Narayanaswamy Balakrishnan is a distinguished university professor in the Department of Mathematics and Statistics at McMaster University Hamilton, Ontario, Canada. He is an internationally recognized expert on statistical distribution theory, and a book-powerhouse with over 24 authored books, four authored handbooks, and 30 edited books under his name. He is currently the Editor-in-Chief of Communications in Statistics published by Taylor & Francis. He was also the Editor-in-Chief for the revised version of Encyclopedia of Statistical Sciences published by John Wiley & Sons. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. In 2016, he was awarded an Honorary Doctorate from The National and Kapodistrian University of Athens, Athens, Greece. In 2021, he was elected as a Fellow of the Royal Society of Canada. Elena Castilla is an assistant professor at the Department of Applied Mathematics at Rey Juan Carlos University, in Spain. She obtained her Ph.D, M.Sc. and Bachelor Degrees in Mathematics and Statistics at Universidad Complutense de Madrid, and is an awardee of the Ramiro Melendreras Award (SEIO, 2021) and Vicent Caselles Award (RSME & Fundación BBVA 2022). Dr. Castilla’s research interests include information theory, categorical data analysis, composite likelihood, logistic regression models, reliability analysis and robust statistics.

• 1. Introduction2. Inference for One-Shot Devices with a Single Failure mode3. Divergence Measures and their Application to One-Shot Devices with a Single Failure mode4. Robust Inference under the Exponential Distribution5. Robust Inference under the Gamma Distribution6. Robust Inference under the Weibull Distribution7. Robust Inference under the Lognormal distribution8. Robust Inference under the Proportional Hazards Model9. Inference for One-Shot Devices with Multiple Failure Modes10. Robust Inference under the Exponential Distribution and Competing Risks11. Robust Inference under the Weibull Distribution and Competing Risks12. Robust Inference under Cyclic Accelerated Life Tests13. Summary and Future DirectionsAppendix A Derivation of the Influence Function of the Weighted Minimum DPD Estimators