I'll try to give you my layman's answer. I am not an MSA / R & R expert, rather I am a metrology engineer with 25 years experience (so take my attempt from that perspective).
R& R is needed for any measuring instrument whose readings/accuracy/stability you depend upon for product specs. I don't know what aspect of the production you are monitoring, but my guess is (based on your wording) that it may be needed. If you are monitoring a quantitative specified parameter or using readings from this monitor to determine whether you are in or out of control on your process, I would think, yes.
If you could elaborate a little more, that may be helpful. I understand if you don't want to put actual process details on the web (you could put fictitious representations of the process).
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