Advancing QE Skills (28) | Accelerated Life Test Design: Models for Temperature, Humidity, and Vibration

1. Treating 1000 Hours at 125°C as "Equivalent to 20 Years"

A manufacturing company was conducting a life test for a product with a plastic-encapsulated electronic control module. The customer required the entire unit to be maintenance-free for 10 years. Due to the tight project timeline, the R&D team decided to place three samples in a 125°C high-temperature chamber for continuous baking for 1000 hours. All samples passed, and they converted the 1000 hours to approximately 20 years using an "acceleration factor of 175" and submitted the conclusion to the customer. The quality engineer identified three critical issues during the review: first, the primary failure mode in the field is electrochemical corrosion of the pins and cracking of the plastic encapsulation due to humidity and heat, but the high-temperature chamber provides a dry heat environment, which fundamentally does not match the failure mechanism; second, 125°C is close to the glass transition temperature of the plastic encapsulation material, and high temperatures can introduce delamination failures that do not occur during normal use; third, with only three samples, zero failures, and no confidence statement, the statistical conclusion is essentially meaningless. This case illustrates that the success or failure of an accelerated life test (ALT) does not depend on how many hours the samples are baked, but rather on whether the model is correctly selected, whether the stress is reasonably applied, and whether the sample size and criteria have been calculated.

2. Acceleration Models: Categorize Stresses Before Discussing Formulas

The basic relationship in accelerated testing is the acceleration factor AF = t_use ÷ t_stress, which means the unit time under stress conditions is equivalent to how many times the unit time under use conditions. The applicable boundaries of the four commonly used models must be clearly understood, as selecting the wrong model can be more dangerous than not conducting the test at all.

1. Arrhenius — Only for Constant High Temperature and Single Thermal Activation Mechanism (oxidation, diffusion, ion migration, insulation aging):

AF = exp[ (Ea/k) × (1/T_use − 1/T_stress) ]

k = 8.617×10⁻⁵ eV/K, temperature is in absolute temperature, Ea is the activation energy (eV). Example: Ea = 0.7 eV, use temperature = 55°C (328 K), stress temperature = 125°C (398 K), resulting in AF ≈ 78. This number itself should raise an alarm — the larger the AF, the more fragile the extrapolation.

2. Eyring/Peck (Temperature and Humidity) — For Mechanisms Involving Both Temperature and Humidity:

AF = (RH_stress / RH_use)^n × exp[ (Ea/k) × (1/T_use − 1/T_stress) ]

For plastic-encapsulated devices, Ea is typically ≈ 0.9 eV, and n is ≈ 2.7 to 3.0. The weight of the humidity term is significant: increasing the relative humidity from 45% to 85% with n = 3 results in approximately 6.7 times acceleration. Ignoring this term can systematically underestimate the entire test's acceleration factor.

3. Coffin-Manson (Temperature Cycling) — For Thermal Fatigue, Solder Joint, and Thermal Mismatch Failures:

AF = (ΔT_stress / ΔT_use)^q

For lead-free solder joints, q is often taken as 2. This model describes the number of cycles rather than constant temperature time, so using a constant temperature chamber to simulate temperature cycling failures is fundamentally incorrect. When cycles have frequency and dwell time effects, the Norris-Landzberg correction must be applied.

4. Inverse Power Law — For Vibration, Mechanical Stress, and Voltage:

AF = (S_stress / S_use)^n

When accelerating random vibration by power spectral density, n is typically taken as 4 (Steinberg model). This means that doubling the vibration magnitude results in a 16 times acceleration, making it the most "sensitive" of the four models. Any magnitude error will be amplified to an unacceptable level, so the stress spectrum must be measured and calibrated.

3. Five Practical Steps: From Environmental Profile to Extrapolated Conclusion

Step One: Quantify the Use Environment Profile. It is essential to obtain the temperature distribution (the proportion and cumulative hours of each temperature segment), relative humidity distribution, power-on duration, vibration magnitude and spectrum, and the ΔT and annual cycle count for temperature cycling. Criterion: Temperature should not be given as a single "maximum 45°C" but should include a distribution or equivalent weighted temperature. If any of the four items are missing, the corresponding model cannot be used, and the test must be downgraded to a qualitative screening test.

Step Two: Use Failure Physics Analysis to Identify the Dominant Mechanism. Conduct 2-3 qualitative pre-tests or analyze failed components to confirm the failure location and mode. Criterion: The failure modes at the highest and lowest stress levels must be consistent (same failure location, same failure mechanism). If new failure modes appear at high stress levels, the "lowest stress level at which the new mechanism appears" should be used as the upper limit for the acceleration stress, and data from two different mechanisms should not be mixed on the same life-stress curve for extrapolation.

Step Three: Select the Model and Determine Stress Levels. Match the model based on the boundaries discussed in the previous section and adhere to three quantitative constraints: ① At least 3 stress levels (at least 3 points are needed to fit the life-stress relationship, more than 3 are not necessary); ② The lowest stress level should not be less than 1.5 times the use condition to avoid an unacceptably long test duration; ③ The highest stress level should leave at least 20% material margin — for plastic-encapsulated devices, this is generally no more than 150°C and below the material's Tg, the humidity upper limit is typically 85% RH (exceeding this can introduce condensation), and the vibration should not exceed 1.6 times the design limit.

Step Four: Calculate the Acceleration Factor and Test Time, and Derive the Sample Size from the Target. First, calculate the AF, then use "target life ÷ AF" to determine the required stress time. Criterion One: In engineering, a single-level acceleration factor should be controlled to within 20 times (conservatively 10 times); if AF exceeds 50, additional evidence of mechanism consistency must be provided or the stress level abandoned. Criterion Two: Under a zero-failure scheme, the total test time T for an exponential distribution assumption is T = χ²(2r+2, C) ÷ 2 × target MTBF, with r = 0 and a 90% confidence level, this is 2.3 times the target value (for r = 0 and C = 60%, it is approximately 0.92 times). If a Weibull assumption is used with a shape parameter β = 2 and a 90% confidence level, then 10 samples each need to run for about 1.5 times the B10 life (5 samples need about 2.1 times). The sample size and test time must be derived from the target life/confidence level, not by first determining "how long to bake" and then calculating the factor.

Step Five: Data Processing and Compliance Check for Extrapolation. Use least squares or maximum likelihood to fit the life-stress relationship. Criterion: The Ea or n obtained from the fit should deviate from the empirical values of similar devices by no more than 30%. If the deviation is too large, suspect the stress setting or data mixing before accepting the result. Censored (non-failed) samples must be handled as censored data and not simply discarded as "passed." The extrapolation range should not exceed one order of magnitude below the lowest test stress; otherwise, it can only be called a "trend judgment" and not a "life conclusion."

4. Four Common Misconceptions

Misconception One: One Arrhenius Model for All. Baking all humidity and temperature cycling failures into high-temperature baking, citing "temperature is the main stress." If the mechanism is incorrect, even the most precise calculation of the acceleration factor will completely bypass the dominant failure mode under use conditions.

Misconception Two: Arbitrary Activation Energy. The Ea for different mechanisms can vary greatly (ion migration ≈ 0.7 to 1.0 eV, intermetallic compound growth ≈ 0.8 to 1.2 eV, some surface corrosion only ≈ 0.3 to 0.5 eV). An error of 0.2 eV in the 125°C ↔ 55°C range can result in an AF difference of 2 to 3 times. Ea should come from test data of similar products, device manuals, or failure physics literature, and the basis for the value should be clearly stated.

Misconception Three: Claiming "1000 Hours at 125°C Equals 20 Years." This statement implies three assumptions: a single mechanism, constant stress, and constant failure rate. Real-world conditions involve multiple stresses (temperature, humidity, vibration, and power cycling) and the failure stage can shift. The correct statement is: "1000 hours at 85°C/85% RH (or corresponding stress) with no failures, according to the Peck model (Ea = 0.9 eV, n = 3.0), the estimated characteristic life under use conditions is ×× years, and the 90% confidence B10 life lower bound is ×× years." Providing the model, parameters, and confidence level is what constitutes a conclusion.

Misconception Four: All Samples Passing Means Qualification. Running three samples with zero failures for a period provides almost no statistical information. In addition to calculating the sample size as per Step Three, note that samples from the same batch do not represent batch differences, and samples from different stress levels should come from different batches as much as possible. For destructive tests, once a sample is used, it cannot be reused for another stress level.

5. Self-Check List

1. □ Is the use environment profile quantified (temperature distribution, humidity, vibration magnitude, cycle count) rather than a single extreme value?
2. □ Is there evidence from failure physics analysis or pre-tests for the dominant failure mechanism, and are the failure modes consistent across all stress levels?
3. □ Do the model and stress type match (constant high temperature → Arrhenius; temperature and humidity → Peck; temperature cycling → Coffin-Manson; vibration → Inverse Power Law)?
4. □ Is the calculation process and parameter source (basis for Ea and n values) provided for the acceleration factor, and is the single-level AF not exceeded 20 times?
5. □ Are the sample size and test time derived from the target life/confidence level, and is the data processing method (censored data, extrapolation boundary) stated?

No matter how large the acceleration factor, it is worthless if the mechanism is wrong.

Knowledge code: 8.2.3

Version: v20261008

Author: QTank QTank is dedicated to providing systematic professional knowledge, methodologies, and practical tools for quality management practitioners, helping companies continuously improve their quality capabilities.