TTF vs. "Test to pass" 

Electronics fail over time. Similar components from the same batch manufactured together subjected to identical conditions fail at different times. In simple words, even if you take parts from a single batch and solder them to the same board at the same time in a controlled reflow cycle – they will still fail at different times.

Weibull distribution

This is basically the “bell” curve from statistics, called the normal distribution. The normal distribution is used in all kinds of applications from engineering to Psychology and economics.

We can plot the failure over time. The most logical plot is to track the percent failure instead of number of failures because this normalizes it over the sample size. A common way to do that is using a Weibull distribution. In electronics reliability, we either use a 3-parameter or more likely a 2-parameter Weibull. To keep it simple, let’s use the 2-parameter Weibull curve.

The two parameters are the Greek letter Eta η or “Characteristic life” (Sometimes called Time To Failure/TTF) and the “Beta” β or slope at the TTF. This chart shows a Beta of 3 and TTF is 1,000. Note that the TTF is the time to 63.2% probability of failure.

This is the behavior of the entire sample population in the test. If we have 100 samples in the test we expect around 63 of them to fail at time 1,000. If we have 200 samples we expect 126 to fail and 25 failure out of 40 samples.

How to lie with statistics

All of this assumes that the test and samples are representative of actual product in the real environment. It is possible to “cherry pick” board for testing based on very high manufacturing standards that don’t represent actual manufacturing conditions. There is also an inherent uniformity in the test samples because they are manufactured in very similar conditions in the same ”lot”. These factors can some times change the Eta/TTF parameter, but they always affect the Beta/Slope parameter. Let’s take a look at the same Weibull curve while changing the Beta:

The TTF has not changed since all the curves cross at time 1,000 and probability of 63.2%, but the slope has changed. A higher slope corresponds to a larger Beta value and in simple terms signifies that the sample population all fail in a narrower band of time. A high value of Beta in a test does not indicate a high Beta in the field.

Time to first failure

Repeat: A high value of Beta in a test does not indicate a high Beta in the field. This is significant when looking at "time to first failure". If we zoom in to the Weibull curves above and assume a population of 50 samples, then the first failure is the 2% or 0.02 POF (Probability Of Failure).

The higher slope value moves the “time to first failure” from 273 for Beta = 3 to 649 for Beta = 9, but this does not fundamentally change the Characteristic life of the test. This simple math shows how the meaningless “time to first failure” can be manipulated by using exacting manufacturing standards for the test. Many qualifications use “test to pass” as an acceptance criteria. That is just a fancy way of saying that the “time to first failure” must exceed the test time. It is impossible to indicate a probability of failure without failures.

Any text book that has a discussion on statistics will include considerations for “statistically significant sample size” including formulas based on population size and other parameters that are relevant to that field of study. In electronics, we find that manufacturing a large enough sample size for test can be very VERY expensive. We typically see a field Beta of 3-6 and test Beta of 9 and sometime as high as 12 due to small sample size. When the sample size is small, you must test longer until there are enough failures to calculate TTF of the test samples. The test Beta should be replaced by your historical field return or observed Beta. This is also the reason that field return data is necessary in a comprehensive reliability program.

The variation in manufacturing is more relevant in mass manufactured products where population size is large (millions) and there may be manufacturing “lots” or changing manufacturing vendors. Implementing lot qualification tests and vendor qualification tests only makes financial sense where there is enough variation to justify it. Small batch electronics (thousands) is less susceptible to manufacturing variations, but is more susceptible to pitfalls in statistics.

Putting it all together

Electronic components fail over time, even when made from the same batch and under identical conditions. This variation in failure timing is typically modeled using the 2-parameter Weibull curve

A higher Beta means failures occur within a narrower time window, while a lower Beta indicates more spread out failures. However, manipulating test conditions like using highly uniform samples can artificially raise Beta and delay the "time to first failure," misleading reliability test results.

In electronics, small sample sizes often lead to higher Beta values during testing (e.g., 9–12), whereas real-world field Betas are typically lower (around 3–6). This discrepancy means field failure data is crucial for comprehensive reliability programs.

Copyright Gil Sharon October 17, 2025. All rights reserved.