1. Crystal Ball Six Sigma Partner Program
Crystal Ball for Six Sigma (DMAIC) Module
Simulation and Optimization
in Six Sigma Projects

2. What Is Included in Six Sigma Training Module?
The module includes:
Training module notes (Six Sigma Training Module Notes.doc)
PowerPoint slides for teaching the basics and the Simulation with DoE case study (Crystal Ball Module for Six Sigma.ppt)
Simulation with DoE case study model without Crystal Ball enhancements (Simulation with DoE and Cost Exercise.xls)
Simulation with DoE case study model with Crystal Ball enhancements (Simulation with DoE and Cost Sim Solution.xls)
Simulation with DoE case study model with Crystal Ball and OptQuest enhancements (Simulation with DoE and Cost Opt Solution.xls)
Optimization settings file for Simulation with DoE case study (Simulation with DoE and Cost Sim Solution.opt)
Step-by-step class exercise for Simulation with DoE case study (Simulation with DoE and Cost Solution.doc)
Overview of Crystal Ball handout (Common Questions about Crystal Ball.doc)

3. How Best to Start?
The best way to begin is to review the slides to see what is covered. You are free to edit these slides as necessary. They feature basic Crystal Ball information, application details of Crystal Ball for Six Sigma (DMAIC), and a review of the Simulation with DoE case study.
Next, we suggest that you open the Simulation with DoE and Cost Exercise.xls model and walk through the step-by-step final solution described in Simulation with DoE and Cost Solution.doc . You can use the Simulation with DoE and Cost Sim Solution.opt file to import the optimization settings into OptQuest, but it is not mandatory for the exercise.
Once you are familiar with the model, you can apply your own teaching methods to this case study. In particular, you will need to determine whether or not you want the students to run through the exercise on their own or as a group.
The handout Common Questions about Crystal Ball.doc is an additional reference meant to answer common questions concerning the software.

4. Crystal Ball for Six Sigma
Simulation and Optimization
in Six Sigma Projects

5. Topics Covered in This Module
Defining Simulation Models
Monte Carlo Simulation
What Is Crystal Ball?
Benefits of Simulation and Optimization for Six Sigma
DoE Example – Simulation
DoE Example – Optimization
Additional Resources

6. Introductory Concepts

7. Models and Simulation
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.
MODELS
SIMULATION
Control
Inputs 1 2 3 LO HI
Noise
Variables
Y = f (x)
Y = f (x)
Outcome
Predictions

8. What is a Mathematical Model?
Models come in many different forms
Mathematical relationships based on established physical principles
Regression equations derived from historical data
Design of Experiments (DOE) response equations from measured observations
General knowledge of business system or product
Y = β0 + β1x1 + β2x2 + β12x1x2 + β11x12 + β22x22

9. Models and Simulation
Once the business process or product behavior is captured with mathematical and logical statements:
Place the model into Excel
Apply Crystal Ball probabilistic methods
Y = f (x) A B C 1 $ 2

10. What Is Monte Carlo Simulation?
A system that uses random numbers to measure the effects of uncertainty.
A computer simulation of N trials where
Each trial samples input values from defined probability distribution functions (PDFs)
Applies the input values to the model and records the output
Sampling statistics then utilized to characterize output variation (mean, standard deviation, fitted probability distributions)
Outputs:
Prediction of Output Variation (DPU, Cpk, PPM, Z-score)
Identification of Primary Variation Drivers (Sensitivity Analysis)

11. Probability Distributions As Inputs
Simulation requires probabilistic inputs.
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

12. Monte Carlo Simulation Results As Outputs
Explore the range of possible outcomes AND the probability of their occurrence
Number of simulation trials performed
Parts within the spec limits are shown in blue, parts outside spec limits are shown red
Lower Spec Limit (LSL)
Upper Spec Limit (USL)
Quality Metrics
such as Cpk, ZST, p(N/C), etc....
Certainty (probability) that the forecast lies between LSL and USL

13. 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)
Operates during the simulation, calculating the relationships between all X’s and Y’s
Similar to Pareto Chart in interpretation but is not a Main Effects plot

14. Sensitivity Analysis: Using the Results
Acts as communication tool to help team understand what’s driving defects
Generally see a few factors having strongest impact on forecast variation
Shows where to focus your energies (and where not to focus them)
After reducing the variation for these few critical X’s, you can rerun the simulation and examine the effects on the output

15. Next Step: Stochastic Optimization
Simulation can help you to understand and reduce variation but does not by itself offer the best solution.
The combination of simulation and optimization lets you make the best (optimal) decisions while accounting for the variability or uncertainty inherent within a process.
You will see this at work in the DoE with Simulation Example.
An optimization model answers the question "What's best?" rather than "What happened?" (statistics), "What if?" (simulation) or "What will happen?" (forecasting).

16. What is Stochastic Optimization?
Stochastic optimization finds the best solution while using the results of simulation.
Goal: Determine a set of input values that will influence multiple outputs to target values.
Example: Decrease Process Cost and Cycle Time while meeting quality requirements
Y1-max X3 X2 X1
Y3-min
Y2-target
Y2 = f2(X1,X3,X4) X4
Y1 = f1(X1,X2,X3)
Y3 = f3(X2,X3,X4) ?

17. Stochastic Optimization
X contains natural variation (sx)
Y required to be between YR1 and YR2 (LSL & USL) with an acceptable defect rate of 3 sigma
GOOD
BAD
Acceptable
Defect Rate
Unacceptable
Defect Rate Y Y
YR2
YR2
Use animations to illustrate concepts of constraints and requirements.
Yopt
Yopt
YR1
YR1 x x
Xgood including sx
Xbad including sx

18. What Is Crystal Ball?

19. is a suite of software for Microsoft® Excel
Professional Edition includes:
Crystal Ball Excel-based Monte Carlo simulation tool, includes plug-in tools for setup and analysis (CB Tools), distribution fitting, sensitivity analysis, and output charts and reports
OptQuest Global optimization for uncertain models
CB Predictor Time-series forecasting and multiple linear regression
Crystal Ball and CB Predictor Developer Kits VBA customization tools

20. How Does Crystal Ball Appear in Excel?
Toolbar
Define Menu
Run Menu
Analyze Menu

21. How Does Crystal Ball Work (in Six Sigma terminology)?
Here’s another way to describe how simulation works:
Describe the Effect (Y) as a function of the causal Factors (X’s)
Describe Factors using probability distributions (e.g., Normal, Uniform, Binomial, etc.)
Repeatedly Sample the Input Factors (X’s) and Compute the Effect (Y)
Describe the Distribution of the Effect (Y) and plot in a histogram

22. Typical Crystal Ball Roles in Six Sigma Projects
Monte Carlo Simulation and Optimization can be used in variety of Six Sigma phases
DEFINE: Project Selection
ALL PHASES: Service Process
ANALYZE/DESIGN: Process Simulation and Optimization (Strongest Application)
Crystal Ball does not replace other statistical packages (Minitab or JMP)
It complements other codes by incorporating their outputs (input variable characterization and response models) into simulations and optimizations
6s PHASES
DEFINE
Project Selection
FISHBONE
MSA
MEASURE
DoE
ANALYZE
Process Simulation
and
Stochastic Optimization
Transactional Service Process Simulation
IMPROVE
CONTROL

23. Benefits of Simulation in Six Sigma Projects
Reduce the Uncertainty Around Project Success
Account for uncertainty of costs and success in initial stages
Understand impacts on customer satisfaction and profitability and prioritize opportunities
Improve Your Understanding of the Critical X’s
Discover and validate underlying causes of variation and waste
Use simulation to predict variation where data is minimal or non-existent
Evaluate Effects of Process Changes Prior to Implementation
Save on expenses and resources by experimenting first
Build team consensus and gain early approval of process owners

24. Case Study: DoE with Simulation

25. Define Measure Analyze Improve Control Problem Statement
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.
Define
Measure
Analyze
Improve
Control

26. Case Study Overview by Phase
Define
- Review problem statement
Measure
- Measure current parameter capability
- Perform Design of Experiments
- Characterize current process state with simulation
Determine variation drivers w/ Sensitivity Analysis
Address drivers and reiterate simulation
Analyze
Improve
- Optimize design for cost and performance
Control
- Run capability study on proposed process settings to confirm quality

27. Step 1: Measure Current Parameter Capability
As part of the Measure Phase, the variation of the Control Parameters (Inputs, Factors) is characterized during Capability Studies
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
Each set of samples passes Normality Test
Means and Standard Deviations are recorded
Define
Measure
Analyze
Improve
Control

28. Step 2: Perform Design of Experiments
23 Full Factorial DOE with 5 replicates is performed (40 runs)
RESPONSE: Part Length
FACTORS : LO HI
Mold Temperature (x1)
Cycle Time (x2)
Hold Pressure (x3)
Response polynomial equation developed (R2adj = 92.5%)
3 Main Effects
1 Interaction Term
Define
Measure
Analyze
Improve
Control
Y = β0 + β1x1 + β2x2 + β3x3 + β23x2x3

29. Step 3: Characterize Current Process State
Define the Inputs (Factors) as Normal Assumptions (Cells E5:E7)
Cell Reference Assumption Name from Column B
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
Cell Reference the USL from Cell G9
Run Simulation
Define
Measure
Analyze
Improve
Control

30. Monte Carlo Simulation to Predict Variation
Nominal Response of mm close to target but 2% will fall out of the spec limits! → Sigma Level of ~ 2.0
Define
Measure
Analyze
Improve
Control

31. Step 4: Review Sensitivity Analysis
Run Sensitivity Analysis to determine major driver of variation.
Define
Measure
Analyze
Can anything be done to reduce standard deviation of Mold Temperature?
Assume standard deviation can be reduced by 50% in Cell G5.
Run simulation.
Improve
Control

32. Step 5: Reiterate Monte Carlo Analysis
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?
Define
Measure
Analyze
Improve
Control

33. Step 6: Optimize Design for Cost & Performance
Define
How can the process settings be configured so that a minimum quality goal is reached while reducing the process cost per part?
Measure
Analyze
Improve
Control

34. Optimize Design for Cost & Performance
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
Define Process Cost Forecast (Cell E10)
Define
Measure
Analyze
Improve
$PROCESS = K1*Temp*Time + K2*Time
Control

35. Exercise: Process DoE Optimization
Characterize Current Quality Levels (Cpk & ZST)
Enable Capability Metrics in Run Preferences
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 Z-score)
Process Parameters
Mold Temp → LO (100) to HI (200), Step = 10
Cycle Time → LO (60) to HI (140), Step = 1
Hold Pressure → LO (120) to HI (140), Step = 2.5
Define
Measure
Analyze
Improve
Control

36. 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).

37. Define Decision Variables
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
Define
Measure
Analyze
Decision Variables
Lower Bound
Upper Bound
Discrete Step Size
Mold Temp
100
200 10
Cycle Time 60
140 1
Hold Pressure
120 2
Improve
Control

38. 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 self-education 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.

39. Optimize Design for Cost & 4s Performance
Run OptQuest and Define Forecast Selections
Optimization Goals:
Primary is to Minimize Cost
Requirement is to Reduce Variation of Part Length to 4s levels
Zst required to have a lower bound of 4
Define
Measure
Analyze
Improve
Control

40. Optimize Design for Cost & 4s Performance
Define
New Design results in a Process Cost of $1.16 per part and increase to 4s quality!
Measure
Analyze
Improve
Control

41. Comparison of Design Performance & Cost
Where have we been, and where are we going?
Define
Iter-ation #
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
130 5
1.94
$2.03 2
2.53 3
150 61
140
4.01
$1.16
Measure
Analyze
Iteration #1) First cut at process settings resulted in ~2 sigma.
Iteration #2) Second cut at process settings while halving the Mold Temperature standard deviation resulted in ~2.5 sigma.
Iteration #3) Optimizing for Process Cost (minimization) with 4 sigma requirement on Part Length results in reduced cost (from iteration #2) and increased quality.
Instructor should be prepared to answer the question: “Why is my best identified solution not exactly the same as the instructor’s best identified solution?” The reason lies in the nature of Monte Carlo analysis in that each and every Monte Carlo run for the same set of Decision Variable values may not yield the same Z-score (due to accuracies associated with Number of Trials). Sometimes Z-scores will be overestimated and sometimes underestimated. Thus, what could’ve been a “best” and feasible (meets Z-score requirement) solution may not be “best” or even feasible in a Monte Carlo simulation with the same set of Decision Variable values.
Improve
Six Sigma team proceeds to run Capability Study on proposed process settings to confirm quality during Control phase.
Control

42. Case Study Conclusions
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.
Process Cost decreases with decreasing Mold Temperature and Cycle Time.
Simply reducing the Temp and Time to their lowest allowed value would result in unacceptable Part Length quality.
Stochastic Optimization of input variable (Factor) means will increase Part Length quality levels while minimizing Process Cost impact.
Define
Measure
Analyze
Improve
Control

43. Crystal Ball for Six Sigma
Summary

44. Benefits of Simulation in Six Sigma
Use insights into what drives variation to improve process or product
Little or no customer exposure to a “bad” process, product, or service
Easy to “change design” — can perform “what-if” analysis with only a mouse click — prior to implementation
Virtual implementation of process changes means little or no waste of materials or staff resources
Instant feedback of results

45. Additional Crystal Ball Resources
Other Six Sigma Example Models with Crystal Ball 7.2
In Excel/CB: Help > Crystal Ball > Examples Guide
Process Capability Guide
Start > All Programs > Crystal Ball 7 > Documentation > Process Capability Guide
Crystal Ball Website (
Risk Resources > Case Studies
Risk Resources > Example Models
Training > Course List
Six Sigma - Articles, Papers & Success Stories (