lecture 6 six sigma - ttu.eeinnomet.ttu.ee/martin/mer0070/wb/ws10/dx_14.5_l06_sixsigma.pdf ·...

© 2013 ANSYS, Inc. September 27, 2013 1 Release 14.5

14. 5 Release

Introduction to ANSYS DesignXplorer

Lecture 6 Six Sigma


• 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?


• 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?


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


1. Specify input parameter distribution

Uniform Triangular

Normal Truncated

Normal

Lognormal

Exponential

Beta Weibull

Six Sigma Analysis Procedure


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.



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.



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).



2. Observe output parameter distribution



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



2. Choose Percentile-Quantile probability table, enter sigma level of -6 and ensure that probability is less than 3.4E-6



2. Observe Global Sensitivities



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

lecture 6 six sigma - ttu.eeinnomet.ttu.ee/martin/mer0070/wb/ws10/dx_14.5_l06_sixsigma.pdf ·...

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