LEAPS-MPS: Prediction issues in progressively censored life-testing experiments: New ideas and applications

LEAPS-MPS：逐步审查的寿命测试实验中的预测问题：新想法和应用

• 批准号: 2316744
• 负责人: Ritwik Bhattacharya
• 金额: $ 24.38万
• 依托单位: University of Texas at El Paso
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316744&HistoricalAwards=false
• 关键词: LEAPS; MPS; Prediction; issues; progressively

A goal of manufacturers is to produce high quality products that satisfy customers’ expectations. Reliability is crucial and is formally defined as the probability that a product will perform a required function adequately for a given period of time when used under the stated operating conditions. Customers want to purchase products which are highly reliable and safe. They expect that the products will perform their intended function without failure for a long period of time. A cost-effective warranty design needs information on the product failure time distribution, which is commonly determined through life-testing experimental data. These types of data are often partially observed. Therefore, there is a need for prediction of the unobserved part of the data. One of the statistical tools for the prediction methodology is the linear estimate. However, the prediction methods are not fully developed in the literature for more complex life-testing experiments. The principal aim of this LEAPS-MPS project is to develop new theoretical results for the prediction in such complex cases and to show its applicability by analyzing failure data obtained through life-testing experiments. The second aim is to implement a sustainable education plan to increase the number of student participants from underrepresented groups, in particular, women and Hispanics in El Paso, Texas.In a reliability life-testing experiment, a fixed number of items are tested and the failure times of those items are recorded. The lifetimes of these items are assumed to be identically and independently distributed random variables. These life-testing experiments are commonly conducted in the framework of censoring mechanisms (either time-censored or failure censored), that is, a part of the testing units are only observed for data collection purposes. Under all censoring mechanisms, the information obtained through a life-testing experiment is often associated with two types of ordered data, namely, the usual ordered data and Progressively Type-II ordered data. Thus, inferences based on ordered statistics play an important role in analyzing life-testing experimental data and a common interest of study is to predict information on the unobserved part of the testing units. There are three basic approaches to address the predictive inferential issues: likelihood based, Bayesian and linear estimate. Among them, linear estimate methods for progressively ordered data have not been explored in the literature. This project will develop modelling and theory for linear estimaes. In particular, simultaneous point and interval predictions will be constructed based on best linear unbiased estimators and best linear invariant estimators. Finally, a framework for statistical process monitoring tools using the simultaneous prediction intervals will be established to bridge between predictive inference and statistical process control.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

制造商的目标是生产满足客户期望的高质量产品。可靠性至关重要，其正式定义为产品在规定的操作条件下使用时在给定时间内充分执行所需功能的概率。客户希望购买高度可靠和安全的产品。他们希望产品能够长期发挥其预期功能而不会出现故障。 具有成本效益的保修设计需要有关产品故障时间分布的信息，这通常是通过寿命测试实验数据确定的。这些类型的数据通常是部分观察到的。因此，需要对数据中未观测到的部分进行预测。预测方法的统计工具之一是线性估计。然而，文献中尚未完全开发出用于更复杂的寿命测试实验的预测方法。 LEAPS-MPS 项目的主要目的是开发新的理论结果来预测此类复杂情况，并通过分析寿命测试实验获得的故障数据来展示其适用性。第二个目标是实施可持续教育计划，以增加来自德克萨斯州埃尔帕索市代表性不足群体的学生参与者数量，特别是女性和西班牙裔学生。在可靠性寿命测试实验中，测试固定数量的项目并记录这些项目的故障时间。假设这些项目的寿命是相同且独立分布的随机变量。这些寿命测试实验通常在审查机制（时间审查或故障审查）的框架内进行，即仅出于数据收集目的而观察部分测试单元。在所有审查机制下，通过寿命测试实验获得的信息通常与两种类型的有序数据相关联，即通常的有序数据和渐进式II类有序数据。因此，基于有序统计的推论在分析寿命测试实验数据中发挥着重要作用，并且研究的共同兴趣是预测测试单元中未观察到的部分的信息。解决预测推理问题有三种基本方法：基于似然、贝叶斯和线性估计。其中，文献中尚未探索针对渐进排序数据的线性估计方法。该项目将开发线性估计的模型和理论。特别是，同时点和区间预测将基于最佳线性无偏估计器和最佳线性不变估计器构建。最后，将建立一个使用同步预测间隔的统计过程监测工具框架，以在预测推理和统计过程控制之间架起桥梁。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。