HASL plating, by its very nature, is inconsistent in terms of thickness and consistency. The plating varies from spot to spot on the pad, as well as pad to pad. This will wreak havoc on your screen printing process and your placement. From talking to board houses, and monitoring their product quality, I have found that the HASL process has a very low Cp and Cpk.
If you are having problems with the plating, I would recommend going to an OSP or immersion gold plating on your boards. These finishes provide a much flatter surface on the pads, reducing many of the issues you are dealing with. In addition, anytime I have ordered OSP, I have gotten a lower price than HASL boards.
Good luck, Brian W.
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