Variability and Throughput

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Topic 8 Variability and Throughput

• Throughput loss
• Resources in sequence
• Natural variability
• Setup and downtime variability
• Variability propagation
• Cellular manufacturing example

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• Variability is any departure from uniformity
• random or controllable
• Randomness is an essential reality and an
  artifact of incomplete knowledge
• Management implications must make system robust
• Sources of variability include
• setups workpace variation
• failures differential skill levels
• shortages engineering change orders
• yield loss/rework customer orders
• operator unavailability product
  differentiation
• operator unavailability material handling

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Probabilistic Intuition

• First Moment Effects (mean-based)
• Throughput increases with worker/machine speed
• Throughput increases with availability
• Inventory increases with lot size
• Our intuition is good for first moments
• Second Moment Effects (variance-based)
• Which is more variable processing times of
  parts or batches?
• Which are more disruptive long, infrequent
  failures or short frequent ones?
• Our intuition is less secure for second moments

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Measuring Process Variability
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Variability Classes
High variability (HV)
Moderate variability (MV)
Low variability (LV)
ce
0.75
0
1.33

• Effective Process Times
• actual process times are generally LV
• effective process times include setups, failure
  outages, etc.
• HV, LV, and MV are all possible in effective
  process times
• Relation to Performance Cases For balanced
  systems
• MV Practical Worst Case
• LV between Best Case and Practical Worst Case
• HV between Practical Worst Case and Worst Case

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Process Variability Example
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Natural Variability

• Definition variability without explicitly
  analyzed cause
• Sources
• operator pace
• material fluctuations
• product type (if not explicitly considered)
• product quality
• Observation natural process variability is
  usually in the LV category.

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Down Time Mean Effects

• Definitions

Availability Fraction of time machine is
up Effective Processing Time Effective
Processing Rate
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Down Time Variability Effects

• Effective Variability
• Conclusions
• Failures inflate mean, variance, and CV of
  effective process time
• Mean increases proportionally with 1/A
• SCV increases proportionally with mr
• For constant availability (A), long infrequent
  outages increase CV more than short frequent ones

Variability depends on repair times in addition
to availability
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Down Time Example

• Data Suppose an injection molding machine has
• 15 second stroke (t0 15sec)
• 1 second standard deviation (s0 1sec)
• 8 hour mean time to failure (mf 8 ? 60 ? 60
  28,800sec)
• 1 hour repair time (mr 1 ? 60 ? 60 3600sec)
• Natural Variability

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Down Time Example (cont.)

• Effective Variability

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Down Time Example (cont.)

• Effect of Reducing MTTR Suppose we can do
  frequent PM which causes mf 8 minutes, mr 1
  minute (60 sec).

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Setups Mean and Variability Effects

• Analysis
• Observations
• Setups increase mean and variance of processing
  times.
• Variability reduction is one benefit of flexible
  machines.
• However, the interaction is complex

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Setup Example

• Fast, inflexible machine 2 hr setup every 10
  jobs
• Slower, flexible machine no setups
• Traditional Analysis No difference!

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Setup Example (cont.)

• Compare mean and variance
• Fast,inflexible machine 2 hr setup every 10 jobs

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Setup Example (cont.)

• Slower, flexible machine no setups
• Conclusion flexibility reduces variability.

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Other Process Variability Inflators

• Sources
• operator unavailability
• recycle
• batching
• material unavailability
• et cetera, et cetera, et cetera
• Effects
• inflate te
• inflate ce2
• Consequences effective process variability can
  be LV, MV,or HV.

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Illustrating Flow Variability
Low variability arrivals
t
High variability arrivals
t
Measuring Flow Variability
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Propagation of Variability
ce2(i)
cd2(i) ca2(i1)
ca2(i)
i
i1

• Single Machine Station
• where u is the station utilization given by u
  rate
• Multi-Machine Station
• where m is the number of (identical) machines and

departure variation depends on arrival
variation and process variation
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Propagation of Variability
High Utilization Station
High Process Var
Low Flow Var
High Flow Var
Low Utilization Station
High Process Var
Low Flow Var
Low Flow Var
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Propagation of Variability
High Utilization Station
Low Process Var
High Flow Var
Low Flow Var
Low Utilization Station
Low Process Var
High Flow Var
High Flow Var
Even these more complex relationships can be
explored with spreadsheets
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Seeking Out Variability

• General Strategies
• look for long queues (Little's law)
• focus on high utilization resources
• consider both flow and process variability
• Specific Targets
• equipment failures, setups and rework
• operator pacing
• anything that prevents regular arrivals and
  process times
• many others - deflate capacity and inflate
  variability
• long infrequent disruptions worse than short
  frequent ones
• Consequences of Variability
• variability causes congestion (i.e., WIP/CT
  inflation)
• variability propagates
• variability and utilization interact

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Exploring Cellular Manufacturing, Process
Variability, and Pooling Synergy using
Spreadsheet-based Flowline Tools
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All Families
Job Shop
Cell
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Job Shop
All Families
Spreadsheets may be used to estimate efficiency-ba
sed performance of a hypothetical job
shop. Example Shop Assumptions 1. 92 unit
throughput per hour 2. General arrival
distribution 3. CoV(.5) arrival distribution 4.
4 machines per department 5. Machine capacity
25 units per hour 5. General processing
distribution 6. CoV(1.0) process distribution
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raarrival rate (units per hour) soSTD of
processing time caCoV of arrival
distribution toavg processing time
(hours) mnumber of machines ceCoV
of processing distribution bmsmax processing
(per hour)
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Muutilization CdCoV of
departure distribution CTqavg wait time
THavg throughput CTavg time at station
WIPavg work in process
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Conclusions from Spreadsheet Analysis
A seven department (4 identical machines per
department) job shop with general arrivals and
general processing, requires 78 units of WIP and,
on average, .85 hours of cycle time per unit to
maintain 92 units of throughput.
Components of cycle time
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Likewise, we can use this spreadsheet methodology
to evaluate performance changes as the
departments become smaller.
Thus, moving from 4-machine departments to
1-machine departments increases average cycle
time from .85 hours to 3.17 hours.
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Using this methodology we may then evaluate the
performance of new shop structures
Individual machine assignments within each shop
structure
Job Shop
Job Queue
Two-Cell Shop
Hybrid Shop
Job Queue
Job Queue
Job Queue
Job Queue
Job Queue
Four-Cell Shop
One-Cell Shop
Job Queue
Job Queue
Job Queue
Job Queue
Job Queue
Job Queue
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Base Case Conditions - High Utilization
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Cycle time performance changes as pooling synergy
is reduced
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Cycle Time Performance at 92 Utilization
Thus, the cycle time cost of moving toward a
cellular layout can be severe. In this example,
if a manager cannot exploit efficiency
advantages from CM, the move from a job shop to
a 4-cell shop increases cycle time by 382
percent. Also note that reducing
arrival variation by 100 percent does not help
much.
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WIP Requirement at 92 Utilization
Not only will cycle time increase, but the level
of WIP required to maintain 92 units of
throughput will also increase by 382 percent.
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Base Case Conditions - Moderate Utilization
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Cycle Time Performance at 82 Utilization
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Required Changes in Base Speed
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Changes in machine speed required to provide
equal cycle time performance at Ca 1.0
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Required Changes in Variability
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Changes in processing variability required to
provide equal cycle time performance at Ca 1.0
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• Managerial Insights and Conclusions
• User-friendly tools can be used to access
  relatively complex phenomena - such as
  variability propagation
• The operational impact of many phenomena are
  counterintuitive - thus a managers intuition may
  be inadequate
• The impact of a loss of pooling synergy that
  accompanies a move to GT provides an excellent
  example
• Many have been surprised by the large
  improvement in process and setup time required
  for a GT shop to outperform a job shop
• These user-friendly tools may help quickly
  explore alternatives such as hybrid layouts,
  limited machine dedication, efficiency gains and
  variability buffering