Presented by: Jennifer Appleyard

1. Systems & Technology Group
© 2013 IBM Corporation
Monte Carlo Simulations in Product
Development Applications
Jennifer Appleyard
SWE’13

2. Systems & Technology Group
© 2013 IBM CorporationTechnical Interlock
Agenda
 Introduction
 Monte Carlo Simulations
– Definition
– Most Suitable
– Examples
 Using Monte Carlo Simulations
– In Product Development
– Steps
– Work through an example
 More information
 Questions

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© 2013 IBM CorporationTechnical Interlock
Monte Carlo Simulations
 Monte Carlo method
– computational algorithms
– repeated random sampling to obtain numerical results
• Ex. by running simulations many times over in order to calculate the same probabilities
 Like actually playing and recording your results in a real casino situation.
 Invented in the late 1940s by Stanislaw Ulam at LANL.

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Monte Carlo Simulations
 This method is good for these situations:
– ‘Realistic’ scenario
– Distribution of input values are known & well understood
– Calculations or application can be checked or monitored
 This method may not be good for these situations:
– High stakes applications
– Best or worst case is expected
– Input values are coupled
– Results will be used in an application, then not checked or monitored

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Steps
 Monte Carlo method:
– Identify the variable and its domain of possible inputs
• Describe mathematically (ex. mean, standard deviation, shape of distribution)
– Generate inputs randomly from a probability distribution over the domain
– Perform a deterministic computation on the inputs
– Aggregate the results
 In a high quality Monte Carlo simulation:
– the (pseudo-random) number generator has certain characteristics (e.g., a long “period”
before the sequence repeats)
– the (pseudo-random) number generator produces values that pass tests for randomness
– there are enough samples to ensure accurate results
– the proper sampling technique is used
– the algorithm used is valid for what is being modeled
– it simulates the phenomenon in question.
mean +3s-3s
Normal distribution

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Product Development Applications
 Product Development
– Product specifications, manufacturing variation, test conditions, yield, test escapes
 Used to calculate the likelihood of an event
– Defective parts per million
– Percent of passing parts
– Impact of a process change
 Methods
– SAS, Excel, R, other
 Document assumptions
– Are they reasonable?
– Will they change in transition from development to manufacturing?

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Examples
Time
Frequency
3. Failures in Time
1. Correlation
2. Manufacturing Variability
3. Failures in Time 1700 1800 1900 2000 2100 2200 2300
Ter Fmax @Apple Temp
1800
1900
2000
2100
2200
2300
AppleMacOSFmax
Apple MacOS Fmax 1.4-1.5v GC Best Fit Line - 60MHz
R-square = 0.854 # pts = 82
y = 424 + 0.807x
GPUL dd2.2
Ter Fmax @Apple Temp
1.4-1.5v, all t
1. Correlation
Parameter 1
Effect 1
Effect 2
Effect 1 and Effect 2
Process Parameter 1
2. Manufacturing Variability
ProcessParameter2
Parameter2

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Try it.
 Identify an application
– Ex. yield projection; test conditions; escape rate; design model
 Identify a variable and domain of possible inputs
– Random, independent, and predicted with a distribution function?
– Mean and standard deviation available?
– Inputs monitored?
 Document the Assumptions
 Identify the tool to use
– SAS, Excel, R, other simulation tool?
 Generate the computations
– Ex. Computation on the input variables
– Ex. Polynomial relationship between the input variables
 Review the assumptions – how will they be maintained?
– ‘by design’
– Statistical process control
– Maverick screens
– Engineering disposition
– Other

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More Information
 Wikipedia
 Sawilowsky, Shlomo S.; Fahoome, Gail C. (2003). Statistics via Monte Carlo Simulation with Fortran.
Rochester Hills, MI: JMASM. ISBN 0-9740236-0-4.
 U.S. Pat. No. 4,924,430
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Thank you
 jenniferappleyard@yahoo.com