Statistics and Data Science seminar: "Within-sample prediction of a number of future failures"

Abstract: The talk overviews a prediction problem encountered in reliability engineering, where a need arises to predict the number of future failures among a cohort of units.  Examples include the prediction of warranty returns or the prediction of the number of product failures that could cause serious harm.  The data consist of a collection of units observed over time where, at some freeze point, inspection ends, leaving some units with observed failure times while other units have not yet failed.  In other words, data are right-censored, where some units have failed by the freeze point while other units continue to "survive."  The problem becomes predicting how many of the "surviving" units will have failures in a next future interval of time, as quantified by a prediction bound or interval.  Because all units belong to the same data set, either by providing direct information (i.e., observed failure times) or by becoming the subject of prediction (i.e., censored times), such predictions are called within-sample predictions and differ from other prediction problems considered in most literature.  A standard plug-in technique for prediction intervals turns out to be invalid for this problem (i.e., for even large amounts of data, prediction intervals fail to have correct coverage probability).  However, several bootstrap-based methods can provide valid prediction intervals. To this end, a commonly used prediction calibration method is shown to be asymptotically.

Host: Soumen Lahiri