Electronics Guide

Density and Cumulative Distribution Functions

The probability density function f(t) describes where failures concentrate in time. The product f(t) dt is the probability that a randomly chosen new unit fails in the small interval from t to t + dt. The density is never negative, and it integrates to one over all positive times, because every unit eventually fails.

The cumulative distribution function accumulates that density:

F(t) = P(T ≤ t) = ∫₀^t f(x) dx

In reliability work F(t) is also called the unreliability, and it is the quantity plotted on probability paper. It starts at zero, never decreases, and approaches one. Read directly, it answers the question a program manager asks first: what fraction of the shipped population will have failed by the end of the warranty period.

The Reliability Function

The reliability function is the complement of the unreliability:

R(t) = P(T > t) = 1 − F(t)

It gives the probability that a unit survives beyond time t. Every unit starts operational, so R(0) = 1, and the function decreases monotonically toward zero. Requirements are usually written in this form because it states the goal positively and attaches a time to it. A specification such as "reliability of at least 0.99 at 10 years under the defined use profile" is complete in a way that a bare mean life is not, since it names both a probability and the period over which it must hold.

The Hazard Function

The hazard function, also called the instantaneous failure rate, is the density conditioned on survival:

h(t) = f(t) / R(t)

The distinction from the density matters. The density measures risk against the original population, while the hazard measures risk against the units still running. Because the surviving population shrinks, a hazard rate can climb steeply even while the absolute number of failures per month falls. The hazard carries units of inverse time and is reported in failures per hour, in percent per thousand hours, or in FIT, where one FIT equals one failure per 10⁹ device-hours.

The shape of the hazard function is the most diagnostic feature of a life distribution. A falling hazard indicates a defective subpopulation being consumed, a flat hazard indicates failures arriving independently of age, and a rising hazard indicates wear-out. These three shapes are precisely the three regions of the bathtub curve, which is why fitting a distribution and inspecting its hazard is the standard way to identify which region a population occupies.

Cumulative Hazard and the Equivalence of the Four Views

Integrating the hazard gives the cumulative hazard, and the cumulative hazard reconstructs the reliability function:

H(t) = ∫₀^t h(x) dx  and  R(t) = exp[−H(t)]

This identity closes the loop. Given any one of the four functions, the remaining three follow: the density is the negative derivative of the reliability function, the unreliability is its complement, and the hazard is their ratio. The identity also explains why hazard plotting works as an estimation technique. Because H(t) = −ln R(t), a nonparametric estimate of the cumulative hazard built up from ordered failure times can be transformed directly into an estimate of reliability, with no distributional assumption required until a model is fitted to the result.

One consequence deserves emphasis: the cumulative hazard grows without bound as reliability approaches zero, while the hazard rate itself may do almost anything in between. Two distributions with very different hazard shapes can share the same value of R at a single time. Matching one point on a reliability curve therefore proves nothing about the model, a point that returns when distributions are compared in the tails.

Distribution Functions

With failure rate λ, the four functions are

f(t) = λ e^−λt,   F(t) = 1 − e^−λt,   R(t) = e^−λt,   h(t) = λ

A single parameter fixes the entire distribution. The mean time to failure is the reciprocal of the failure rate, MTTF = 1/λ, and the standard deviation is also 1/λ, so the coefficient of variation always equals one. The median is shorter than the mean: t₅₀ = ln(2)/λ ≈ 0.693/λ. Roughly 63.2 percent of an exponential population has failed by the mean life, a fact that surprises engineers who read a mean as a typical service life.

The Memoryless Property

The exponential distribution is the only continuous distribution that is memoryless:

P(T > t + s | T > t) = P(T > s)

A surviving unit is statistically indistinguishable from a new one, whatever its age. This assumption has hard operational consequences, and each of them is testable. Burn-in provides no benefit, because screening cannot remove a weak subpopulation that the model says does not exist. Preventive replacement provides no benefit either, since a new part carries exactly the hazard rate of the part it replaced. If a program conducts burn-in and sees the field failure rate drop, the exponential model has been falsified for that population.

The compensating advantage is algebraic simplicity. For a series system in which any component failure fails the system, hazard rates add:

λ_system = λ₁ + λ₂ + … + λ_n

That additivity is why part-count prediction, Markov availability models, and most fault-tree arithmetic assume constant rates. It is also why the same assumption propagates silently through a reliability program once it has been made at the component level.

Where the Constant-Rate Assumption Is Defensible

The exponential model is well founded when failures are triggered by events external to the part rather than by its accumulated age. Electrostatic discharge, line transients, mechanical shock, and single-event upsets in radiation environments all arrive on schedules set by the environment, not by the age of the device, and they produce approximately constant rates.

A second and subtler argument applies to complex systems. When a large number of independent components, each with its own non-constant hazard and its own installation date, are combined and repaired over time, the pooled stream of failures tends toward a Poisson process with a constant rate. The result is usually credited to Drenick, and it explains a common observation: a repairable system made of wear-out-prone parts can nevertheless exhibit a nearly constant system-level failure rate once the replacement ages have been thoroughly mixed.

The assumption is weakest exactly where design decisions concentrate. It cannot represent infant mortality, so it will understate early returns from a population containing manufacturing defects. It cannot represent wear-out, so it will badly overstate the life of electrolytic capacitors, fans, connectors, relays, and anything else with a consuming mechanism. The exponential model should be adopted because data or physics support it, not because it makes the spreadsheet close.

A Worked Calculation

Consider a component rated at 50 FIT, that is, λ = 50 × 10⁻⁹ failures per hour. Its mean time to failure is 1/λ = 2 × 10⁷ hours, roughly 2,300 years. No one expects the part to last 2,300 years, and that is the point: for a constant-rate model the mean is a statement about a rate, not about a service life.

The useful question is the reliability over the design life. Ten years of continuous operation is 87,600 hours, so

R(87,600 h) = exp(−50 × 10⁻⁹ × 87,600) = exp(−0.00438) ≈ 0.9956

About 4,400 parts per million of that component population fail over ten years. Now assemble 200 such components into a series system. Rates add, giving 10,000 FIT, or λ = 10⁻⁵ per hour and a system MTTF near 100,000 hours. Over the same ten years,

R(87,600 h) = exp(−0.876) ≈ 0.42

Fewer than half the systems survive the design life, even though every individual part looked excellent. Series accumulation, not any single weak component, is what usually sets the reliability of an electronic assembly.

Estimating the Rate and Bounding It

For exponential data the point estimate is simply the total accumulated operating time T divided among the observed failures. The estimated failure rate is r/T, and the estimated MTTF is its reciprocal, T/r. Because T may pool many units running for different durations, the estimate handles censored tests naturally, which is a large part of the model's appeal.

The point estimate alone is misleading, especially when failures are few. The chi-square distribution supplies the bounds. For a time-terminated test with r failures and total accumulated time T, the upper confidence bound on the failure rate at confidence level C is

λ_upper = χ²_{C, 2r+2} / (2T)

where χ²_{C, v} is the C quantile of the chi-square distribution with v degrees of freedom. The corresponding lower bound on MTTF is 2T divided by the same quantile. A failure-terminated test uses 2r degrees of freedom instead of 2r + 2.

The zero-failure case is the one most often misread. Suppose 1,000 units run for 1,000 hours with no failures, accumulating 10⁶ device-hours. The point estimate of the failure rate is zero, but the 60 percent upper bound is 916 FIT and the 90 percent upper bound is about 2,300 FIT. A clean qualification lot does not demonstrate a low failure rate; it demonstrates only that the rate is below a bound set by the amount of time accumulated. JEDEC codifies this arithmetic in JESD85, Methods for Calculating Failure Rates in Units of FITs, which combines the chi-square bound with Arrhenius acceleration to convert elevated-temperature life-test hours into an equivalent number of use-condition device-hours.

Distribution Functions

In the two-parameter form, with shape parameter β and scale parameter η,

R(t) = exp[−(t/η)^β],   F(t) = 1 − exp[−(t/η)^β]

f(t) = (β/η)(t/η)^β−1 exp[−(t/η)^β],   h(t) = (β/η)(t/η)^β−1

The hazard function is a power law in time, and the exponent is β − 1. That single structural fact accounts for the distribution's flexibility: a negative exponent produces a falling hazard, a zero exponent produces a flat one, and a positive exponent produces a rising one.

Reading the Shape Parameter

The shape parameter is the diagnostic output of a Weibull fit, and it maps onto physical behavior directly.

• β < 1: Decreasing hazard rate. A weak subpopulation is being consumed. The response is screening, process control, or a defect-reduction effort, not a design change to the good population.
• β = 1: Constant hazard rate. The Weibull reduces exactly to the exponential distribution with λ = 1/η.
• β = 2: Linearly rising hazard. This special case is the Rayleigh distribution.
• β > 1: Increasing hazard rate and wear-out. The response is derating, redesign, or a scheduled replacement interval.
• β between 3 and 4: A nearly symmetric density. The skewness of the Weibull passes through zero near β = 3.60, which is why fits in this range look normal on a histogram and why a normal model can appear adequate for tightly clustered wear-out.

Large shape parameters indicate a sharply defined end of life, with most failures arriving in a narrow window around the characteristic life. Values well below one indicate a population dominated by defects. Because β determines what should be done, not merely how the curve looks, its confidence interval matters: a fit that cannot exclude β = 1 has not established wear-out, however suggestive the point estimate.

Characteristic Life and Percentile Lives

The scale parameter η is called the characteristic life because R(η) = e⁻¹ ≈ 0.368 regardless of β. In other words, 63.2 percent of the population has failed by the characteristic life for every Weibull distribution, which makes η a fixed reference point for comparison across products.

The mean is a separate quantity:

MTTF = η Γ(1 + 1/β)

For β = 1 the mean equals η. For β = 2 it is about 0.886η, and near β = 3.6 it is about 0.901η. Once wear-out is established, the mean and the characteristic life stay within roughly ten percent of each other, so neither is a useful measure of early failures.

Percentile life is the quantity that actually drives warranty reserves and maintenance intervals. The time by which a fraction q of the population has failed is

t_q = η [−ln(1 − q)]^1/β

For β = 2.5 and η = 10,000 hours, the B10 life, at which 10 percent have failed, is about 4,065 hours. The mean for that distribution is about 8,873 hours. Quoting the mean would overstate the useful interval by more than a factor of two for any decision keyed to the first tenth of the population, which is why mechanical and rotating-equipment practice has long preferred B10 or L10 life to a mean.

The Three-Parameter Weibull

Adding a location parameter γ shifts the time origin. Every formula holds with t replaced by (t − γ), and no failures are possible before γ. The parameter is defensible when physics guarantees a failure-free period, for example when a wear mechanism must consume a known thickness of material or a known amount of margin before any failure can occur.

The parameter is also easy to abuse. Three parameters fit small samples too well, γ is poorly identified by the data, and an unjustified positive threshold produces optimistic early-life predictions in exactly the region where optimism is most expensive. A fitted negative γ is a diagnostic in its own right: it usually means the units accumulated stress before the clock started, as when field returns are dated from shipment rather than from installation. Use the third parameter only when a mechanism argues for it, and report the two-parameter fit alongside.

Weibull Plotting and Median Ranks

Taking logarithms twice linearizes the Weibull cumulative distribution:

ln[−ln(1 − F(t))] = β ln t − β ln η

Plotted against ln t, Weibull data fall on a straight line whose slope is β. The characteristic life is read from the time axis where the fitted line crosses F = 63.2 percent. This is the geometry that Weibull probability paper implements, and it remains the fastest way to see what a data set is doing.

Plotting requires an estimate of F at each observed failure. The standard choice is the median rank, approximated by Bernard's formula for the i-th of n ordered failures:

F_i ≈ (i − 0.3) / (n + 0.4)

When some units are suspended without failing, their ranks are redistributed among the later failures by rank adjustment, so censored units contribute the information they carry without being counted as failures. Departures from the fitted line are as informative as the line itself. A dogleg or S-shape suggests a mixed population or two competing mechanisms, systematic downward curvature suggests a nonzero threshold or the wrong distribution family, and a handful of early points far off the line suggests a small defective subpopulation. IEC 61649:2008, Weibull analysis, is the international standard covering these procedures.

Why the Weibull Fits So Much Data

The Weibull distribution has an extreme-value pedigree, not merely an empirical one. If an item fails when the weakest of many nominally identical, independent elements fails, then the failure time is the minimum of many random variables. Minima of large samples converge to one of a small number of limiting laws, and for quantities bounded below by zero the limit is the Weibull. The distribution is therefore the natural model for any weakest-link mechanism.

Electronics supplies the canonical example. Time-dependent dielectric breakdown in thin gate oxides is treated as a weakest-link process: breakdown occurs at the first defective site, so failure times follow a Weibull distribution and the failure probability scales with area according to Poisson statistics. That area scaling is what allows measurements on small test structures to be projected onto a full die, and the consistency of the projection is itself evidence that the weakest-link assumption holds. The same reasoning applies to breakdown in capacitor dielectrics and to defect-driven failures in large-area interconnect.

Distribution Functions

With log-mean μ and log-standard-deviation σ, and with Φ denoting the standard normal cumulative distribution,

F(t) = Φ[(ln t − μ)/σ],   R(t) = 1 − Φ[(ln t − μ)/σ]

f(t) = 1/(tσ√(2π)) · exp[−(ln t − μ)²/(2σ²)]

The parameters describe the distribution of ln t, not of t. Note in particular that σ is dimensionless: it is a shape parameter measured in log-time, and it is what an analysis reports when comparing the spread of one mechanism against another.

Key Properties

The lognormal is right-skewed, with a long tail toward long lives. Its summary statistics separate:

• Median: t₅₀ = e^μ, which is also the geometric mean
• Mean: e^{μ + σ2/2}, always larger than the median
• Mode: e^{μ − σ2}, always smaller than the median

Because the three separate as σ grows, the median is the only stable descriptor of a lognormal life, and mechanism models are conventionally written for the median rather than the mean. The value of σ translates directly into dispersion: a σ of 0.5 spreads the middle 80 percent of failures over a time span of about 3.6 to 1, while a σ of 1.0 spreads the same fraction over roughly 13 to 1.

The hazard function is the structurally important feature. It rises from zero, reaches a maximum, and then declines toward zero at long times. No Weibull distribution behaves this way, since the Weibull hazard is monotonic. The practical consequence is that a lognormal model implies falling risk among aged survivors, which is difficult to justify for a mechanism that consumes material or margin. That behavior is also the reason lognormal fits are optimistic far out in the upper tail and, as shown below, in the lower tail as well.

The Multiplicative Origin

The lognormal has the same theoretical standing for products that the normal has for sums. If damage accumulates through a long sequence of independent multiplicative increments, then the logarithm of accumulated damage is a sum of independent terms, the central limit theorem applies in log space, and the time to reach a fixed damage threshold is lognormal. Fatigue crack growth is the classic mechanical example, because the increment of growth per cycle is roughly proportional to the current crack size.

In electronics the lognormal is the conventional distribution for electromigration in metal interconnect. Black's equation expresses the median time to failure of a line in terms of current density and temperature, and the lognormal supplies the spread about that median. The convention is not unanimous: published analyses argue that a Weibull model describes some interconnect geometries better, particularly short lines and redundant structures where the weakest-link argument reasserts itself. Oxide breakdown data have been fitted with both families historically, though weakest-link reasoning and area scaling now favor the Weibull for thin gate dielectrics.

Two lessons follow. First, the applicable distribution belongs to the mechanism, not to the part, so a device with several active mechanisms may need several distributions. Second, conventions are worth knowing but are not evidence. Where the convention and the data disagree, the data and the physics decide.

Choosing Between the Weibull and the Lognormal

The two distributions are the principal competitors in life data analysis. Both take two parameters, both are right-skewed, both are defined only for positive times, and both fit typical censored data sets well enough that goodness-of-fit statistics rarely separate them. They diverge where the data are thin.

A concrete comparison makes the size of the divergence clear. Take a Weibull distribution with β = 2.5 and η = 10,000 hours, and fit a lognormal forced to agree with it exactly at two points: the median, 8,636 hours, and the B10 life, 4,065 hours. That match requires μ = ln(8,636) and σ ≈ 0.588. Within the region where data usually exist, the two models are indistinguishable. Below it they part company:

• B1 life (1 percent failed): 1,588 hours for the Weibull against 2,199 hours for the lognormal, a difference of 38 percent
• B0.1 life (0.1 percent failed): 631 hours against 1,403 hours, a factor of 2.2

Neither model is wrong about the data. The divergence is a property of the families, and it grows the further the extrapolation runs. When a decision depends on a low percentile, the choice of distribution deserves the same scrutiny as the test data, and carrying both models to report the more conservative bound is often the honest course.

Distribution Functions

With mean μ and standard deviation σ,

f(t) = 1/(σ√(2π)) · exp[−(t − μ)²/(2σ²)],   F(t) = Φ[(t − μ)/σ]

The distribution is symmetric, and its hazard function increases without bound.

Why It Rarely Describes Failure Times

The normal distribution assigns probability to negative values, which have no meaning as failure times. The error is negligible only when the mean sits several standard deviations above zero. A wear-out population with a mean life of 10,000 hours and a standard deviation of 4,000 hours would place Φ(−2.5), about 0.6 percent of the population, at negative life, which is enough to distort any calculation aimed at the first percentile.

Symmetry is the second problem. Failure time distributions are almost always right-skewed, since a mechanism can be delayed indefinitely but cannot complete faster than its physics permits. Third, the normal offers no shape parameter, so it cannot represent infant mortality or a constant hazard at all. Where a normal model does appear to fit tightly clustered wear-out, a Weibull with β in the range of 3 to 4 will usually fit as well while respecting the positive support.

Where the Normal Does Belong

The normal distribution earns its place in reliability engineering away from the time axis.

• Parameter distributions: Threshold voltages, amplifier offsets, resistor values within a lot, and similar characteristics are shaped by many small additive contributions and are often approximately normal. Process capability analysis rests on this.
• Degradation amount: The amount of drift measured at a fixed inspection time is frequently normal even when the time to cross a failure threshold is not.
• Log-time models: The lognormal is a normal model in disguise, so every normal technique applies once the data are transformed.
• Statistical inference: Confidence intervals, regression residuals, and the asymptotic behavior of maximum-likelihood estimators all rely on normal theory, whatever life distribution is being fitted.

The normal distribution therefore remains indispensable to reliability analysis while seldom being the right model for a failure time.

Gamma and Erlang

The gamma distribution has a shape parameter k and a rate parameter λ. When k = 1 it reduces to the exponential, and when k is a positive integer it is the Erlang distribution, which is exactly the sum of k independent exponential times.

That construction gives the gamma a clear physical reading: it models a unit that survives k − 1 shocks and fails on the k-th, or a standby-redundant assembly with k − 1 spares and perfect switching. Its hazard rate is monotonic, rising for k > 1 and falling for k < 1, but it is bounded and approaches λ asymptotically in both cases. That boundedness is the reason the gamma is a poor model for hard wear-out, where the hazard must keep climbing, and it is the main structural difference from the Weibull.

Inverse Gaussian

The inverse Gaussian distribution is the first-passage time of a Brownian motion with positive drift to a fixed threshold. It is therefore the natural model when a measurable characteristic drifts steadily toward a failure limit while fluctuating around its trend, which is precisely the situation in degradation testing.

Its hazard rises to a maximum and then settles toward a positive constant, reflecting the exponential tail of the first-passage density. Where a degradation path can be measured directly, an inverse Gaussian model uses far more information than a life test does, since every measured trajectory contributes even when the unit never fails.

Birnbaum-Saunders

The Birnbaum-Saunders distribution, also called the fatigue-life distribution, was derived from a cumulative-damage model of crack growth under cyclic loading. It relates to the normal by a simple transformation: with shape α and scale β,

F(t) = Φ{ (1/α)[√(t/β) − √(β/t)] }

The scale parameter is the median, since the bracketed term vanishes at t = β. Like the lognormal, its hazard rises and then falls, approaching a positive constant rather than zero. The distribution closely mimics the lognormal through the body of the data while differing in the tails, which makes it a useful sensitivity check when a lognormal fit is being extrapolated for a fatigue-driven mechanism such as solder joint cracking under thermal cycling.

Smallest Extreme Value and Gumbel

If a failure time follows a Weibull distribution, its logarithm follows the smallest extreme value distribution, a member of the Gumbel family. This relationship is more than a curiosity. Life data software commonly fits in log-time, where the Weibull becomes a location-scale model and the lognormal becomes a normal one. Seen that way, the Weibull-against-lognormal comparison is a comparison between an extreme-value model and a normal model for the same transformed variable, which explains why the two agree in the middle and diverge in the tails.

Mixtures and Competing Risks

Real populations often violate the assumption of a single mechanism, and two distinct violations are frequently confused.

• Mixtures: Each unit belongs to one subpopulation. A small fraction p carries a manufacturing defect and the remainder does not, so R(t) = p R₁(t) + (1 − p)R₂(t). Reliability is a weighted sum.
• Competing risks: Every unit is exposed to every mechanism and fails at whichever acts first, so R(t) = R₁(t) × R₂(t) × …. Reliability is a product, and the system is always less reliable than its weakest mechanism alone.

Both produce curvature on a Weibull plot, and distinguishing them requires knowing the failure mode for each unit, which is one of the strongest practical arguments for physical failure analysis of every returned part. Estimation uses maximum likelihood or the expectation-maximization algorithm, and both need enough failures per mode to identify the parameters. A defective subpopulation of a few hundred parts per million is invisible in a fifty-unit qualification sample and still dominates field returns from a million shipped units, so the absence of curvature in a small sample is weak evidence of a homogeneous population.

Start with the Mechanism

The most reliable selection criterion is the physics of the failure. A weakest-link, defect-driven mechanism implies a Weibull. A multiplicative degradation process implies a lognormal. A drift-to-threshold process implies an inverse Gaussian. Externally triggered, age-independent events imply an exponential. When failure analysis identifies the mechanism, the distribution follows from the mechanism rather than from a search over families, and the resulting model can be extrapolated with some confidence because its shape is justified independently of the data.

Precedent is a legitimate secondary criterion. Where an industry has accumulated decades of data on a mechanism, its conventional distribution encodes far more evidence than any single qualification lot. Precedent should still be checked against the current data rather than assumed.

Plot Before Testing

A probability plot should precede any numerical fit statistic. Plotting the data on the candidate distribution's paper and looking for a straight line reveals what a single number cannot: outliers, batch effects, a threshold, a mixed population, or a systematic curvature that indicates the wrong family entirely. Comparing the same data on Weibull and lognormal paper is often more informative than any test, since the eye detects patterned deviation efficiently. Hazard plots and quantile-quantile plots serve the same purpose from different angles.

Goodness-of-Fit Tests and Model Comparison

Formal tests quantify what the plots suggest, and each has a distinct character.

• Chi-square: Compares observed and expected counts in bins. It requires enough data for adequate expected counts in every bin and depends on arbitrary binning choices, which limits its use for small life-test samples.
• Kolmogorov-Smirnov: Uses the maximum vertical distance between the empirical and fitted cumulative distributions. It is most sensitive near the center of the distribution and least sensitive in the tails. Its standard critical values assume fully specified parameters and are invalid when the parameters are estimated from the same data.
• Anderson-Darling: A quadratic statistic in the Cramer-von Mises family, formed by integrating the squared difference between the empirical and fitted cumulative distributions with weight 1/[F(1 − F)]. That weighting is what places extra emphasis on the tails and makes the test the usual choice in reliability, where the tails carry the decision. It is not a weighted Kolmogorov-Smirnov test, and the distinction matters because the two are sensitive in different regions.
• Likelihood ratio: Valid for comparing nested models, such as testing whether a Weibull fit is significantly better than the exponential special case β = 1. It does not apply to non-nested comparisons.
• Information criteria: AIC and BIC compare non-nested candidates such as the Weibull against the lognormal, penalizing additional parameters. Small differences between criteria are not meaningful evidence.

One caveat governs all of them. With the sample sizes and heavy censoring typical of electronics life testing, these tests seldom have the power to distinguish the Weibull from the lognormal. Failure to reject a distribution is not confirmation of it, and a marginally better statistic is not grounds for preferring a model whose shape the physics does not support.

Sensitivity Analysis and Conservative Choices

Because the model carries the extrapolation, the useful question is not which distribution is best but whether the choice changes the decision. Fit the credible candidates, propagate parameter uncertainty into confidence bounds, and compute the quantity the program actually needs from each. If the candidates agree within the accuracy the decision requires, the choice is not critical and the analysis can proceed. If they disagree, as they did by a factor of 2.2 at B0.1 in the comparison above, the disagreement is the finding. The response is to report the conservative bound, to state the assumption explicitly, and where the stakes justify it, to acquire the data that discriminate: more units, longer exposure, higher stress, or failure analysis that identifies the mechanism directly.

Documentation makes the analysis reproducible. Record the fitted family, the parameter estimates and their confidence bounds, the estimation method, the treatment of censored units, the plotting positions, and the mechanism argument behind the choice. IEC 61649:2008 covers Weibull analysis, and JEDEC JESD85 covers constant-rate FIT calculation, so an analysis that follows a recognized standard and states which one it followed is far easier for a customer or an auditor to accept.