Weibull Analysis II: The Curse of the Early First Failure


In continuing our discussion on Weibull Analysis, let’s assume we assembled some SMT and through-hole PCBs with lead-free solder paste. On this board are also some bottom-side terminated (BTC) components (often called QFNs), that are also assembled with solder preforms.  A stress test is performed to test the BTCs. In such a test, the first fail in Weibull analysis is the most important data point. No matter the results of remainder of the data, these later fails cannot undo the effect of a very early first fail.

To understand this concept, let’s look at the Weibull chart below. In many high reliability applications, there may be a requirement that some small percentage of the components under test have at least some minimum reliability.


Figure 1.  Weibull Analysis with an Early Fail.

As an example, let’s say that 1% of the components cannot have less than 500 cycles of life.  By looking at Figure 1, we see that 1% have less than 150 cycles of life (see arrow.)  This one early outlier dramatically affects the Weibull Analysis.

However, if that outlier was removed, as seen in Figure 2, the data suggest that 1% of the components will have a life of 900 cycles. We can see the dramatic effect the first fail has on this result. Note that the first fail does not affect the “scale” or characteristic life much (2647 vs 2682). Hence, the characteristic life, is not a robust metric to use in a high reliability environment. However, the shape or slope is dramatically affected by the early fail as it changes from 2.22 to 4.23 when the early fail is “censored.”

Figure 2. Weibull analysis with the early fail removed (censored).

Why might an outlier like this exist? Almost certainly there is something unusual about the early fail. It might be something like an oxidized pad preventing good wetting of the solder. Perhaps something like this failure mode might be discovered in root cause failure analysis. However, I am typically opposed to censoring data, even with supportive failure analysis. I think the test should be done over. It is often too easy to talk yourself into accepting inconclusive failure analysis.

What is your opinion?


Dr. Ron

Interpreting Weibull Plots: I


A while ago I discussed the Weibull Distribution and its importance in electronics reliability analysis. This distribution has been used to evaluate the life of solder joints whether formed in SMT, wave, or even using solder preforms. In the next few posts, I would like to discuss how to interpret Weibull plots.

Let’s consider two Weibull plots from thermal cycle testing of lead-free solder joints as seen in Figure 1.

Figure 1. A Weibull plot of thermal cycle data for Alloy 2 and Alloy 4.

Both alloys have almost exactly the same scale, or characteristic life. You will remember that characteristic life is the number of cycles at which 63% of the test subjects fail. For Alloy 2 it is 2,593 cycles and for Alloy 4 it is slightly better at 2,629 cycles. However, these two alloys performed dramatically differently. The most striking difference is in their “spread.” We see this much greater spread for Alloy 4, when we plot a fit to the data as a normal distribution, as in Figure 2 below.

Figure 2. The best fit normal distribution plot for Alloy 2 and Alloy 4.

In the Weibull plot, the data for Alloy 2 has a very steep slope or shape factor, this indicates a tight distribution. A tight distribution is desirable as it facilitates more accurate prediction of thermal cycle life. Alloy 2 is clearly superior. So, in a Weibull distribution, not only is a large scale factor or characteristic life desired, but so is a steep slope or larger shape factor.

Next time we will talk about outliers.

Dr. Ron