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

制造商的一个目标是生产出满足客户期望的高质量产品。可靠性是至关重要的，其正式定义为产品在规定的操作条件下使用时，在给定的时间段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。他们期望产品能够在很长一段时间内无故障地发挥预期的功能。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，有必要对数据中未观察到的部分进行预测。预测方法的统计工具之一是线性估计。然而，对于更复杂的寿命测试实验，预测方法在文献中并没有得到充分的发展。LEAPS-MPS项目的主要目的是为这种复杂情况下的预测开发新的理论结果，并通过分析通过寿命试验获得的失效数据来展示其适用性。第二个目标是实施可持续教育计划，以增加来自代表人数不足的群体的学生人数，特别是德克萨斯州埃尔帕索的妇女和西班牙裔学生。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失败次数。假设这些项的寿命是相同且独立分布的随机变量。这些寿命试验通常是在审查机制(时间审查或失败审查)的框架下进行的，也就是说，部分试验单元仅为数据收集目的而观察。在所有的筛选机制下，通过寿命试验获得的信息通常与两类有序数据相关联，即通常的有序数据和渐进式II类有序数据。因此，基于有序统计的推理在寿命试验数据的分析中起着重要的作用，一个共同的研究兴趣是预测试验单元中未观察到的部分的信息。有三种基本的方法来解决预测推理问题：基于似然、贝叶斯和线性估计。其中，递进有序数据的线性估计方法尚未见文献报道。这个项目将发展线性估计的模型和理论。特别地，将基于最佳线性无偏估计和最佳线性不变估计来构建同时的点和区间预测。最后，将建立一个使用同时预测区间的统计过程监控工具的框架，以在预测推理和统计过程控制之间架起桥梁。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.