I've looked at this a couple of times before, but especially in 2016, which by almost any reckoning was a very wet summer in Fairbanks. In that work I combined the monthly total precipitation with the number of days with measurable precipitation to come up with a simple cumulative index that looks like this:
Here I've used the same combination (total precipitation times days with measurable precipitation) but applied this over a running 15-day window, so that each day gets an index value. So, to illustrate, on June 30, the index is calculated as the total precipitation from June 16-30ᵗʰ times the number of days with measurable precipitation in the same 15 day period. For July 1ˢᵗ, the window is June 17 to July 01. Do that for the whole of the warm season. For the last few years, the daily plot of this index looks like this (through Aug 25, 2018):
Of course, we can derived multi-month summary statistics from the daily index. Here's a plot of the average daily May-August index value:
Perhaps a future improvement of this kind of index would be to incorporate some temperature measure, which might improve resolving between days with convective showers and those day-long steady rains.