Weibull Life Analysis

A datasheet claim of 50,000 hours is a projection, not a measurement. Somebody had to test samples for a few thousand hours, model the degradation, and extrapolate the rest. Buyers who understand how that extrapolation is built can tell a substantiated lifetime claim from a marketing number, and can specify the testing they need for their own application. This white paper covers the three components of a defensible lifetime projection: accelerated test design, degradation modelling, and statistical treatment of the failure distribution.

1. The three-part structure of a lifetime claim

A credible lifetime projection rests on three separate pieces of work, and a claim that omits any of them is not verifiable.

Accelerated test data establishes how fast the device degrades under stress. Without it, there is no basis for extrapolation. A degradation model converts measured stress response into a projection at use conditions. Without it, accelerated data says nothing about field life. A statistical distribution quantifies the spread between samples and produces a confidence bound. Without it, a projected lifetime is a single number with unknown reliability.

The consequence for specification writing is that a supplier should be able to state all three: the test conditions and duration, the model and its parameters, and the confidence level attached to the result.

2. Selecting stress levels

Accelerated testing trades time for stress. The stress must be high enough to produce measurable degradation within a practical test window, and low enough that it does not activate a mechanism that would never occur in the field. Activating the wrong mechanism is the single most common failure of an accelerated test programme: the resulting lifetime estimate is precise and wrong.

For LED packages, three stress variables matter, and they should be applied at three or more levels each so that the acceleration model can be fitted rather than assumed.

For steady-state lumen maintenance, IES LM-80 defines the accepted test conditions: a minimum of 6,000 hours at three case temperatures (55 °C, 85 °C and a third temperature selected by the manufacturer), with lumen maintenance measured at 1,000-hour intervals. For J-01 (3535 ceramic) and J-02 (5050 ceramic), the ceramic body makes high case temperatures practical, so all three LM-80 temperatures can be reached by heat-sink design alone without over-driving the die.

3. The degradation model

Lumen maintenance for LEDs is conventionally modelled with an exponential decay:

Φ(t) = B · exp(-α t)

where Φ(t) is the normalised luminous flux at time t, and B and α are fitted constants. Solving for the time at which flux reaches a fraction f of its initial value gives the L-threshold time:

t_f = - ln(f / B) / α

For L70, f = 0.70. IES TM-21 restricts extrapolation to six times the available test duration, so 6,000 hours of data supports a projection to 36,000 hours. A claim beyond that range requires longer testing, not a longer extrapolation.

Arrhenius extrapolation moves the decay rate between temperatures:

α(T) = α₀ · exp[ -Ea / (k T) ]

Plotting ln(α) against 1/T yields a straight line whose slope gives the activation energy. That slope, not an assumed value, is what makes the projection specific to the tested product.

Note that J-15 (3535 UVC 275 nm) has a markedly shorter projected life than the visible-light parts, which is expected: ultraviolet photons drive encapsulant degradation directly, so the decay constant is higher at every temperature. Lifetime discussion for UV-C devices must be conducted separately from white-light devices. It must also be kept separate from Z-14, the 254 nm / 365 nm mercury-lamp tube, whose degradation follows lamp-chemistry physics rather than LED encapsulant physics.

4. Weibull treatment of the sample distribution

Lumen maintenance describes the average device. Weibull analysis describes the spread, and buyers care about the spread because a specification is a promise about the population, not the mean.

The two-parameter Weibull cumulative distribution function is:

F(t) = 1 - exp[ -(t / η)^β ]

where η is the scale parameter (characteristic life, the time at which 63.2 % of the population has failed) and β is the shape parameter. The shape parameter carries physical meaning: β < 1 indicates a decreasing hazard rate (infant mortality, typically process defects); β ≈ 1 indicates a constant hazard (random failures); β > 1 indicates an increasing hazard (wear-out).

For LED packages under steady-state thermal stress, β typically falls between 1.5 and 3.0 for the lumen-depreciation failure definition, which confirms wear-out behaviour and justifies an L-threshold specification.

The B10 life is the number most often quoted in commercial documents, but for automotive and medical applications the relevant figure is usually B1 or even B0.1, because the acceptable failure fraction is far below ten percent. J-01, J-02 and J-03 ceramic packages are the parts most often specified to automotive-grade failure fractions; note that the automotive qualification status is AEC-Q102 in progress and the Weibull data supports the reliability argument but is not itself a qualification certificate.

5. Confidence bounds and sample size

A Weibull fit from a finite sample carries sampling uncertainty. The standard remedy is a confidence bound on the life estimate, commonly the 90 % lower confidence bound, which states that the true value is above the quoted figure with 90 % probability.

Sample size drives how tight that bound can be. With all samples failing (complete data), a sample of 20 gives a B10 confidence bound roughly 25–35 % below the point estimate; a sample of 60 tightens that to roughly 12–18 %. With censored data (a test stopped before all units fail), the bound widens, and the number of failures rather than the number of samples governs the result.

6. Test planning checklist

A defensible accelerated life test for an LED package should specify the following before any sample is mounted:

• The failure definition (L70, L80, catastrophic open, or a parameter shift threshold) and the measurement instrument.
• Three or more stress levels, with at least 20 samples per level, and the rationale for each level.
• The measurement interval, which must be frequent enough to fit the decay curve, typically every 1,000 hours.
• The case temperature control method, held within ±2 K, with the measurement point defined physically.
• The extrapolation limit: no more than six times the test duration per TM-21.
• The statistical method and the confidence level to be reported alongside the point estimate.
• The board stack-up, which must match production, because thermal resistance depends on it.

7. Common extrapolation errors

8. Conclusion

An LED lifetime claim becomes engineering data when it names the test conditions, the fitted degradation model and its activation energy, the statistical distribution of the population, and the confidence bound on the reported figure. Buyers specifying J-01, J-02, J-03, J-05 or J-15 should require LM-80-format data at a case temperature at or above the application’s expected operating case temperature, a TM-21-format projection with its extrapolation limit stated, and a Weibull B10 or B1 figure with the sample size and confidence level disclosed.

9. Referenced standards

• IES LM-80-21 — Approved method: measuring luminous flux and colour maintenance of LED packages, arrays and modules
• IES TM-21-19 — Projecting long term lumen maintenance of LED light sources
• IES TM-28 — Projecting long-term luminous flux maintenance of LED lamps and luminaires
• JESD91 — Method for developing acceleration models for electronic component failure mechanisms
• JESD22-A104 — Temperature cycling
• JESD22-A105 — Power and temperature cycling
• IEC 60068-2-78 — Damp heat, steady state

10. Contact us

QUEENDOM can provide LM-80-format lumen maintenance data, fitted TM-21 projections and Weibull analysis for the ceramic and high-reliability parts in the J-series. Contact the component engineering group with the intended case temperature, drive current and expected service life so that the test plan can be matched to the application.

Related products and applications

The packages for which accelerated-life data is held are listed below.

• High-power SMD LED (J-01)
• High-power SMD LED (J-02)
• UVC 275 nm LED (J-15)
• Infrared emitter LED (J-05)
• Application overview: LED components application solutions
• More technical papers: LED knowledge resources