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

制造商的目标是生产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。他们希望产品能够在很长一段时间内执行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。这些类型的数据往往是部分观察。因此，需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，在文献中的预测方法还没有完全发展到更复杂的寿命测试实验。这个LEAPS-MPS项目的主要目的是开发新的理论结果，在这种复杂的情况下预测，并通过分析寿命测试实验获得的故障数据，以显示其适用性。第二个目标是实施一项可持续的教育计划，以增加来自代表性不足的群体，特别是德克萨斯州埃尔帕索的妇女和西班牙裔学生的参与人数，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。这些项目的寿命被假定为相同的和独立分布的随机变量。这些寿命试验通常是在截尾机制（时间截尾或故障截尾）的框架下进行的，即部分试验单元仅用于数据收集目的。在所有的删失机制下，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II型有序数据。因此，基于有序统计量的推断在分析寿命测试实验数据中起着重要作用，并且研究的共同兴趣是预测测试单元的未观察部分的信息。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，线性估计方法的渐进有序数据尚未在文献中探讨。这个项目将发展线性估计的模型和理论。特别是，将根据最佳线性无偏估计量和最佳线性不变估计量构建同时点和区间预测。最后，将建立一个使用同步预测区间的统计过程监控工具框架，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知识价值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.