I'm not familiar with the options available in JMP12, but you could probably use Quantile Regression to deal with censored values in the Generalized Regression options.
The idea is either to use a regression model that doesn't estimate the conditional mean of the response variable across factors values, as it will be biased towards censored values (unlike estimating conditional median in Quantile Regression), and/or lower the importance of the censored data points on the model fit (to avoid the leverage effects of these censored values points).
Hope this answer will help you,
Victor GUILLER
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)