A Random Coefficient Degradation Model With Ramdom Sample Size

In testing product reliability, there is often a critical cutoff level that determines whether a specimen is classified as failed. One consequence is that the number of degradation data collected varies from specimen to specimen. The information of random sample size should be included in the model, and our study shows that it can be influential in estimating model parameters. Two-stage least squares (LS) and maximum modified likelihood (MML) estimation, which both assume fixed sample sizes, are commonly used for estimating parameters in the repeated measurements models typically applied to degradation data. However, the LS estimate is not consistent in the case of random sample sizes. This article derives the likelihood for the random sample size model and suggests using maximum likelihood (ML) for parameter estimation. Our simulation studies show that ML estimates have smaller biases and variances compared to the LS and MML estimates. All estimation methods can be greatly improved if the number of specimens increases from 5 to 10. A data set from a semiconductor application is used to illustrate our methods.     

Mentoring to Achieve Diversity in Graduate Programs

The discipline of statistics has a celebrated, diverse, and colorful past. With a definite international flavor, we continue to make great strides in keeping our discipline relevant and accessible for addressing significant societal concerns. Unfortunately, we lag behind many other disciplines when it comes to fully tapping into the potential of all demographic groups within the United States. Mentoring provides one of many opportunities to change this narrative. This article looks at hard numbers related to diversity, points to some existing successful mentoring programs, and is a reflection of lessons learned through personal experiences.