Statistical Prediction Based on Censored Life Data

Abstract

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 simulationbased 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).

KEY WORDS:

• Bootstrap
• Maximum likelihood
• Reliability
• Simulation
• Warranty