Statistical prediction based on censored life data

This article describes methods for using censored life data to construct prediction bounds or intervals for future outcomes. Both new-sample prediction (e.g,, using data from a previous sample to make predictions on the future failure time of a new unit) and within-sample prediction problems (e.g., predicting the number of future failures from a sample, based on early data from that sample) are considered. The general method, based on an assumed parametric distribution, uses simulation-based calibration. This method provides exactly the nominal coverage probability when an exact pivotal-based method exists and a highly accurate large-sample approximation, otherwise. To illustrate new-sample prediction, we show how to construct a prediction interval for a single future observation from a previously sampled population/process (motivated by a customer's request for an interval to contain the life of a purchased product). To illustrate within-sample prediction, we show how to compute a prediction interval for the number of future failures in a specified period beyond the observation period (motivated by a warranty prediction problem). Then we present an example that requires more general methods to deal with complicated censoring arising because units enter service at different points in time (staggered entry).