My only experience with dilution formulas are wrc 92 diagrams for the prediction of ferrite content in austenitic stainless steels. Whereby lines are drawn between the weld metal and filler metal chromium and nickel equivalencies. However this formula is not specifically for the dilution of chromium in a weld joint and assumes a static 50%
Obviously dilutions acts more upon the walls of the joint then the centre.  Dilution also varies by process where deep penetrating processes like SAW produce more dilution than something like GMAW-Short circuit. However at 4mm thickness I'm going to assume the process was GTAW.

I wish I could give you some definitive answer and I'll be paying attention to when the seasoned users leave some input.
My final guess would be chromium depletion due, excessive heat input, carbide preciptation or some other heat related mechanic. If the weld puddle temp is raised too high; low melt point alloys can boil, oxidize or mix with fluxing agents to form slag.

In addition was 304 and 316 material used? or 304L and 316L to help reduce the tendency of carbide precipitation?

I wouldn't concern myself with whether or not the Cr content of your fdeposit is less than the base metal unless you have specific customer requirement to do so. 316 is used on 304 by the ton. You will see a greater difference generally in corrosion between base metals and weld deposits than whatever little Cr difference you may show.
The chemistries of base metals and filler metals of stainless steels such as 304, 308, 316 all vary, but overlap, and it is possible to vary the deposit becasue of it. But keep in mind that the chemistries are varied based upon manufacturing and welding needs. For example, filler metals are balanced to provide some ferrite at welding cooling rates. Base metals have no concern for ferrite for the most part, they balance their chemistries for the exigencies of manufacturing such as minimizing cracks in hot forming.
Quite frankly I would re-evaluate the PMI. Where'd your Mo go? Even at very high dilution you will still have enough Mo to register and your machine still says 308?
The other thing is, what if your service is a reducing fluid as opposed to oxidizing. The higher Mo and Ni of 316 will help you.
Yes, there are formulas for dilution but what the most convenient way to do it non destructively is to gage your chemistry from a PMI to establish weld parameters to control it.
Doing it backwards you can say the 50% dilution will give me such and such chemisty. But you are still left with verifying your chemistry with PMI.

Here are the spec requirements for Cr:

304, 304L base metal - 19.0-20.0%
316, 316L base metal - 16.0-18.0%
ER308, ER308L - 19.5-22.0%
ER316, ER316L - 18.0-20.0%

So, for a 316 weld on 304 base metal it would be possible that Cr would be lower than the base metal.  I don't see it as a concern unless your specs require a minimum Cr content.  We would typically consider 316 base metal to provide corrosion resistance equal to 304 for our applications in cooling water systems.

I'm surprised your PMI did not call it 316 since 308 does not have Mo.