Will A Few Failed Solder Joints Make Me RoHS Non Compliant?

I had someone in another forum tell me that my assembly would fail if I had a few solder joints over the 1000ppm RoHS threshold, with all other solder joints within spec. So, I followed up with this illustration. Please let me know what you think.

For my assembly, I am assuming my PCB and my parts are all compliant, so let's take those out of the equation. I am adding lead-free solder paste to 5,000 terminations to make 5000 solder joints. Let’s assume that all 5000 solder joints are of the same size and require the same mass of solder. The solder that I'm adding is considered a homogeneous material, right? A single homogeneous material?

Now, let's say that during touch-up, a technician finds insufficient solder on a single chip resistor, and inadvertently adds leaded solder to both terminations of that resistor, and doesn't touch the rest of the board. I have 4998 solder joints that are all well below spec, and two solder joints on the aforementioned resistor that has leaded solder. If I shoot all 5000 joints with an XRF gun and 4998 joints all read "None Detected" for lead, and the other two joints read 2,000ppm (or 2X over spec, per joint) for lead, I think my assembly should still pass.

The single homogeneous material that I added was solder. The overwhelming majority of it was lead free. Are you saying that my assembly would fail because two solder joints out of 5000 failed?

If so, this makes no sense to me. Let’s call the board I just described Board 1. And let’s say I have another board that we’ll call Board 2. Same board but processed differently. Let’s say the XRF gun detects 990ppm of lead in each of the 5000 solder joints. 990ppm of lead per solder joint is within spec, so the board is within spec, right?

You would have to agree with me that Board 2 (990ppm of lead per joint) has substantially more lead than Board 1 (0ppm of lead in 4998 joints, and 2000ppm of lead in each of 2 joints).

For the sake of argument, let’s say that each solder joint has a mass of 1,000,000 units of solder. Then 5000 solder joints would equal 5,000,000,000 units of solder, by weight. Board 2 has 990 units of lead per joint. Multiply that by 5000 joints and I have a grand total of 4,950,000 units of lead on my assembly. But, because I’m under 1000ppm per joint, this assembly is within spec, right?

Now, let’s look at my Board 1. The 4998 joints on this board are all reading zero for lead. But, two joints are reading 2000 units of lead, per joint (two times over spec). Add this up and I have a grand total of 4000 units of lead on my assembly. But this board fails?

By my calcuations, Board 2 has over 1200 times more lead, by mass, than Board 1. How would Board 1 fail and Board 2 pass?

As I understand the RoHS directive, there must be no more than 0.1% (<1000ppm) of lead, when calculated by weight of raw homogeneous materials. I believe that I make a good case that the combined mass of all of my solder joints (a single homogeneous material) is under 1000ppm of lead. Shouldn’t Board 1 be considered RoHS compliant?

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