I am using an accelerated failure time model with the Weibull distribution to predict failure times. My failure times range from 1 - 365, with many (80%) data points that are right censored (no observed failure). Among the observations that did have a failure, the median time to failure was 90 days. When you include the machines that make it all the way through the year, the distribution of failure time is U shaped - lots of mass between 1-90 days, and lots of mass for the machines that last the year.
According to survreg I can get the scale and shape parameters for the Weibull distribution from a survreg fit. The scale parameter is equal to
exp(intercept term) from survreg, which in my case is exp(9.3) ~ 11k. This seems excessively large, for example
hist(rweibull(100000, scale = 11000, shape = 0.5))
shows failure times that are extremely large - the median of that histogram is 5000 days, nearly 14 years! I understand that for most of the data we could not observe a failure, so the estimated time until failure would be somewhat large, but this is a bit unreasonable for prediction. Is there anything I can do with the model or the data, or is this phenomenon because 80% of the data is right censored and we don't know any failure times beyond a year?