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  1. Free, publicly-accessible full text available August 1, 2023
  2. 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.
  3. In recent years, accelerated destructive degradation testing (ADDT) has been applied to obtain the reliability information of an asset (component) at use conditions when the component is highly reliable. In ADDT, degradation data are measured under stress levels more severe than usual so that more component failures can be observed in a short period. In the literature, most application-specific ADDT models assume a parametric degradation process under different accelerating conditions. Models without strong parametric assumptions are desirable to describe the complex ADDT processes. This paper proposes a general ADDT model that consists of a nonparametric part to describe the degradation path and a parametric part to describe the accelerating-variable effect. The proposed model not only provides more model flexibility with few assumptions, but also retains the physical mechanisms of degradation. Due to the complexity of parameter estimation, an efficient method based on self-adaptive differential evolution is developed to estimate model parameters. A simulation study is implemented to verify the developed methods. Two real-world case studies are conducted, and the results show the superior performance of the developed model compared with the existing methods.