The research team of Waseda University Grants for “Tokutei Kadai” [Research Base Creation] (2025C-768) consisted of the following members:

Principal Investigator: Yu Hayakawa, Waseda University
Research Collaborator: Professor Richard Arnold, Victoria University of Wellington, New Zealand
Research Collaborator: Former Associate Professor Stefanka Chukova, Victoria University of Wellington, New Zealand
Research Collaborator: Dr Sarah Marshall, University of Auckland, New Zealand

In a range of engineering systems, the occurrence of a failure may increase the likelihood of subsequent failures, resulting in sequences of events that exhibit clustering behaviour. Such phenomena are commonly modelled using Hawkes processes, which are well-suited for capturing self-exciting dynamics in event occurrences. In many practical applications, additional information associated with each event—such as failure severity or repair time—can be incorporated as marks, thereby enriching the modelling framework. By embedding these marks into the conditional intensity function, one can obtain more informative and flexible models for inference. The primary objective of this research project was to develop new specifications of conditional intensity functions for marked Hawkes processes, with a focus on enhancing their applicability as reliability models. In particular, we adopted a Bayesian non-parametric approach in order to allow greater flexibility in capturing complex and potentially unknown structural features in failure processes. As part of this effort, we examined standard inference methodologies for marked Hawkes processes in the context of failure time data.

A significant outcome of the project was a joint research paper authored by Arnold, Chukova, and Hayakawa, which explored two applications of Bayesian non-parametric modelling in reliability theory. The first application addresses a software reliability problem, where reviewers are grouped according to similar levels of skill, and faults are simultaneously classified based on their detectability. This joint clustering framework enables the estimation of the number of undetected faults in the system, providing valuable insights into software quality assessment. In the second application, we considered the non-parametric estimation of bathtub-shaped hazard rate functions. In this case, we used the gamma process prior as the basis for several specifications of such hazard rate functions. This work was presented by Professor Arnold as a keynote lecture at the 44th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, held on 14–19 December 2025 at the University of Auckland, New Zealand.

In addition, the research team investigated a novel method for generating synthetic warranty data based on fully observed product trajectories. In practice, warranty data are often subject to censoring and limited availability, which can hinder robust statistical analysis. The proposed approach aims to overcome these limitations by constructing realistic synthetic datasets that preserve essential characteristics of real-world warranty data. The results of this study have been compiled into a paper submitted to the 12th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2026). The paper is currently under review and, if accepted, will be presented by Dr Sarah Marshall in July 2026 in Singapore.