Zero failures in qualification: what reliability figures really tell you

Zero failures sounds like the end of a reliability discussion. Statistically, it is the point at which the amount of testing becomes especially important. One hundred devices surviving a short test and several thousand surviving a long one have both produced a zero. They have not produced the same evidence.

A failure rate quoted in FIT means failures per billion device hours. The figure is often an upper confidence bound derived from accelerated testing, rather than a direct count of failures observed in normal service. Its meaning depends on the sample size, duration, confidence level and assumptions used to translate test stress into operating conditions.

### The same result can produce different FIT values

Texas Instruments provides a worked example using 231 devices tested for 1,000 hours at 125°C, with no failures. Applying an activation energy of 0.7eV and translating the result to 55°C gives 50.9 FIT at 60% confidence. At 90% confidence, the table gives 127 FIT.

No extra devices have failed between those two calculations. The higher figure expresses a more demanding statistical confidence requirement. TI’s example also shows the bound falling as the sample grows: with 922 devices and the same test duration, its values become 12.8 FIT and 32 FIT respectively.

A comparison between two suppliers is therefore incomplete if one value uses 60% confidence and the other 90%. Different temperatures, acceleration assumptions and tested populations can make an apparently simple ranking equally misleading.

### A worked example without temperature acceleration

Consider an illustrative test accumulating one million device hours with zero failures, all at the operating condition being assessed. Under an exponential constant failure rate model, the one-sided 95% upper bound is:

Failure rate = −ln(0.05) ÷ total device hours.

That gives approximately 0.000002996 failures per hour, or 2,996 FIT. The calculation follows the zero-failure confidence-bound method in NIST’s reliability handbook.

This is a bound under the stated statistical model, not a forecast that a particular batch will suffer exactly that many failures. Doubling the accumulated test hours, while still seeing zero failures, halves the bound. Increasing the confidence requirement raises it.

The example deliberately avoids acceleration. Applying the same equation directly to a high-temperature test and calling the answer a normal-use failure rate would omit the relationship between test stress and operating conditions.

### Reliability also needs an operating history

A single temperature cannot describe equipment that spends most of its life cool and short periods hot. A mission profile records the time spent in the relevant operating states, allowing the model to account for their different contributions.

The model’s scope matters just as much. TI’s application report addresses powered silicon reliability; it explicitly excludes package reliability and non-volatile memory retention. A quoted FIT number from that calculation cannot establish solder-joint life, connector durability or retained-data life.

Constant failure rate models also concern the useful-life region. They do not establish when wear-out begins. Converting a small FIT value into a very large mean time to failure is a mathematical operation, not evidence that an individual component will operate for that length of time.

A defensible reliability comparison keeps the number attached to its conditions: what was tested, for how long, at what stress, with which failures, and using which model and confidence level. <p><a href="https://www.ti.com/lit/an/spraby3/spraby3.pdf">TI: Calculating FIT for a Mission Profile</a>. <a href="https://itl.nist.gov/div898/handbook/apr/section4/apr451.htm">NIST: exponential model and confidence bounds</a>. <a href="https://www.ti.com/quality-reliability/reliability/calculators.html">TI reliability calculators and model limitations</a>.</p>