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The accelerated degradation test (ADT) is an efficient tool for assessing the lifetime information of highly reliable products. However, conducting an ADT is very expensive. Therefore, how to conduct a cost‐constrained ADT plan is a great challenging issue for reliability analysts. By taking the experimental cost into consideration, this paper proposes a semi‐analytical procedure to determine the total sample size, testing stress levels, the measurement frequencies, and the number of measurements (within a degradation path) globally under a class of exponential dispersion degradation models. The proposed method is also extended to determine the global planning of a three‐level compromise plan. The advantage of the proposed method not only provides better design insights for conducting an ADT plan, but also provides an efficient algorithm to obtain a cost‐constrained ADT plan, compared with conventional optimal plans by grid search algorithms.

 

Multi-type recurrent events are often encountered in medical applications when two or more different event types could repeatedly occur over an observation period. For example, patients may experience recurrences of multi-type nonmelanoma skin cancers in a clinical trial for skin cancer prevention. The aims in those applications are to characterize features of the marginal processes, evaluate covariate effects, and quantify both the within-subject recurrence dependence and the dependence among different event types. We use copula-frailty models to analyze correlated recurrent events of different types. Parameter estimation and inference are carried out by using a Monte Carlo expectation-maximization (MCEM) algorithm, which can handle a relatively large (i.e. three or more) number of event types. Performances of the proposed methods are evaluated via extensive simulation studies. The developed methods are used to model the recurrences of skin cancer with different types. 

Geyser eruption is one of the most popular signature attractions at the Yellowstone National Park. The interdependence of geyser eruptions and impacts of covariates are of interest to researchers in geyser studies. In this paper, we propose a parametric covariate-adjusted recurrent event model for estimating the eruption gap time. We describe a general bivariate recurrent event process, where a bivariate lognormal distribution and a Gumbel copula with different marginal distributions are used to model an interdependent dual-type event system. The maximum likelihood approach is used to estimate model parameters. The proposed method is applied to analyzing the Yellowstone geyser eruption data for a bivariate geyser system and offers a deeper understanding of the event occurrence mechanism of individual events as well as the system as a whole. A comprehensive simulation study is conducted to evaluate the performance of the proposed method. 

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 cannot 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 article 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. 

This paper investigates degradation modeling under dynamic conditions and its applications. Both univariate and multiple competing degradation processes are considered with individual degradation paths being described by Wiener processes. Parametric and non-parametric approaches are used to capture the effect of environmental conditions on process parameters. For competing degradation processes, we obtain the probability that a particular process reaches a pre-defined threshold, before other processes, over future time intervals. In particular, we consider the potential statistical dependence among the latent remaining lifetimes of multiple degradation processes due to unobserved future environmental factors. Two case studies, aircraft piston pump wear and US highway performance deterioration, are presented. Comprehensive comparison studies are also performed to generate some critical insights on the proposed approach. Data have been made available on GitHub.