Yes, I have an idea. please read Help > JMP Documentation Library > Reliability and Survival Methods > Chapter 3: Life Distribution. You will find lots of ideas there.
Enter your data like this:
I do not think that the interval censoring is appropriate in this case. You simply observed the status every 30 days. I assume that each 30 day period is another sample. That is, you have a total sample size of 108. Enter columns in the analysis roles for launching Life Distribution
Click OK and then you can either use the non-parametric estimates or fit a chosen model.
You enter Start and End, in that order, in the Y role together in a case with interval censoring.