Abstract

This article describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of future product failures that could cause serious threats to property or life. Important decisions such as whether a product recall should be mandated are often based on such predictions. Data, generally right-censored (and sometimes left truncated and right-censored), are used to estimate the parameters of a time-to-event distribution. This distribution can then be used to predict the number of events over future periods of time. Such predictions are sometimes called within-sample predictions and differ from other prediction problems considered in most of the prediction literature. This article shows that the plug-in (also known as estimative or naive) prediction method is not asymptotically correct (i.e., for large amounts of data, the coverage probability always fails to converge to the nominal confidence level). However, a commonly used prediction calibration method is shown to be asymptotically correct for within-sample predictions, and two alternative predictive-distribution-based methods that perform better than the calibration method are presented and justified. Supplementary materials for this article are available online.

摘要

本文描述了从与正在进行的事件发生时间过程相关的一组单元中预测未来事件数量的方法。示例包括保修退货的预测以及可能对财产或生命造成严重威胁的未来产品故障数量的预测。诸如是否应强制召回产品等重要决策通常基于此类预测。数据，通常是右删失（有时是左截断和右删失），用于估计事件时间分布的参数。然后可以使用此分布来预测未来一段时间内的事件数量。这种预测有时称为样本内预测，与大多数预测文献中考虑的其他预测问题不同。本文表明，插件（也称为估计或朴素）预测方法不是渐近正确的（即，对于大量数据，覆盖概率总是无法收敛到标称置信水平）。然而，一种常用的预测校准方法被证明对样本内预测是渐近正确的，并且提出并证明了两种替代的基于预测分布的方法，它们的性能优于校准方法。本文的补充材料可在线获取。一种常用的预测校准方法被证明对样本内预测是渐近正确的，并且提出并证明了两种替代的基于预测分布的方法，它们的性能优于校准方法。本文的补充材料可在线获取。一种常用的预测校准方法被证明对样本内预测是渐近正确的，并且提出并证明了两种替代的基于预测分布的方法，它们的性能优于校准方法。本文的补充材料可在线获取。