Simulation and Six Sigma
How to Complete a Six Sigma
Project with Little of No Data
(Or “Why Simulation Can Help
Solve the Unsolvable”)
Larry Goldman
Decisioneering – Crystal Ball
May 7, 2007
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Simulation and Six Sigma
Today’s Agenda

The Problem: Little or No Data
Simulation Basics & the Fit Within
Six Sigma?

Project 1: Loan Process

Project 2: Inventory Optimization

Project 3: Simulation with DOE

Conclusion
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Simulation and Six Sigma
Why Do Bad Things Happen to Good Projects?
• Staffing changes
• Lack of strategic focus
• No buy in from Process Owner
• Not enough dedicated resources
• Project takes too long & loses momentum
• Lack of support from the top
• …(what else?)…
• Little or no data available
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Simulation and Six Sigma
The Less-Than-Ideal Project
Time is not on your side. Takes way too long to:
– Collect statistically viable project data
– Implement process or design changes
– Measure the effect of Improve solutions
– Can only run limited DoEs
– Find a solution in a competitive market
Or your data…
– Is too costly to obtain
– Can only be estimated
– Just doesn’t exist prior to project
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Simulation and Six Sigma
The Less-Than-Ideal Project
The project X’s and Y’s are complicated:
– Past data was not collected or poor measuring
system
– Many likely X’s (possible root causes in system)
– Many non-normal distributions (skewed variation)
– Physical models (generally designs) are impractical
– Non linear equation is difficult to predict
– Forecast relies on uncertain demand
– Poor understanding of fluctuation of input values
– Process becomes out of control despite
“optimization” of inputs
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Simulation and Six Sigma
Healthcare Example: Healthcare software provider ran
simulation to reduce cycle time on new software installation
and implementation process by 50%.
PROBLEM:
Misys Healthcare Systems produces software used by physicians and
hospitals. Installation and implementation of the Misys hospital
enterprise software took 18 to 36 months, far too long. The team
needed to design a new, faster process.
SOLUTION:
Given the long cycle time for this process, a simulation was the only
viable option to determine the anticipated cycle time. The team
simulated the high-level components of the new design to determine
the capability of the new process and identify those elements in the
new process that were having the greatest impact on cycle time.
RESULTS:
The project will allow for reduced cycle time and accelerated revenue
recognition (in half previous time). The solution validated the intuition
of the LSS team that the 50% cycle time reduction goal was realistic.
The solution also provided a level of confidence to senior management
that the team met their goals.
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Simulation and Six Sigma
Reliability Example: Simulation assesses Customer Reliability CTQ,
finds the delinquent component in a complex system, and saves over
400 man-hours of calculations
THE SITUATION
Perform analyses on engines to determine reliability characteristics. The objective
is to establish reliability predictions, evaluate how the variability of individual part
reliability affects the system-level reliability CTQ, and make recommendations to
Project Management Team (PMT).
THE SOLUTION
Build a model that accounts for the different distributions of the parts, including
hundreds of assumptions and forecasts. Simulate over 400,000 trials to assess
variability in failure rates and identify delinquent component.
THE RESULTS
- Save over 400 man-hours of calculations by automating analysis w/simulation
- Determine that Customer reliability CTQ can be met 93.7% of the time
- Identify the delinquent component that contributes the largest effect on system
mean (24.3% ) and variability (97.3%) and recommend further analysis of this
component to determine whether sub-components are at fault
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Simulation and Six Sigma
Process Control Example: At Motorola, a design process
was brought back into control by simulating data to
determine the hidden critical factor.
PROBLEM:
Field emission from carbon nanotubes (CNT) for display purposes was
optimized using Design of Experiments (DOE). The brightness was
improved by three orders of magnitude but the achieved gains could
not be sustained in the “Control” phase of a DMAIC project, and the
process reverted to poor performance.
SOLUTION:
It took an intense effort of circa two months to recover the process.
Monte Carlo simulations were used to provide an excellent fit to all the
measured emission data over the course of eight months in both
range and shape.
RESULTS:
The simulations indicated the cause of the process drift. A hidden
factor that was too time- and labor-intensive to measure in real-time
was responsible and uncovered. With the aid of the simulations, the
process could have been recovered within days instead of months.
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Simulation and Six Sigma
Types of Simulation
• Monte Carlo (Stochastic) Simulation:
Random sampling experiment used to generate multiple
scenarios. Each trial is a complete event.
• Discrete Event Simulation:
Time-based analysis. The operation of a system is
represented as a chronological sequence of events. Each
event occurs at an instant in time and marks a change of
state in the system.
• CAD-based Simulation:
Tools that animate CAD designs to simulate motion.
• Instructional Simulation:
3-D simulators used for testing and training.
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Simulation and Six Sigma
Why Do You Need a Model?
• Models are an attempt to capture behavior and performance
of business processes and products.
• Simulation is the application of models to predict future
outcomes with known and uncertain inputs.
SIMULATION
MODELS
1
F = m∗a
2
3
LO
HI
Control
Inputs
Noise
Variables
Y = f (x)
Y = f (x)
Outcome
Predictions
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Simulation and Six Sigma
Where Do Models Come From?
16d 0T
τ=
π d0 4 − di 4
(
Models come in many different forms
• Regression equations derived from historical
data (e.g., transactional processes)
• Design of Experiments (DOE) response
equations from measured observations
• Mathematical relationships based on
established physical principles (e.g.,
Shear stress in torsion tube)
• General knowledge of business system or
product (e.g., expert opinion)
Data comes from the same sources.
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)
Simulation and Six Sigma
What Is Monte Carlo Simulation?
• Definition: A system, or sampling method, that uses random
numbers to measure the effects of variation or uncertainty.
• The inputs: Probability distributions that represent variable or
uncertain X’s (assumptions). Inputs can be defined by:
– Existing process or design data (best)
– Limited data (e.g., DoE, process with long cycle time)
– Expert opinion (little to no data!)
• The outputs: Any response / Y / formula / effect (visual forecasts)
• The tool: Desktop simulation programs
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Simulation and Six Sigma
Inputs: Probability Distributions
y Simulation requires probabilistic inputs.
y Distributions use ranges of values and assign a likelihood of
occurrence for values (e.g., a normal distribution could represent
variation of the part dimensions).
Probability
Range
Parameters
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Simulation and Six Sigma
Outputs: Charts and Tables
Number of
simulation trials
Parts within the
spec limits are
shown in blue,
parts outside spec
limits are shown
red
Certainty (probability) that
the forecast lies between LSL
and USL
Upper Spec Limit
(USL)
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Quality Metrics such as
Cpk, ZST, p(N/C), etc....
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Simulation and Six Sigma
Sensitivity Analysis: A Critical Tool
• Examine which few critical
factors (X’s) in your analysis
cause the predominance of
variation in the response
variable of interest (Y) – like
a Pareto Chart
• Operates during the
simulation, calculating the
relationships between all X’s
and Y’s
• Acts as communication tool
to help team understand
what’s driving defects and
where to focus (or not to
focus) your improvement
efforts
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Simulation and Six Sigma
Stochastic Optimization
Simulation can help you to understand and reduce
variation but does not by itself offer the best solution.
An optimization model answers the question "What's
best?" rather than "What happened?" (statistics), "What if?"
(simulation) or "What will happen?" (forecasting).
The combination of simulation and optimization lets you
make the best (optimal) decisions while accounting for
the variability or uncertainty inherent within a process.
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Simulation and Six Sigma
Where Do Professionals Apply Monte Carlo
Simulation in Six Sigma?
1. Product and Process Design (Little to No data)
–
Robust design is required.
–
Tolerance analysis is performed.
–
Process is relatively simple.
–
Project success and/or process risk are uncertain.
2. Project Management
–
Project has financial or schedule uncertainty.
–
Project has cost controls.
–
Project is high risk.
3. Systems Model Exists
–
You have a quantifiable process or spreadsheet.
–
Mathematical relationship exists.
–
Physical models are impractical.
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Simulation and Six Sigma
Typical Applications for Monte Carlo
Simulation and Optimization
• Process Optimization
• Sales Forecasting
• Market Sizing & Penetration
• Cost Estimating
• Tolerance Design/Analysis
• Critical Parameter
• Material Selection
• Risk Analysis
• Design for Variability
• Reliability Studies
• Product/Service Launch
• Total Life Cycle Cost
• Resource Allocation
• Inventory Optimization
• Value Stream Analysis
• Queuing Analysis
Identification
• Project Selection
• Strategic Analysis
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Simulation and Six Sigma
Project 1: Loan Process Improvement
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Simulation and Six Sigma
Problem Statement
Identify Value
Value Stream
• A financial organization wishes to use
Lean Six Sigma techniques on increasing
the efficiency and decreasing the
variation of their Loan Process.
• Customer: Loan Applicants
Improve Flow
• Note: This could really be any simple
Customer Pull
process or sub-process / cell
Process Perf.
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Simulation and Six Sigma
Project Overview by Phase
Identify Value
- Define Problem
Value Stream
-
Improve Flow
Create high-level process map
Refine process map to include variation (distributions)
Measure or estimate process step variation
Monte Carlo Simulation to predict variation
Determine variation drivers w/ Sensitivity Analysis
- Address drivers and reiterate simulation to improve
flow
Customer Pull
Process Perf.
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Simulation and Six Sigma
Step 1: High-Level Process Map
Identify Value
Value Stream
Improve Flow
1
4
2
Customer
Inquiry
5
Loan
Underwriting
Loan
Application
Loan
Closing
3
6
Document
Verification
Loan
Disburse
• Delays and Rework in Loan Process do not
add value to customers.
Customer Pull
Process Perf.
• Use Process Map and Value Stream
techniques to identify delays and rework
(assuming all identified process execution
steps are Value-Added).
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Simulation and Six Sigma
Refinement of High-Level Process Map
Execution
of Process
Delay
Rework
Decision
OUTPUT
Measure
INPUT
Define
Analyze
• Unfortunately, high-level process maps generally
Improve
• Using Monte Carlo techniques, we can model the
Control
do not consider delay times or rework cycles at
each process step (“Hidden Factory”).
variation in execution & delay times, in addition
to defects (reworks) occurring at each high-level
process step!
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Simulation and Six Sigma
Refinement of High-Level Process Map
• Six Steps
• Four can be broken into Execution and Delay
• Three rework loops
• Upper Spec Limit = 96 hours
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Simulation and Six Sigma
Step 3: Measure or Estimate Process Step
Variation
Identify Value
As part of the Value Stream Phase, an estimate or
measurement of the process step times needs to be
captured:
Value Stream
• Sampling: Samples of steps 1 and 6 indicate these steps
vary lognormally and normally, respectively.
• Expert opinion: No reliable measures of Steps 2 through 4
Improve Flow
Customer Pull
exist so expert opinion is utilized
– Step 2 has a most likely, a minimum, and a maximum
estimated process time
– Step 3 has an 80% chance of being anywhere between
16 and 32 hours and a 20% chance of being anywhere
between 32 and 48 hours
– Step 4 can be anytime between 1 and 8 hours
Process Perf.
• Collection System: No data was measured for Step 5 so a
measurement collection system was put in place for 100
processed loans.
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Simulation and Six Sigma
Building the Model - 1
For Execution inputs,
define each step as the
appropriate distribution
?
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Simulation and Six Sigma
Building the Model - 2
For Delay, define each
step as an Exponential
distribution
For Delay, define each
step as a Yes / No
(Binomial with 1 trial)
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Simulation and Six Sigma
Building the Model - 3
• Now, just calculate Cycle Time (91 hours with delay and no rework)
• Cycle Time = Execution steps + Delay steps + Rework when it occurs
• Can also calculate VA Efficiency (is it always that high?)
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Simulation and Six Sigma
Step 4: What Does the Simulation tell us?
After simulating 10,000 loans:
• Mean loan process cycle time is
93 hours (vs. base case of 91
hours)
• Standard deviation = 40 hours!
• ~40% of loans (3,839/10,000)
are over USL
• Sigma level is a dismal 0.084
• As-is state has serious
problems. What is driving the
variation?
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Simulation and Six Sigma
Monte Carlo Simulation to
Predict Variation
Identify Value
Value Stream
VA Efficiency is reduced by including effect of
added Cycle Time due to delay times and
rework cycles (non-value-added steps)
– VA Efficiency mean less than 100% (~ 35%)
Improve Flow
Customer Pull
Process Perf.
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Simulation and Six Sigma
Step 5: Review Sensitivity Analysis
Identify Value
Value Stream
Improve Flow
Customer Pull
Process Perf.
• Run Sensitivity
Analysis to
determine major
driver of variation.
• Can anything be
done to reduce
Document
Verification Delay
times?
– Assume average
delay time can
be reduced by
50% in Cell K33.
– Run simulation.
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Simulation and Six Sigma
Step 6: Reiterate Monte Carlo Analysis
Identify Value
Value Stream
• Run Monte Carlo again → less than 20% of
process loans are out of specification → Sigma
Level of ~ +0.8
• The Loan Process Cycle Time quality has been
improved.
Improve Flow
Customer Pull
Process Perf.
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Simulation and Six Sigma
Reiterate Monte Carlo Analysis
Identify Value
• By reducing the primary non-value-added
Cycle Time variation (Verification Delay), the
Value-Added Efficiency mean has also been
increased (from ~ 35% to ~ 40%)!
Value Stream
Improve Flow
Customer Pull
Process Perf.
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Simulation and Six Sigma
Comparison of Results
Stage
Mean
Cycle
Time
Mean VA
Efficiency
Standard
Deviation
Sigma
Level
Base Case
91 hours?
31.5%?
???
???
As-Is Sim
93 hours
~35%
40 hours
.08
To-Be Sim
75 hours
~40%
26 hours
.83
Analysis is iterative and the model will be adjusted
(improved) as the project continues…
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Simulation and Six Sigma
Project 2: Inventory Optimization
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Simulation and Six Sigma
Problem Statement
• The two basic inventory decisions that managers face
are: (1) how much additional inventory to order or
produce, and (2) when to order or produce it.
• Although it is possible to consider these two decisions
separately, they are so closely related that a
simultaneous solution is usually necessary.
• Given variable (uncertain) demand over a 52-week
period, you need to determine an optimal order quantity
and reorder point that results in the lowest possible total
annual costs.
• Demand is estimated for each week, based on expert
opinion or limited data.
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Simulation and Six Sigma
Project Overview by Phase
Define
- Review problem statement
Measure
- Create and validate system model
Analyze
- Characterize current process state with simulation
- Determine variation drivers w/ Sensitivity Analysis
- Address drivers and reiterate simulation
Improve
Control
- Optimize process for cost and performance
- Implement changes in ordering process
- Moving forward, process owner compares results
with simulation results, adjusts model as needed
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Simulation and Six Sigma
Step 1: Create Excel Model
Define
Measure
Analyze
• Determine amounts for inventory and ordering
Improve
• Create calculation for whether or not to place order
Control
• As-is state: $7,090 in Annual costs for order of 250 units
• Calculate individual weekly costs and roll up to annual
costs
and reorder of 250 units
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Simulation and Six Sigma
Step 2: Define Key Assumptions
All 52 weeks have same Poisson distribution for demand
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Simulation and Six Sigma
Step 3: Run the Simulation
Define
Measure
Analyze
Improve
Control
• After 10,000 trials, find that mean annual
inventory costs is around $25,500.
• The base case of $7,090 is far from realistic
given the uncertainty of demand.
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Simulation and Six Sigma
Running Simulation with Optimization
• Define objective: minimize mean of annual inventory costs
• Define controllable variables: Order Quantity (200-400
units) and Reorder Point (200-400 units)
Optimization
(1 = 1000
trials)
Order
Quantity
Reorder
Point
Minimized
Cost (mean)
1
250
265
$18,474
2
345
320
$2,791
3
325
275
$7,705
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Simulation and Six Sigma
Running Simulation with Optimization
Define
Measure
Analyze
Improve
Control
• After 10
minutes,
optimization
has converged
on Order Point
of 330 and
Reorder Point of
325.
• This will
minimize the
Annual Costs to
a mean of
~$2825.
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Simulation and Six Sigma
Running Simulation with Optimization
Define
Re-run simulation with new controls and see
optimized inventory problem at 10,000
simulation trials.
Measure
Analyze
Improve
Control
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Simulation and Six Sigma
Project 2 Conclusions
• Modeling demand of as-is state can show weaknesses of
base case estimations for forecasts with uncertainty.
• Stochastic optimization lets you run simulations while
changing controlled variables for each consecutive
simulation.
• By adjusting controlled variables during optimization, you
can determine settings that will optimize your output (e.g.,
minimize costs, maximize profit).
• Final optimization solution results in reduced inventory
waste and substantial cost savings.
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Simulation and Six Sigma
Project 3: Simulation with DOE
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Simulation and Six Sigma
Problem Statement
Define
Measure
Analyze
Improve
Control
• Situation: An Injection Mold Process has
resulted in incomplete filling of the mold or
different part lengths. A Six Sigma Project team
has been assigned to reduce the variation not
meeting length requirements.
• Customer: Part Buyers
• Approach:
– Perform 23 Full Factorial DoE (5 replicates) to
determine Response Surface model of Part Length
– Use Crystal Ball Capability features to predict
current quality metrics
– Use OptQuest Optimization techniques to
determine process settings that minimize process
cost while meeting minimum quality targets.
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Simulation and Six Sigma
Project Overview by Phase
Define
- Review problem statement
Measure
- Measure current parameter capability
Analyze
-
Perform Design of Experiments
Characterize current process state with simulation
Determine variation drivers w/ Sensitivity Analysis
Address drivers and reiterate simulation
Improve
- Optimize design for cost and performance
Control
- Run capability study on proposed process settings
to confirm quality
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Simulation and Six Sigma
Step 1: Measure Current Parameter
Capability
Define
As part of the Measure Phase, the variation
of the Control Parameters (Inputs, Factors)
is characterized during Capability Studies
Measure
– Input Factors are Mold Temp, Cycle Time, and
Hold Pressure
– 30 samples of each are made during the studies
and Factors are assumed to behave normally
Analyze
Each set of samples passes Normality Test
Means and Standard Deviations are recorded
Improve
25
20
18
16
20
14
15
12
15
10
10
Control
8
10
6
5
4
5
2
0
140
150
160
170
MoldTemp
180
190
0
48
80
90
100
CycleTime
110
120
0
120
124
128
132
HoldPres
136
140
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Simulation and Six Sigma
Step 2: Perform Design of Experiments
Define
• 23 Full Factorial DOE with 5 replicates is
performed (40 runs)
– RESPONSE: Part Length
Measure
Analyze
Improve
– FACTORS:
LO
HI
Mold Temperature (x1) 100
200
Cycle Time (x2)
60
140
120
140
Hold Pressure (x3)
• Response polynomial equation
developed (R2adj = 92.5%)
– 3 Main Effects
– 1 Interaction Term
Control
Y = β0 + β1x1 + β2x2 + β3x3 + β23x2x3
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Simulation and Six Sigma
Step 3: Characterize Current Process State
Define
• Define the Inputs (Factors) as Normal
Assumptions (Cells E5:E7)
– Cell Reference Assumption Name from Column B
Measure
Analyze
– Cell Reference Assumption Mean from Column F
– Cell Reference Assumption StDev from Column G
• Define the Response (Length in Cell E9) as
a Forecast
– Cell Reference the LSL from Cell F9
Improve
– Cell Reference the USL from Cell G9
• Run Simulation
Control
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Simulation and Six Sigma
Monte Carlo Simulation to Predict Variation
Define
Nominal Response of 64.59 mm close to
target but 2% will fall out of the spec
limits! → Sigma Level of ~ 2.0
Measure
Analyze
Improve
Control
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Simulation and Six Sigma
Step 4: Review Sensitivity Analysis
Define
• Run Sensitivity Analysis to determine major
driver of variation.
Measure
Analyze
Improve
Control
• Can anything be done to reduce standard
deviation of Mold Temperature?
– Assume standard deviation can be reduced by
50% in Cell G5.
– Run simulation.
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Simulation and Six Sigma
Step 5: Reiterate Monte Carlo Analysis
Define
Measure
• Run Monte Carlo again → ~ 1% are out of
specification → Sigma Level of ~ 2.5
• The Part Length quality has been improved
– Can it be improved even more while minimizing
cost to run the process?
Analyze
Improve
Control
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Simulation and Six Sigma
Step 6: Optimize Design for Cost & Performance
Define
Measure
How can the process settings be
configured so that a minimum quality
goal is reached while reducing the
process cost per part?
Analyze
Improve
Control
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Simulation and Six Sigma
Optimize Design for Cost & Performance
Define
Measure
Analyze
Improve
Control
• Must consider relationship between process
parameters and cost.
– Energy consumed by molding equipment is
proportional to product of Cycle Time and Mold
Temperature ($ ∞ Temp * Time)
– Labor Cost to run molding equipment proportional
to Cycle Time ($ ∞ Time)
• Create Cost Response as a function of
– Cycle Time
– Mold Temperature
$PROCESS = K1*Temp*Time + K2*Time
• Define Process Cost Forecast (Cell E10)
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Simulation and Six Sigma
Process DoE Optimization
Define
• Characterize Current Quality Levels (Cpk &
ZST)
– Enable Capability Metrics in Run Preferences
Measure
Analyze
Improve
Control
– In Define Forecast, use cell references for LSL &
USL and auto-extract Capability Metrics
• Assuming you can control the nominal
process settings but not the variation, use
Optimization to determine the settings that
results in the best quality (maximum Zscore)
• Process Parameters
– Mold Temp → LO (100) to HI (200), Step = 10
– Cycle Time → LO (60) to HI (140), Step = 1
– Hold Pressure →
Step = 2.5
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56 LO (120) to HI (140),
Simulation and Six Sigma
Helping You Optimize: Decision Variables
Decision variables are Crystal Ball model elements for
quantities over which you have control (e.g., percentage
of dollars to allocate in a project, amount of product to
produce, man-hours required for a project, unit cost for
a given product, go/no-go decision).
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Simulation and Six Sigma
Define Decision Variables
Define
Measure
Analyze
Improve
Control
• Define Decision Variable Lower and Upper
Bounds of all Factor means (Cells E5:E7) by cell
referencing corresponding adjacent cells:
Cell reference Name from Column B
Cell reference Upper Bound from Column C (LO)
Cell reference Lower Bound from Column E (HI)
• Ensure the correct Discrete Step Size is used
within each Decision Variable as listed below
Decision
Variables
Lower Bound
Upper Bound
Discrete Step
Size
Mold Temp
100
200
10
Cycle Time
60
140
1
Hold Pressure
120
140
2
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Simulation and Six Sigma
OptQuest: A Blend of Approaches
OptQuest excels at stochastic optimization because it:
• Uses several optimization techniques (Scatter Search and
Advanced Tabu Search) vs. relying on a single method or
genetic algorithm,
• Employs heuristics (problem solving techniques that use selfeducation to improve performance),
• Has both short-term and long-term Adaptive Memory,
• Can escape local optimal solutions to find global optimal
solution,
• Uses neural network technology that predicts performance
after only running 10% of simulation and typically reduces
number of required simulations by 50%, and
• Features a wizard tool that makes setup easy.
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Simulation and Six Sigma
Optimize Design for Cost & 4σ
Performance
Define
• Run OptQuest and Define Forecast
Selections
Optimization Goals:
Measure
Analyze
– Primary is to Minimize Cost
– Requirement is to Reduce Variation of Part Length
to 4σ levels
Zst required to have a lower bound of 4
Improve
Control
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Simulation and Six Sigma
Optimize Design for Cost & 4σ Performance
Define
New Design results in a Process Cost of $1.16 per
part and increase to 4σ quality!
Measure
Analyze
Improve
Control
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Simulation and Six Sigma
Comparison of Design Performance & Cost
Define
Measure
Analyze
Improve
Control
Where have we been, and where are we going?
Iteration
#
Mold
Temp
Mean
Mold
Temp
StDev
Cycle
Time
Mean
Cycle
Time
StDdev
Hold
Press
Mean
Hold
Press
StDev
Sigma
Level of
Flow
Rate
Process
Cost
1
160
10
100
10
130
5
1.94
$2.03
2
160
5
100
10
130
5
2.53
$2.03
3
150
5
61
10
140
5
4.01
$1.16
Six Sigma team proceeds to run Capability
Study on proposed process settings to
confirm quality during Control phase.
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Simulation and Six Sigma
Project 3 Conclusions
Define
Measure
• Quality Levels will be increased by decreasing
variation on driving input variables.
– Monte Carlo analysis predicts quality levels.
– Sensitivity analysis identified Mold Temperature
as most influential design variable.
Analyze
• Knowledge of variation drivers allows one to
Improve
• Stochastic Optimization of input variable
experiment with the process in the simulation
world and determine improvements.
(Factor) means will increase Part Length quality
levels while minimizing Process Cost impact.
Control
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Simulation and Six Sigma
Benefits of Simulation in Six Sigma Projects
with Little or No Data
• Provides a virtual recreation of the Process or Product needing
improvement, even when data is estimated.
• Can be used as a scoping tool early in DMAIC to guide project
direction and project management issues.
• Establishes current capability (as-is state) and tests potential
improvements (to-be state).
• Identifies defect-producing process steps driving unwanted
variation (as well as CTQs).
• Avoids extended wait for post-improve results and potential high
cost of implementation.
• Eliminates costly redesign-and-test loops and automates search for
optimal solution.
• Leads to Greater Customer Satisfaction
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Simulation and Six Sigma
Next Steps?
• We will be here for the
remainder of the event and
can give demos and answer
questions.
• Trail versions (30 days) and
informational materials are
available with this event.
Larry Goldman
Decisioneering – Crystal Ball
[email protected]
303-626-0129
• Visit the Crystal Ball Web site
for free Web seminars, white
papers, example models, and
more.
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