Lecture 6 Six Sigma - ttu.eeinnomet.ttu.ee/martin/MER0070/WB/WS10/DX_14.5_L06_SixSigma.pdf ·...
Transcript of Lecture 6 Six Sigma - ttu.eeinnomet.ttu.ee/martin/MER0070/WB/WS10/DX_14.5_L06_SixSigma.pdf ·...
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14. 5 Release
Introduction to ANSYS DesignXplorer
Lecture 6 Six Sigma
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• Typical analyses assume a fixed value for each input quantity and assigns a safety factor to account for these assumptions (deterministic)
• Design For Six Sigma provides a mechanism to include and account for scatter in input and provide insight into how they affect the system response (probabilistic)
• A product has Six Sigma quality if only 3.4 parts out of every 1 million manufactured fail
Six Sigma Analysis What is it?
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• Helps answer the following questions:
– How large is the scatter of the output parameters? How robust are the output parameters?
– If the output is subject to scatter due to the variation of the input variables, then what is the probability that a design criterion given for the output parameters is no longer met?
– How large is the probability that an unexpected and unwanted event takes place (i.e., what is the failure probability)?
– Which input variables contribute the most to the scatter of an output parameter and to the failure probability? What are the sensitivities of the output parameter with respect to the input variables?
Six Sigma Analysis What is it?
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If you are performing a thermal analysis and want to evaluate the thermal stresses, the equation is:
σtherm = E α ΔT
because the thermal stresses are directly proportional to the Young's modulus as well as to the thermal expansion coefficient of the material.
The table below shows the probability that the thermal stresses will be higher than expected, taking uncertainty variables into account.
Six Sigma Analysis Example
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1. Specify input parameter distribution
Uniform Triangular
Normal Truncated
Normal
Lognormal
Exponential
Beta Weibull
Six Sigma Analysis Procedure
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1. Specify input parameter distribution • Beta Distribution
- Useful for random variables that are bounded at both sides. If linear operations are applied to random variables that are all subjected to a uniform distribution, then the results can usually be described by a Beta distribution.
• Exponential Distribution
- Useful in cases where there is a physical reason that the probability density function is strictly decreasing as the uncertainty variable value increases.
• Gaussian (Normal) Distribution
- Fundamental and commonly-used distribution for statistical matters. It is typically used to describe the scatter of the measurement data.
Six Sigma Analysis Procedure
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1. Specify input parameter distribution • Lognormal Distribution
- Typically used to describe the scatter of the measurement data of physical phenomena, where the logarithm of the data would follow a normal distribution. The lognormal distribution is suitable for phenomena that arise from the multiplication of a large number of error effects.
• Uniform Distribution
- For cases where the only information
available is a lower and an upper limit. It is
also useful to describe geometric tolerances.
• Triangular Distribution
-Helpful to model a random variable when
actual data is not available. It is very often
used to capture expert opinions.
Six Sigma Analysis Procedure
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1. Specify input parameter distribution • Truncated Gaussian Distribution
-Used where the physical phenomenon
follows a Gaussian distribution, but the
extreme ends are cut off are eliminated
from the sample population by quality
control measures.
• Weibull Distribution
- Most often used for strength or strength-
related lifetime parameters, and is the
standard distribution for material strength
and lifetime parameters for very brittle
materials (for these very brittle material
the "weakest-link theory" is applicable).
Six Sigma Analysis Procedure
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2. Observe output parameter distribution
Six Sigma Analysis Procedure
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2. Observe output parameter distribution
At the bottom of the table,
specify an output
parameter value and the
probability and sigma
level will be returned
Quantile-Percentile
Probability Table
Percentile-Quantile
Probability Table
At the bottom of the table,
specify a probability value
(or sigma level) and the
corresponding output
parameter value and
sigma level (or probability
value) will be returned
Six Sigma Analysis Procedure
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2. Choose Percentile-Quantile probability table, enter sigma level of -6 and ensure that probability is less than 3.4E-6
Six Sigma Analysis Procedure
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2. Observe Global Sensitivities
Six Sigma Analysis Procedure
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Problem Description
This workshop walks you through a 6-sigma analysis.
The problem to be analyzed is a crane hook which is known to have some variability in manufacturing. The objective of this study is to consider the variability in manufacturing to determine the probability of failure and understand whether the design satisfies 6-sigma requirements (that less than 3.4 our of every 1,000,000 hooks fail).
Input
• Back_ds
• Bottom_ds
• Depth_ds
Output
• Minimum Safety Factor
• Maximum Von Mises Stress
• Maximum Deformation
Back_ds
Bottom_ds
Depth_ds