It sounds as if you have your AOI set up off-line, and you're "AOIing" a sampling of the PCBs produced. If that’s the case, then the responsibility of who drives the inspection really depends on how you configure it. If it's based on the number of PCBs, then I would say it's the SMT Operators responsibility to insure that the sample PCBs get pulled for inspection. If you base the sampling on time, then the AOI operator should be instructed to pull a PCB for AOI every "so many" minutes.
Do you have a number of lines that are all feeding sample PCBs to the same AOI? If so, then I would look at the duties assigned to both the SMT Operators and the AOI Inspector. Based on cycle times of their individual tasks, you should be able to determine who has enough time to perform this task. And then set the sampling criteria up on either a PCB count, or time period, based on these findings.
Just my 2 cents. Others might have differing opinions.
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