1. Robust Optimisation of Processes and Products by Using Monte Carlo Simulation Experiments
Robert Anderson – JMP

2. How Do We Optimise a Process/Product?
JMP provides a few different ways of tackling this problem
I’m going to contrast two of these methods in this talk
Maximise Desirability vs. Simulation Experiment
I’ll show using an example that they don’t always lead to the same answer or solution

3. Minimise the Number of Defects or ‘Out of Spec’ Points
Want to minimise or eliminate defects or unacceptable results
Find factor or input settings that give the most desirable values for the outputs or responses
3.285
30.63
100%
£ 0
But inputs are often subject to variation or drift so we need to be able to find factor or input settings that make the variations in these settings produce as few ‘out of spec’ results as possible
LSL
USL
Find factor or input settings that give the most desirable values for the outputs or responses
Note: Simulation experiment needs to have spec limits defined for the method to work

4. First Step is to Find a Good Model for the Process/Productx1 x2 x3 x4
Factors/inputs
Process (black box) y1
Responses/outputs
Sometimes we will use historical data to build a good model
Equation
y = f(x) + Error y2
If we don’t have good historical data to build a model, we often run a designed experiment to allow us to build a good model y3
The model is just an equation or expression that defines the relationship between the inputs and the outputs

5. 13 Run Definitive Screening Design Experiment
In the example we are going to look at, a 13 run definitive screening design experiment is used to obtain a good model for the process we are trying to optimise

6. Prediction Profiler Allows the Model to be Visualised
This is the prediction profiler for the model from the definitive screening design experiment

7. Monte Carlo Simulation Quantifies the Output Variation
Initial factor settings - the starting point before any optimisation
Initial process set points
Right on edge of lower spec limit
Monte Carlo simulation allows us to explore the effects of variation in the inputs on the outputs. It allows us to answer the question; how much variation in the output will these variations in the inputs produce?

8. Maximise Desirability Finds Settings For ‘Best’ Response
First Optimisation Approach
Maximise Desirability Finds Settings For ‘Best’ Response
Maximise desirability factor settings
Maximise desirability
settings
Maximum value of response is located here
Maximise Desirability searches the factor space to find the particular factor settings that give the most desirable value for the response

9. Simulation Experiment Finds Settings that Minimise Defects
Second Optimisation Approach
Simulation Experiment Finds Settings that Minimise Defects
Simulation experiment factor settings
Simulation experiment
settings
Slightly lower response but less susceptible to variation in the process input variables here
Simulation experiment searches the factor space to find the particular factor settings that give the lowest overall defect rate or the smallest number of ‘out of spec’ results

10. How Does Simulation Experiment Work?
Space filling design determines where the lowest overall defect rate occurs
Space filling design run to explore the factor space and generate defect rates for 128 points within the factor space +
Lowest defect rate

11. Built-in ‘Gaussian Process’ Script Models the Defect Rate
Running ‘Maximise desirability’ on the overall defect rate finds the process settings that minimise the defect rate or ‘out of spec’ points

12. Initial process set up
Sitting right on lower spec limit
Initial process set points
After Maximise Desirability
Maximum value of response is located here
Maximise desirability
Slightly lower response but less susceptible to process variation here
After Simulation
Experiment
Simulation experiment
Lowest defect rate and the most robust operating conditions
Takes account of the variation in the inputs
Simulation experiment has exploited the 2-factor interaction between modifier and temperature to reduce the variation in the output

13. Lets look at this example in JMP now

14. Conclusions on Optimising Processes
Simulation Experiment finds the most robust process set points taking account of the amount of variation we have in these
Maximise desirability doesn’t take account of the variation in the input variables and may give a different solution to simulation experiment
Maximise desirability and simulation experiment may suggest different optimum process set points when 2-factor interactions are present
When optimising processes, I recommend comparing the results from both approaches