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# Using capability assessment during product design

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### Using capability assessment during product design

1. 1. Using Capability Assessment During Product Design Mark Turner
2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 14. Monte Carlo Analysis Example (8 of 14) The sensitivity chart shows the contribution of each assumption.
15. 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. 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. 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. 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. 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. 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. 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. 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.