Degradation data provide a useful resource for obtaining reliability information for some highly reliable products and systems. In addition to product/system degradation measurements, it is common nowadays to dynamically record product/system usage as well as other life-affecting environmental variables, such as load, amount of use, temperature, and humidity. We refer to these variables as dynamic covariate information. In this article, we introduce a class of models for analyzing degradation data with dynamic covariate information. We use a general path model with individual random effects to describe degradation paths and a vector time series model to describe the covariate process. Shape-restricted splines are used to estimate the effects of dynamic covariates on the degradation process. The unknown parameters in the degradation data model and the covariate process model are estimated by using maximum likelihood. We also describe algorithms for computing an estimate of the lifetime distribution induced by the proposed degradation path model. The proposed methods are illustrated with an application for predicting the life of an organic coating in a complicated dynamic environment (i.e., changing UV spectrum and intensity, temperature, and humidity). This article has supplementary material online.

Big data features not only large volumes of data but also data with complicated structures. Complexity imposes unique challenges on big data analytics. Meeker and Hong (2014; Quality Engineering, pp. 102–16) provided an extensive discussion of the opportunities and challenges on big data and reliability; they also described engineering systems which generate big data that can be used in reliability analysis. Meeker and Hong (2014) focused on large-scale system operating and environment data (i.e., high-frequency multivariate time series data) and provided examples on how to link such data as covariates to traditional reliability responses such as time to failure, time to recurrence of events, and degradation measurements. This article intends to extend that discussion by focusing on how to use data with complicated structures to do reliability analysis. Such data types include high-dimensional sensor data, functional curve data, and image streams. We first provide a review of recent developments in those directions, then we provide a discussion on how analytical methods can be developed to tackle the challenging aspects that arise from the complex features of big data in reliability applications. The use of modern statistical methods such as variable selection, functional data analysis, scalar-on-image regression, spatio-temporal data models, and machine-learning techniques will also be discussed.

Artificial intelligence (AI) systems are increasingly popular in many applications. Nevertheless, AI technologies are still developing, and many issues need to be addressed. Among those, the reliability of AI systems needs to be demonstrated so that AI systems can be used with confidence by the general public. In this paper, we provide statistical perspectives on the reliability of AI systems, focusing on the time dimension. That is, the system can perform its designed functionality for the intended period of time. We introduce a so-called “SMART” statistical framework for AI reliability research, which includes five components: Structure of the system, Metrics of reliability, Analysis of failure causes, Reliability assessment, and Test planning. We review traditional methods in reliability data analysis and software reliability, and discuss how those existing methods can be transformed for reliability modeling and assessment of AI systems. Different from traditional reliability studies, the focus of AI reliability is on the software system to include the training data. Thus, we describe recent developments in modeling and analysis of AI reliability for software systems. The paper outlines statistical research challenges in this area, including out-of-distribution detection, the effect of the training set, adversarial attacks, model accuracy, and uncertainty quantification. We discuss how those topics can be related to AI reliability, with illustrative examples. The final element of SMART (test planning), is critical for the demonstration of AI reliability. Therefore we discuss data collection and testing planning, highlighting methods for improving system design in order to achieve higher AI reliability. The paper closes with some concluding remarks.

For several decades, the resampling based bootstrap has been widely used for computing confidence intervals (CIs) for applications where no exact method is available. However, there are many applications where the resampling bootstrap method can not be used. These include situations where the data are heavily censored due to the success response being a rare event, situations where there is insufficient mixing of successes and failures across the explanatory variable(s), and designed experiments where the number of parameters is close to the number of observations. These three situations all have in common that there may be a substantial proportion of the resamples where it is not possible to estimate all of the parameters in the model. This paper reviews the fractional-random-weight bootstrap method and demonstrates how it can be used to avoid these problems and construct CIs in a way that is accessible to statistical practitioners. The fractional-random-weight bootstrap method is easy to use and has advantages over the resampling method in many challenging applications.

Reliability analysis of multicomponent repairable systems with dependent component failures is challenging for two reasons. First, the failure mechanism of one component may depend on other components when considering component failure dependence. Second, imperfect repair actions can have accumulated effects on the repaired components and these accumulated effects are difficult to measure. In this paper, we propose a parametric statistical model to capture the failure dependence information with general component repair actions. We apply the maximum likelihood method to estimate the model parameters by utilizing the historical failure data. Statistical hypothesis tests are developed to determine the dependence structure of the component failures based on the proposed reliability model. The proposed methodology is demonstrated by a simulation study and case studies of a car body assembly process and a forklift vehicle system.