# Presentation: 143759

## Statistical Analysis of PEM Life Test Data

- Implications for PEM Usage in High Reliability Long Duration Space Missions

- Extracting More Information Electrical Parameters Measurements During Life Testing

## Purpose

- Review analyses performed so far
- Suggest additional work (analysis)

## Purpose of Life Testing

- “Mimics” early mission usage
- Accelerates failures and parameter changes by employing high junction temperature
- Mission failure probability is reduced by transferring flight parts to lower failure rate region
- Burn-in
- Assumes (without test) decreasing failure rate applies to early mission usage
- Life test validates infant mortals removed from flight population with known confidence (Chi-square distribution)
- Life test sample size (woefully) inadequate to demonstrate long term failure rate
- Some projects (Minuteman) removed from flight population parts “drifting”
- Electrical parameters selected arbitrarily
- Criteria for removal is qualitative
- Technical literature does not contain objective assessment of validity of this technique
**What can be objectively “squeezed” out of life test data electrical parameter changes and what does it mean?**

## Method to Assess PEM Life Test Data

- Measure all electrical parameters _*feasible*_* *across industrial temperature range
- Measure interim values (during course of life test)
- Plot electrical parameters on probability scales
- Evaluate parameters that change significantly (standard deviation is at least 10% of part manufacturer specification) (*Significance Test*_)_
- Initial, post-burn-in, interim measurements (as available), final measurements
- Curve fit experimental data to known statistical distributions
- Normal
- Student t
- Log normal
- Bimodal
- Etc.
- Use known characteristics of these statistical distributions to estimate **RANGE**
- Perform *longitudinal* analysis
- Look at predicted range during the course of life tests
- If the predicted range is stable compare to parts manufacturer specification limits
- Remember manufacturer limits are not determined by statistical criteria
- Typically marketing considerations are more important
- Review circuit applications with CogE to ensure circuit error budget can tolerate Range (so computed) to an acceptable confidence level
- Use JPL-D8545 as initial guide

## Formulas from Statistics

## Facts about Statistical Distributions

- Distributions that fit experimental PEM life test data are typically central
- Average less than standard deviation
- Normal distribution has lean tails
- Population falls off rapidly after a few standard deviations
- Student t distribution can describe experimental data with fat tails
- Less rapid falloff of population
- Rate of falloff dependent on degrees of freedom used to curve fit
- Range is larger than normal distribution
- Both distributions do not have skew
- Distributions symmetrical around average
- Range is maximum minus minimum value measured
- For a distribution that fits experimental data, range may be predicted from standard deviation, sample size (number of parts used in circuit), and probability (in this case, similar to confidence level)

## Range of Normal Distribution (W)

| Sample Size (n) | W (90%) | W(99%) |
| --- | --- | --- |
| 5 | 3.48  | 4.60  |
| 10 | 4.13  | 5.16  |
| 20 | 4.69  | 5.65  |

## Student t Distribution Plotted on Probability Scale

## Student t Distribution

| Degrees of Freedom (f) | Standard Deviation |
| --- | --- |
| 10 | 1.05 |
| 5 | 1.12 |
| 4 | 1.15 |
| 2 | 1.41 |

- Studentized Range

## Examples

## LT1028

- Ultra low noise, high speed, operational amplifier
- 10 piece life test sample measured at 500 and 1000 hours of life test
- Vos (input offset voltage) at 1000 hours and room and cold temp and Ib (input bias current) at 1000 hours and room temp had changes whose standard deviation was significant
- I also show some open loop gain data
- Open loop gain should not be used in good circuit design
- Circuits should employ substantial negative feedback
- MATLAB used to plot experimental data on probability scales

## Slide 12

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## Slide 15

## Voltage Offset 25C

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | 5.0 | 27 | 139 | +/- 80 |
| Post burn-in | -6.1 | 28 | 144 | +/- 80
 |
| 500 hours | 2.2 | 28 | 144 | +/- 80
 |
| 1000 hours | 3.4 | 29 | 149 | +/- 80
 |

## Slide 17

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## Slide 20

## Voltage Offset at -40C

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | -14 | 35 | 178 | +/- 150 |
| Post burn-in | -24 | 37 | 192 | +/- 150
 |
| 500 hours | 2.0 | 38 | 195 | +/- 150
 |
| 1000 hours | 26 | 47 | 244 | +/- 150
 |

## Slide 22

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## Slide 25

## Input Bias Current 25C

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | -0.2 | 31 | 162 | +/- 90 |
| Post burn-in | -5.1 | 33 | 172 | +/- 90
 |
| 500 hours | 7.4 | 34 | 175 | +/- 90
 |
| 1000 hours | 18 | 36 | 188 | +/- 90
 |

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## Assessment

- Input offset voltage fits normal distribution (25C and -40C)
- Input bias current fits normal distribution (25C)
- (FYI) Log Open loop gain fits normal distribution better than open loop gain
- e.g. open loop gain fits log normal distribution
- Critical application parameters fit within part manufacturer specified range to high confidence

## LT1813

- Dual high speed very high slew rate operational amplifier
- 22 piece life test sample measured at 1000 hours
- Vos (input offset voltage) at 1000 hours (25C) and Iio (input offset  current) at 1000 hours (25C) had changes whose standard deviation was significant
- MATLAB used to plot experimental data on probability scales

## Slide 33

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## Slide 35

## Input Voltage Offset (25C)

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | 0.34 | 0.38 | 1.9 | +/- 1.5 |
| Post burn-in | 0.47 | 0.37 | 1.9 | +/- 1.5
 |
| 1000 hours | 0.34 | 0.38 | 1.96 | +/- 1.5 |

## Slide 37

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## Slide 39

## Input Offset Current (25C)

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | 1.7 | 8.7 | 45 | +/- 400 |
| Post burn-in | 1.5 | 8.8 | 45 | +/- 400
 |
| 1000 hours | 1.9 | 9.0 | 46 | +/- 400 |

## Assessment

- Parameters well fit to normal distribution
- Ranges within part manufacturer data sheet limits to high confidence
- Most parameters changed very little

## LT1175

- Negative low dropout micropower voltage regulator
- 22 piece life test with measurements at 500 and 2000 hours
- Parameters with significnat changes include line regulation, load regulation, sense current
- Only parameters with greatest changes are shown in this presentation
- MATLAB was used to plot experimental data on probability scales

## Slide 43

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## Slide 45

## Line Regulation (85C)

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | 0.001 | 0.0015 | 0.0077 | 0.015 |
| 500 hours | 0.001 | 0.0015 | 0.0077 | 0.015

 |
| 2000 hours | 0.00 | 0.038 | 0.4 | 0.015
 |

## Slide 47

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## Slide 49

## Load Regulation (-40C)

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | =0.29 | 0.15 | 0.78 | 0.035 |
| 500 hours | 0.019 | 0.12 | 0.61 | 0.035

 |
| 2000 hours | -0.18 | 0.12 | 0.63 | 0.035
 |

## Slide 51

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## Sense Current 85C

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | 58 | 19 | 101 | 150 |
| 500 hours | 43 | 22 | 111 | 150

 |
| 2000 hours | 0.1 | 0.004 | 0.02 | 150 |
| 2000 hour data was reviewed and is bad at both temperature extremes |  |  |  |  |

## Assessment

- Line regulation (85C) fits normal distribution except at 2000 hours where the fat tails require a student t fit with 3 degrees of freedom
- Load regulation (-40C) fits normal distribution
- Sense current (85C) fits normal distribution except 2000 hour data is corrupt
- Extra derating is needed for circuit applications at temperature extremes
- Distributions at room temperature are well fitted to normal distribution and have less predicted range

## AD780BR

- High Precision (Band Gap) Voltage Reference
- 49 devices subjected to life test and measured at 250 hours, 500 hours, 1000 hours
- Output voltage (3V nom) had significant standard deviation of the change at -40C and 250 hours
- Load regulation (sink mode B) had significant standard deviation of change at 25C and 500 hours; output voltage at 85C and 500 hours
- Load regulation (sink mode B) had significant standard deviation of changes at four temperatures and 1000 hours; output voltage at 125C/85C/-40C and 1000 hours and load regulation (sink mode A) load regulation (shunt mode) at 125C/-40C and 1000 hours
-  MATLAB used to plot changes for significant recurring parameters

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## Output Voltage (3V nom) (85C)

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Manufacturer Limits |
| --- | --- | --- | --- | --- |
| Initial | 2.9998 | 0.00045 | 0.0023 | +/- 0.001 |
| Post Burn-in | 2.9997 | 0.00045 | 0.0023 | +/- 0.001
 |
| 250 hours | 2.9998 | 0.00039 | 0.0020 | +/- 0.001

 |
| 500 hours | 2.9999 | 0.0004 | 0.0022 | +/- 0.001
 |
| 1000 hours | 2.9993 | 0.0004 | 0.0021 | +/- 0.001
 |

## Slide 63

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## Load Regulation Sink Mode B (25C)

|  | Average | Standard Deviation | Predicted Range (10 parts; 99% probability) | Predicted Range (log normal fit) | Manufacturer Limits |
| --- | --- | --- | --- | --- | --- |
| Initial | 0.007 | 0.057 | 0.29 * |  | 0.75 |
| Post Burn-in | 0.027 | 0.046 | 0.24 |  | 0.75 |
| 250 hours | 0.017 | 0.038 | 0.19 |  | 0.75 |
| 500 hours | 0.021 | 0.060 | 0.31* |  | 0.75 |
| 1000 hours | 0.022 | 0.062 | 0.32 * |  | 0.75 |

- * Log normal fit to positive values is better fit

## Assessment

- Load regulation (sink mode B) (25C) fits normal distribution
- Outlier analysis may require bimodal fit
- Significant outliers only at initial and 1000 hour points
- Output voltage (3V nominal) fits normal distribution
- Other parameters had smaller changes during life test
- Output voltage (2.5V nominal) showed small changes; however 3V nom output voltage requires derating in circuit application
- Load regulations are within part manufacturer specified ranges

## AD8028

- Low Distortion Dual Rail to Rail Operational Amplifier
- 10 pieces tested after burn-in (herein identified as initial measurements), after 500 hours life test, after 1000 hours life test.
- This is a dual device, and, where applicable, measurements on same parameters combined to increase sample size for statistical validity improvement
- Measurements were taken at 25C, +110C, -40C.

## Slide 70

## Slide 71

## Slide 72

## Note:  Input Offset voltage specified at 25C as 0.8 millivolts max.  No specification at temperature extremes.

|  | Initial | 500 hours | 1000 hours |
| --- | --- | --- | --- |
| Average | -0.484 | -0.461 | -0.457 |
| Standard Deviation | 0.154073 | 0.142465 | 0.138103 |
| Predicted Range | 0.795017 | 0.73512 | 0.712613 |

- Measurements hardly changed at all during life test.

## ISL43110

- Low-Voltage, Single Supply, SPST, High Performance Analog Switches
- 48 pieces were tested initially and after 80 hours, 160 hours of burn-in and 240 hours of burn-in
- Typical circuit critical parameters are On resistance, On resistance flatness, various leakage currents.
- Measurements were taken at 25°C, -40°C and +85°C.

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## Distributions are reasonably matched to normal.  Small changes observed in average and standard deviations.  Predicted range in all cases was less than 1.1 ohm.  Vendor datasheet specified maximum is 20 ohms at 25C.  Therefore statistical scatter is small and remains so for the population throughout the burn-in.

| Average | 12.858 | 15.706 | 11.269 | 11.587 |
| --- | --- | --- | --- | --- |
| Standard deviation | 0.176851 | 0.120816 | 0.127684 | 0.154643 |
| Predicted range | 0.912552 | 0.623411 | 0.658847 | 0.797956 |

- Ron 25C statistical values after 160 hours burn-in

| Average | 12.935 | 15.756 | 11.341 | 11.665 |
| --- | --- | --- | --- | --- |
| Standard deviation | 0.17158 | 0.100202 | 0.123671 | 0.15427 |
| Predicted range | 0.885351 | 0.517041 | 0.638144 | 0.796035 |

- Ron 25C statistical values after 240 hours burn-in

| Average | 12.943 | 15.803 | 11.365 | 11.681 |
| --- | --- | --- | --- | --- |
| Standard deviation | 0.207219 | 0.127929 | 0.154025 | 0.184966 |
| Predicted range | 1.069252 | 0.660114 | 0.794768 | 0.954427 |

## General Conclusions

- Performing statistical analysis to actual experimental data showed the large majority of data is well fitted to normal distribution
- Most parameters have predicted range within part manufacturer datasheet specified range
- Some parameters require derating in circuit application depending on quantity of parts used and confidence levels required
- Some experimental data is suspect and tests should be repeated if feasible
- It is recommended that an analysis of the accuracy of experimental measurements be made in all cases so there is more confidence in validity of test data