Love all the equations for the accuracy!
All inaccurate unfortunately.
If the decade box is made from 1 % resistors, then ignoring contact resistance, the accuracy of the decade box is 1%, the linearity is 2%.
The use of statistical tools are not really relevant, because 10 resistors made sequentially in a production run could all have similar errors and not random errors over the full +-1%, and more importantly, the resistance dialed up in the decade box will in many cases be a single resistor (1K, 10K, 100K, 1M, etc) and the accuracy of that single resistor is 1%, even if all the other resistors in the box had perfectly random error distributions. So you cannot quote less the 1% accuracy.
The accuracy cannot be over 1%. Say every resistor was exactly 1% high - the worst case situation. This will give the maximum possible error.
If you dialed up 99,999,999 ohms, the what would the error be?
1% high.
So the accuracy cannot be over 1% and it cannot be under 1%.