The Warranty Problem: Its Statistical and Game Theoretic Aspects

保修问题：统计和博弈论方面

• 批准号: 9122494
• 负责人: Nozer Singpurwalla
• 金额: $ 18.58万
• 依托单位: George Washington University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-02-15 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9122494&HistoricalAwards=false
• 关键词: Warranty; Problem; Its; Statistical; Game

Consumer products often carry warranties which are either one- dimensional (indexed by time in service or amount of usage) or two- dimensional (indexed by both of these variables). The focus of this project is on two-dimensional warranties, virtually an unaddressed topic. The warranty scenario raises at least two classes or research issues: the specification of an optimum price/warranty combination, and the forecast of a reserve fund to meet future claims. The former is multidisciplinary, involving aspects of economics, game theory, marketing, operations research, and probabilistic modeling. The latter involves the analysis of time series and point processes in two dimensions, for which the use of Bayesian methods is appropriate. This project addresses the following aspects of these issues. 1. Formalization of the first issue to facilitate mathematical development of the individual pieces. 2. Development of probabilistic models for the occurrence of events (failures) indexed by time and usage. 3. Renewal theory for points in a plane generated by the models developed. 4. Development of meaningful utility functions based on subjective probability considerations which describe the competitive behavior between manufacturers and consumers, and between manufacturers. 5. Development of a technology for undertaking times series analysis in two dimensions. 6. Statistical inference for point processes in a plane. Although all aspects of the project are motivated by the warranty problem, items 2, 3, 5, and 6 have scientific merit of their own and will provide new tools for the decision sciences.

消费品通常携带保证，这些保证要么是一维（由服务时间或使用量索引）或二维（由这两个变量索引）。 该项目的重点是二维保证，实际上是一个未解决的主题。 保修方案至少提出了两个课程或研究问题：最佳价格/保修组合的规范以及储备基金的预测以满足未来的索赔。 前者是多学科的，涉及经济学，游戏理论，市场营销，运营研究和概率建模的各个方面。 后者涉及对时间序列和点过程的分析，以二维的方式使用贝叶斯方法是适当的。 该项目解决了这些问题的以下方面。 1。第一个问题的形式化，以促进各个部分的数学发展。 2。开发概率模型，以通过时间和用法索引事件（故障）。 3。在开发模型产生的平面中的点的续订理论。 4。基于主观概率考虑的有意义的实用功能的开发，这些功能描述了制造商和消费者之间以及制造商之间的竞争行为。 5。开发用于二维的技术分析技术分析。 6。平面中点过程的统计推断。 尽管该项目的所有方面都是出于保修问题的动机，但项目2、3、5和6具有自己的科学优点，并将为决策科学提供新的工具。