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.

消费品通常带有保修，这是一个- 二维（按服务时间或使用量索引）或二维- 维度（由这两个变量索引）。 的焦点 这个项目是二维保证，几乎是一个 未解决的话题 保修方案提出了至少两个类或研究 问题：最佳价格/保修的规格 合并，并预测储备基金，以满足未来 索赔 前者是多学科的，涉及以下方面： 经济学、博弈论、市场营销、运筹学，以及 概率建模 后者涉及时间的分析 系列和点过程在两个维度，其中使用 贝叶斯方法是合适的。 该项目解决了 这些问题的后续。 1. 正式提出第一个问题， 数学发展的各个部分。 2. 发展发生的概率模型 按时间和使用情况索引的事件（故障）。 3. 生成平面上点的更新理论 模型开发。 4. 开发有意义的效用函数， 主观概率考虑，描述了 制造商和消费者之间的竞争行为，以及 制造商之间。 5. 一种时间序列提取技术的开发 从两个维度进行分析。 6. 平面中点过程的统计推断。 尽管项目的各个方面都是由 保修问题，第2、3、5和6项具有科学价值， 它将为决策科学提供新的工具。