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

University Of Texas At El Paso, El Paso TX

Investigators

Abstract

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.