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Statistical prediction plays an important role in many decision processes, such as university budgeting (depending on the number of students who will enroll), capital budgeting (depending on the remaining lifetime of a fleet of systems), the needed amount of cash reserves for warranty expenses (depending on the number of warranty returns), and whether a product recall is needed (depending on the number of potentially life-threatening product failures). In statistical inference, likelihood ratios have a long history of use for decision making relating to model parameters (e.g., in evidence-based medicine and forensics). We propose a general prediction method, based on a likelihood ratio (LR) involving both the data and a future random variable. This general approach provides a way to identify prediction interval methods that have excellent statistical properties. For example, if a prediction method can be based on a pivotal quantity, our LR-based method will often identify it. For applications where a pivotal quantity does not exist, the LR-based method provides a procedure with good coverage properties for both continuous or discrete-data prediction applications.

 

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. 

Many industrial products consist of multiple components that are necessary for system operation. There is an abundance of literature on modeling the lifetime of such components through competing risks models. During the life‐cycle of a product, it is common for there to be incremental design changes to improve reliability, to reduce costs, or due to changes in availability of certain part numbers. These changes can affect product reliability but are often ignored in system lifetime modeling. By incorporating this information about changes in part numbers over time (information that is readily available in most production databases), better accuracy can be achieved in predicting time to failure, thus yielding more accurate field‐failure predictions. This paper presents methods for estimating parameters and predictions for this generational model and a comparison with existing methods through the use of simulation. Our results indicate that the generational model has important practical advantages and outperforms the existing methods in predicting field failures. Copyright © 2016 John Wiley & Sons, Ltd.