Foreword Special Issue on New Frontiers in Reliability and Risk Analysis: A Tribute to Nozer Darabsha Singpurwalla

Nozer D. Singpurwalla (1939–2022)

We are honored to be guest editors for this special issue of Applied Stochastic Models in Business and Industry which is a tribute to Nozer D. Singpurwalla's scholarly work and achievements. The special issue contains seventeen papers. Four of these papers were based on presented talks at the 2-day conference entitled New Frontiers in Reliability and Risk Analysis, held on October 13–14, 2023 at The George Washington University in Washington, DC. The conference, which was dedicated to Nozer, brought together leading experts and young researchers in the fields in which Nozer was a major contributor, that is reliability, risk analysis, and Bayesian statistics. The special issue includes contributions on these topics from Nozer's friends and colleagues as well as from other researchers.

The first article by Soyer and Spizzichino presents an overview of Nozer's work in reliability and risk analysis as well as his interests in foundational aspects of statistics, probability, and decision analysis. The paper by Li, Tierney, Hellmayr, and West deals with sequential Bayesian analysis of multivariate time series models with a focus on causal inference which were both areas of interest to Nozer.

The next two papers are on topics that attracted Nozer's attention due to their foundational implications. Sellers and Booker describe their collaborations with Nozer regarding the connections of fuzzy sets with probability and reliability theory. The authors further discuss subsequent advances in this space and the perceptions across disciplines (particularly among statisticians and data scientists) over the last 20 years. The article by Polson and Sokolov presents an introduction to the notions of negative probability, which was of interest to Nozer during his final years, and the authors give a version of Bayes rule for such probabilities.

The article by Arkadani, Asadi, and Soofi builds on earlier work by Nozer on the comparison of informativeness of failures versus survivals in life testing. The authors consider a comparison of the information on moments and the model parameters and develop information measures. Finkelstein and Cha present an overview of mixture failure rates (that Nozer often referred to as “predictive failure rate”) to model heterogeneity in reliability and discuss recent developments on the topic including the stochastic intensity paradox.

The articles by Limnios, and Palayangoda and Balakrishnan deal with gamma processes for degradation modeling. Nozer used the gamma process in his study of Bayesian life testing, and failure processes in dynamic and multiple failure mode environments. Limnios considers a gamma process for degradation under a random environment modeled by a Markov process and presents results for averaging and normal deviation. Palayangoda and Balakrishnan consider a complete likelihood for the gamma processes and develop inference using the EM algorithm.

Lindqvist and Taraldsen present a data-generating function-based approach for simulating exact confidence intervals for reliability and discuss the connection with fiducial inference. Equivalence results are presented for confidence bands for fatigue-life and fatigue-strength models in the article by Liu, Hong, Escobar, and Meeker. The equivalence results are shown for quantile and cumulative distribution functions. Kim and Wilson consider reliability demonstration tests and present a Bayesian approach to identify a set of binomial test plans by taking into account posterior consumer and producer risks.

The next two articles deal with system reliability modeling. Lei and Kuo utilize order statistics associated with unit failure times to simplify and make more efficient system reliability calculations. Joint probability distributions for multi-state series and parallel systems with independent components are obtained in Kulkarni, Sabnis, and Ghosh and they are compared with the probability functions from the respective binary versions.

Motivated by queueing, Sethuraman considers systems that are subject to interruptions, such as power outages, that cause re-starting of the service provided by the system. Asymptotic results are obtained for a stochastic process, with independent increments, based on “time to complete a service.” Stochastic ordering properties and identifiability issues in latent activation failure models are discussed by Jiang and Basu who consider latent fixed order statistics models as well as hierarchical activation models. The next paper is by Cui, Li, Wan, and Zhang who use model averaging and a jackknife-based weight selection criterion to estimate the conditional average treatment effect in binary response models.

The final article by Misaii et al. presents a comparison of the predictive performance of statistical and AI/ML models in the analysis of degradation data and provides insights on different modeling approaches using a case study.

This special issue not only serves to honor Nozer's contributions and legacy—it further advances research in the fields of reliability, risk, and Bayesian analysis.

The authors declare no conflicts of interest.