Introduction To Six Sigma Crystal Ball

Slide 1: 

Introduction to Crystal Ball Six Sigma 1

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 2 Topics Covered in This Module

Slide 3: 

3 MODELS SIMULATION Y = f (x) Y = f (x) 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.

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 4 What is a Mathematical Model? Y = β0 + β1x1 + β2x2 + β12x1x2 + β11x12 + β22x22

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 5 Models and Simulation Y = f (x)

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) 6 What Is Monte Carlo Simulation?

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). 7 Probability Distributions As Inputs Range Probability Parameters

Monte Carlo Simulation Results As Outputs : 

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

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 9 Sensitivity Analysis: A Critical Tool

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 10 Sensitivity Analysis: Using the Results

Next Step: Stochastic Optimization : 

11 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).

What is Stochastic Optimization? : 

12 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

Stochastic Optimization : 

13 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 Y x Yopt Xgood including sx YR1 YR2 Y x Yopt Xbad including sx YR1 YR2 GOOD BAD Unacceptable Defect Rate Acceptable Defect Rate

is a suite of software for Microsoft® Excel : 

14 is a suite of software for Microsoft® Excel 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 Professional Edition includes:

How Does Crystal Ball Appear in Excel? : 

How Does Crystal Ball Appear in Excel? 15 Define Menu Run Menu Analyze Menu Toolbar

How Does Crystal Ball Work (in Six Sigma terminology)? : 

16 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

Typical Crystal Ball Roles in Six Sigma Projects : 

17 Typical Crystal Ball Roles in Six Sigma Projects DEFINE MEASURE ANALYZE IMPROVE CONTROL 6s PHASES 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 Transactional Service Process Simulation Project Selection Process Simulation and Stochastic Optimization

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 18 Benefits of Simulation in Six Sigma Projects

Case Study: DoE with SimulationProblem 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 Opt Quest Optimization techniques to determine process settings that minimize process cost while meeting minimum quality targets. 19 Case Study: DoE with SimulationProblem Statement Measure Define Analyze Improve Control

Case Study Overview by Phase : 

- Measure current parameter capability 20 Case Study Overview by Phase Define Control Measure Analyze - Perform Design of Experiments - Characterize current process state with simulation Determine variation drivers w/ Sensitivity Analysis Address drivers and reiterate simulation - Review problem statement Improve - Optimize design for cost and performance - Run capability study on proposed process settings to confirm quality

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 21 Step 1: Measure Current Parameter Capability Measure Define Analyze Improve Control

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) 100 200 Cycle Time (x2) 60 140 Hold Pressure (x3) 120 140 Response polynomial equation developed (R2adj = 92.5%) 3 Main Effects 1 Interaction Term 22 Step 2: Perform Design of Experiments Measure Define Analyze Improve Control Y = β0 + β1x1 + β2x2 + β3x3 + β23x2x3

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 23 Step 3: Characterize Current Process State Measure Define Analyze Improve Control

Monte Carlo Simulation to Predict Variation : 

Nominal Response of 64.59 mm close to target but 2% will fall out of the spec limits! → Sigma Level of ~ 2.0 24 Monte Carlo Simulation to Predict Variation Measure Define Analyze Improve Control

Step 4: Review Sensitivity Analysis : 

Run Sensitivity Analysis to determine major driver of variation. 25 Step 4: Review Sensitivity Analysis Can anything be done to reduce standard deviation of Mold Temperature? Assume standard deviation can be reduced by 50% in Cell G5. Run simulation. Measure Define Analyze Improve Control

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

Step 6: Optimize Design for Cost & Performance : 

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

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) 28 Optimize Design for Cost & Performance $PROCESS = K1*Temp*Time + K2*Time Measure Define Analyze Improve Control

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 29 Exercise: Process DoE Optimization Measure Define Analyze Improve Control

Helping You Optimize: Decision Variables : 

30 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).

Define Decision Variables : 

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 31 Measure Define Analyze Improve Control

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. 32 OptQuest: A Blend of Approaches

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 33 Optimize Design for Cost & 4s Performance Measure Define Analyze Improve Control

Optimize Design for Cost & 4s Performance : 

New Design results in a Process Cost of $1.16 per part and increase to 4s quality! 34 Optimize Design for Cost & 4s Performance Measure Define Analyze Improve Control

Comparison of Design Performance & Cost : 

Comparison of Design Performance & Cost 35 Where have we been, and where are we going? Six Sigma team proceeds to run Capability Study on proposed process settings to confirm quality during Control phase. Measure Define Analyze Improve Control

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. 36 Case Study Conclusions Measure Define Analyze Improve Control

Summary - 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 37 Summary - Benefits of Simulation in Six Sigma

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 (www.crystalball.com) Risk Resources > Case Studies Risk Resources > Example Models Training > Course List Six Sigma - Articles, Papers & Success Stories (www.crystalball.com/sixsigma/papers.html) 38 Additional Crystal Ball Resources