2. Topics Covered in this Presentation
Design Capability.
Monte Carlo Analysis.
Monte Carlo Analysis Example
Prototype Capability.
Capability Refinement.
Objectives
Understand the benefits of capability analysis in the
design and development process.
Gain proficiency in using Crystal Ball® for conducting
Monte Carlo analysis.
Understand through practical example how capability
can be designed into a product.
3. Design Capability (1 of 3)
Capability assessments helps to identify design limits and potential
problems early in the design process.
All parameters have distributions in their operating point. The closer a
parameter is to the specification limits, the more opportunity there is for the
product to fail in the field due to insufficient margins or component
degradation.
Upper
Nominal
Lower
limit
operating point
limit
Collecting capability metrics is often left until the production ramp, but
there is a hug benefit in conducting an academic analysis far sooner, in
fact as soon as the paper design has been completed.
In fact capability assessments can be conducted:
At the academic design stage.
During all prototype builds.
During the production volume-ramp.
4. Design Capability (2 of 3)
This technique applies to both simple and complex designs equally. For
presentation simplification an extremely basic example will be presented,
an adjustable voltage regulator.
The output is Critical To Quality (CTQ), and is governed by the inputs (Xs).
5. Design Capability (3 of 3)
Over a large production run there will be unit-to-unit variation on all three
Xs, which will result in a variation on Y.
The portion of the distribution that falls outside the specification limits
represent failures. The portion that is close to the specification limits
represents an opportunity for long term failures due to component
degradation.
The combination of the two areas is termed the “probability of failure.”
6. Monte Carlo Analysis
Estimate capability through Monte Carlo analysis before the initial
prototype build. This can save a significant amount of development time as
it can identify potential tolerancing issues before the first prototypes are
built.
DEFINE
TRANSFER
FUNCTION
Mathematical derivation
Design of Experiments
Technical documentation
CONDUCT MONTE
CARLO ANALYSIS
BASED ON SELECTED
COMPONENT
TOLERANCES
Improvement
needed?
Yes
ADJUST COMPONENT
TOLERANCES AND/OR DESIGN
APPROACH AND RE-RUN
ANALYSIS
No
The prototype build can now
be started
7. Monte Carlo Analysis Example (1 of 14)
For simplicity this will focus on the simple voltage regulator
that has already been introduced.
Process steps:
Define the characteristic(s) of interest.
Identify the output (Y).
Identify the inputs (Xs).
Develop the transfer function.
Determine the variation of Xs.
Calculate the resultant variation of Y.
8. Monte Carlo Analysis Example (2 of 14)
Characteristic of interest: Output voltage, tolerance 4.9V to 5.1V.
Inputs: R1, R2, TL431 reference voltage and the Input voltage.
Transfer function:
R1
VO = 1 + Vref
R
2
Here the input voltage can be ignored because it does not appear in the
transfer function.
This example will start off using a TL431C, which has a reference voltage
tolerance of 2.44V to 2.55V. Assume a 1% tolerance of R1 and R2.
9. Monte Carlo Analysis Example (3 of 14)
The Crystal Ball® software tool, which is an Excel plugin will be used for this
example, although there are numerous other software packages available
that can also be used.
Firstly data has to be input for the
Xs.
Next distributions have to be
defined. At this stage the actual
distributions may be unknown, in
which case a uniform distribution
could be used, as this will
represent a worse case scenario.
10. Monte Carlo Analysis Example (4 of 14)
The next stage is to define a forecast for Y.
Note that the number of decimal places
in both assumptions and forecasts is
defined by the value cell.
11. Monte Carlo Analysis Example (5 of 14)
Now the simulation can be run.
Select 3000 runs
and a confidence
factor of 95%.
Now start the simulation
12. Monte Carlo Analysis Example (6 of 14)
Crystal Ball® will now displays the frequency chart.
The first pass suggests that there is a high probability for dissatisfaction since the
output voltage is frequently outside the specification limits.
Cpk = 0.64, Zst = 1.09 and Defects Per Million Units (DPMLT) = 659,097.
The cause of variation in this circuit needs to be determined.
13. Monte Carlo Analysis Example (7 of 14)
Crystal Ball® provides a sensitivity chart that shows the influence that
each assumption cell has on a particular forecast cell. Sensitivity charts
provide a number of benefits:
Quick determination of
which assumptions
influence the forecast the
most, reducing the time
needed to refine
estimates.
Identification of which
assumptions influence the
forecast the least, so that
they can be addressed as
a lower priority.
Select Analyze >
Sensitivity Charts.
Select New.
Select VOUT checkbox.
14. Monte Carlo Analysis Example (8 of 14)
The sensitivity chart shows the contribution of each assumption.
15. Monte Carlo Analysis Example (9 of 14)
Revision 1: Select a better regulator: use a TL431AQ, which has a
reference voltage tolerance of 2.47V to 2.52V.
Change the tolerance in the assumption
cell and re-run the simulation.
Cpk = 1.06, Zst = 2.49 and Defects Per
Million Units (DPMLT) = 161,087 .
16. Monte Carlo Analysis Example (10 of 14)
Cpk = 1.74, ZST = 3.09 and Defects Per Million Units = 55,917.
This is encouraging. None of the units exceed the limits, but two
problems exist:
0.1% resistors are expensive.
Zst is still not high enough for six sigma quality level.
17. Monte Carlo Analysis Example (11 of 14)
Revision 3: Control the R1/R2 ratio.
This could improve the design and reduce the cost.
A resistor network would be cheaper than changing to a
TL431BC, and is also cheaper than 0.1% discrete
resistors.
To account for using a resistor network in Crystal Ball
we specify R1 as 10,000 ± 0.1%. In the transfer
function replace R2 with R2=(R1+R2A). Specify R2A as
0±2.5Ω.
Therefore the new transfer function becomes:
R1
VO = 1 +
V ref
R1 + R 2 A
18. Monte Carlo Analysis Example (12 of 14)
Simulating this results in:
The capability has been improved, but only slightly.
The circuit cost has been reduced but there is little improvement to the
capability.
Neither R1 or R2 contribute to the variation, so the only way the circuit
capability can be improved is by selecting a regulator with a tighter
reference voltage.
19. Monte Carlo Analysis Example (13 of 14)
Revision 4: Define assumption based on real data.
The TL431 is supplied by a company who promotes its six sigma program,
so it should be of high quality, suggesting the reference voltage tolerance
may be tighter than the data sheet suggests.
50 samples are taken from stock, including samples from different date
codes, and the reference voltage measured.
From the measurements it is concluded that the mean is 2.497V with a
standard deviation of 7.7mV.
20. Monte Carlo Analysis Example (14 of 14)
Vref can now be modified.
The obtained data can be used to more accurately model the reference
voltage.
Crystal Ball returns a Cpk of 2.04 and a Zst of 6.11.
Even accounting for the 1.5 Z shift over the entire production run, Zlt
should not fall below 4.61, which represents a long term failure rate of 2
units per million.
21. Prototype Capability
Once the prototypes have been debugged and results obtained, the
capability study can be repeated to verify the earlier Monte Carlo
analysis conclusions.
This provides a revised
short term capability
metric.
However, over a long
term production run Zst
will degrade by 1.5
sigma. The ideal for the
long term Z is 4.5,
which relates to a
capability of 4.5 sigma.
It is important to repeat this using the results of other testing such as
environmental tests in order to assess how external factors such as
temperature and humidity affect the circuits capability.
22. Take Aways
Capability is not just a production metric, it is not just influenced by
the process but by the product design as well.
High capability equates to higher manufacturing yields.
A target for Critical To Quality parameters should be a Zst of 6.0 –
world class!
Statistically, there will be a long term 1.5 sigma shift.
Capability assessment can be started before the first prototype has
been produced.
Capability assessment should be repeated during prototype
development.
Capability studies are simple to conduct. Products should not be
released for volume manufacture without having ensured capability
targets have been achieved in advance of the volume ramp.
The manufacturing process cannot compensate for
inherent variation present in a product’s design.
