on the length of the line
From Conway’s findings of the average recovery
proportion graph, the following observations can be
made:
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For Z/CV = 10, about 80% of the capacity lost due to
random processing times is recovered.
For Z/CV = 20, about 90% of the capacity lost due to
random processing times is recovered.
First, we can find the capacity lost because of random
processing times from Case 1 i.e., using CV
Second, we can find the portion of the loss that can be
recovered by buffering from Case 2 i.e., using Z
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Optimal Buffer Location
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For one buffer (Z = 1), the optimal location is the center of the
line such that all the upstream workstations will have the same
availability as those of the downstream workstations
For lines with identical workstations, the best allocation is
many buffers of nearly equal size.
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The largest buffers should be in the middle
The difference between the largest and smallest buffers should be
no more than one slot
Buffer sizes should be symmetric from the center moving to the
front and rear of the line
For lines with unequal workstations, the less reliable
workstations should have larger input and output buffers
In case of failures or high processing time variability at a
workstation other than the bottleneck workstation, the input
and output buffers play a significant role in maintaining its
utilization
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Constant Processing Times, Random Failures and Repair
Times - Case 3
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To avoid the possibility of the stages to lose synchronization, it is
worthwhile to employ asynchronous part transfer even in a
balanced, constant-processing-time environment
Assume identical workstations and buffers are placed between
every pair of adjacent workstations
From Conway's findings, throughput is determinant on the ratio
Z.b/(1 + CV2R) where
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CVR is the coefficient of variation of repair time distribution
b-1 is the average repair time measured in processing time cycles
Z.b is the size of the buffer measured in multiples of average repair
time
Effect of the buffer (improvement) is measured by the proportion of
possible improvement gained form the addition of the buffer i.e.,
(EZ – E0) / (E – E0)
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Case 3 (contd..)
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Conway’s Findings
Effect of Buffers with Random Failures and Repair Times
Z.b/(1 + CV2R)
0
0.25
0.5
1
2
4
8
(EZ – E0) / (E - E0)
0.0
0.25
0.35
0.5
0.7
0.8
0.9
Note: CVR is 1 for an exponential distribution.
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Buffers and production control
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If the availability of the portion of the line in front of the buffer
is larger than that of the portion behind it, the buffer will tend
to be full
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If the availability of the portion of the line in front of the
buffer is smaller than that of the portion behind it, the
buffer will tend to be empty
If the availabilities are similar, the buffer will tend to be
half-full
Buffering is closely related to the pull-push system
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Output buffer capacities are limited in pull system (JIT) and
workstations stop when these are full
In a push system (MRP), workstations continue to produce even
when there is no pull for stock down the line i.e, when the
downstream stations break down
Team Exercise
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Four automatic insertion machines are set up for series,
without intermediate buffers, to add components to printed
circuit boards. Each machine inserts 20 different
component types. Due to board design and component
requirements, automatic setup and insertion times for
machines vary from 2 minutes to 6 minutes per
workstation. Assuming that machines do not fail, estimate
the number of boards produced by this line/hr while the
machines are all operational.
Solution
Number of reliable workstations = 4
Cycle time Є [2,6] and let us assume uniform distribution
Mean processing time (µ) = (2 + 6)/2 = 4 minutes
Standard deviation of processing time (σ) is given by
σ = (max–min)/√12 = (6 - 2)/√12 = 1.15 minutes
Hence, the coefficient of variation (CV) = σ/µ = 0.29
From Conway's findings (Figure 3.6, Askin & Stanridge), we find
that the relative output factor is 0.8.
Hence, output/hr = 0.8 * (1 cycle/4 min) * (60 min/1 hr)
= 12/hr
Homework
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Consider a six-stage serial processing system with
identical workstations and random processing times.
Details about the unpaced line are given below:
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Mean processing time at each workstation is 30 minutes
Standard deviation of processing times at each station is
about 9 minutes
Find the production rate of the line while it is
operating.
Conclusion
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Coefficient of variation is required to estimate
the production rate in case of reliable
workstations and random processing times.
To estimate the effect of buffers when
workstations fail, average repair time and the
coefficient of variation for repair time are
needed.