Machine learning/Statistics in Business
Lyu, Q., & Wu, S. (2025). An explainable machine learning framework for recurrent event data analysis. European Journal of Operational Research. 328(2): Pages 591-606 https://doi.org/10.1016/j.ejor.2025.09.005
This paper introduces a novel explainable temporal point process (TPP) model, Stratified Hawkes Point Process (SHPP), for modelling recurrent event data (RED). Unlike existing approaches that treat temporal influence as a black box or rely on post-hoc explanations, SHPP structurally decomposes event intensities into semantically meaningful components for describing self-Markovian, and joint influences. This decomposition enables direct quantification of how past events contribute to future event risks, termed as influence values. We further provide a sufficient condition for mean-square stability based on kernel decay, ensuring long-term boundedness of intensities and realistic behavioural predictions. Experiments and an e-commerce case study demonstrate SHPP’s ability to deliver accurate, interpretable, and stable modelling of complex event-driven systems.
Ren, J., & Wu, S. (2025). Boosting global time series forecasting models: a two-stage modelling framework. Conference: European Conference on Artificial Intelligence, at: Bologna, Italy, Volume: 413, Pages 2969-2976. https://doi.org/10.3233/FAIA251157
A time series forecasting model—which is typically built on a single time series—is known as a local time series model (tsLM). In contrast, a forecasting model trained on multiple time series is referred to as a global time series model (tsGM). tsGMs can enhance forecasting accuracy and improve generalisation by learning cross-series information. As such, developing tsGMs has become a prominent research focus within the time series forecasting community. However, the benefits of tsGMs may not always be realised if the given set of time series is heterogeneous. While increasing model complexity can help tsGMs adapt to such a set of data, it can also increase the risk of overfitting and forecasting error. Additionally, the definition of homogeneity remains ambiguous in the literature. To address these challenges, this paper explores how to define data heterogeneity and proposes a two-stage modelling framework: At stage one, a tsGM is learnt to identify homogeneous patterns; and at stage two, tsLMs (eg, ARIMA) or sub-tsGMs tailored to different groups are learnt to capture the heterogeneity. Numerical experiments on four open datasets demonstrate that the proposed approach significantly outperforms six state-of-the-art models. These results highlight its effectiveness in unlocking the full potential of global forecasting models for heterogeneous datasets.
Wu, S. (2023) A copula-based approach to modelling the failure process of items under two-dimensional warranty and applications, European Journal of Operational Research DOI: https://doi.org/10.1016/j.ejor.2023.10.043
Hundreds of scholarly papers on optimisation of preventive maintenance policies for items under warranty have been published in the reliability related literature. They typically have two limitations: they make a simplified assumption on the relationship between age and usage for items under two-dimensional warranty and they assume that it is cost-effective to conduct preventive maintenance (PM) on each sold product item. These assumptions may not reflect the reality. This paper therefore proposes a copula-based approach to modelling the relationship between age and usage of items under two-dimensional (2D) warranty.
Wu, S. (2022) The double ratio geometric process for the analysis of recurrent events. Naval Research Logistics (NRL), 69(3), 484-495.
This paper extends the GP to a new stochastic model. Probabilistic properties of the proposed model are investigated. The maximum likelihood method is used to estimate the parameters in the model. Case studies are performed to illustrate the parameter estimation process and obtain favourable performance.
Wang, X., Jiang, B., Wu, S., Lu, N., & Ding, S. X. (2021). Multivariate relevance vector regression based degradation modeling and remaining useful life prediction. IEEE Transactions on Industrial Electronics, 69(9), 9514-9523.
This article proposes a degradation path-based RUL prediction framework using a dynamic multivariate relevance vector regression model. Specifically, a multistep regression model is established for describing the degradation dynamics and extending the classical RVR into a multivariate one with consideration of the multivariate environment. The article introduces a matrix Gaussian distribution-based RVR approach and then estimates the hyperparameters with Nesterov’s accelerated gradient method to avoid the exhausting re-estimation phenomenon in seeking analytical solutions. It further forecasts the degradation path for monitoring the degradation status.
Wu, S. (2019) A failure process model with the exponential smoothing of intensity functions. European Journal of Operational Research 275 (2), 502-513
Modelling times between the occurrences of events is of interest to physical asset managers and insurance firms. In the system reliability related literature, many models, or failure process models, have been proposed, but they are rarely compared with other models, in terms of model performance, on more than ten real datasets, which poses uncertainty. This paper proposes two mathematical models that describe times between failures of a multicomponent system. The models are based on the simple exponential average of the failure intensities. The Bayesian information criterion, a widely used measure of model performance, of the proposed model is compared with those of nine other models based on 9 artificially generated datasets and 15 real-world datasets, respectively. The results show that the proposed models outperform the nine other models.
Wu, S. (2018) Doubly geometric processes and applications. Journal of the Operational Research Society 69 (1), 66-77
The geometric process is an extension of the renewal process and has been applied in maintenance policy scheduling, modelling of the outbreak of an epidemic disease, and modelling of electricity price, among others. The geometric process has several limitations in the sense that it can only model a monotonously, stochastically trend and its coefficients of variation over different gap times remain unchanged. This paper extends the geometric process and overcomes those limitations. Some probabilistic properties of the proposed model are investigated.
Wu, S. (2014) Construction of asymmetric copulas and its application in two-dimensional reliability modelling, European Journal of Operational Research, 238 (2), pp 476-485.
Precisely forecasting warranty claims is important for warrantors. Some products are protected by 2-dimensional warranty: one dimension is age and the other is accumulated usage. For instance, the warranty of a car may expire if it is older than 5 years or has been driven for more than 50,000 miles, which ever comes first. However, for a set of cars, one can observe this phenomenon: normally younger cars have smaller mileage, while older cars do not implies larger mileage. This phenomenon can be translated into a mathematical language that the upper-lower tail dependence is smaller than or equals the lower-upper tail dependence of the joint probability distribution of the age and accumulated usage. This paper proposes a method to model such a phenomenon and validates the proposed method on a warranty claim dataset collected from a car manufacturer.
Wu, S., & Akbarov, A. (2011). Support vector regression for warranty claim forecasting. European Journal of Operational Research, 213(1), 196-204.
This paper proposes two different SVR (support vector regression) approaches to forecasting warranty claims.
Flach, P. & Wu., S. (2005) Repairing Concavities in ROC Curves, the International Joint Conference on Artificial Intelligence, 702--707
The receiver operating characteristic (ROC) curve is a graphical plot that illustrates the performance of a classification model in machine learning. The AUC (area under the ROC curve) is a useful measure of the performance. A ROC curve may have a concavity. By properly flopping such a concavity on the ROC curve can increase the AUC and result in a better performed classification model. This paper proposes this method and validates the result on 24 datasets.
Applied Stochastic Processes
Luo, M. & Wu, S. (2018) A value-at-risk approach to optimisation of warranty policy, European Journal of Operational Research 267 (2), 513-522
Building a mathematical model on warranty claims can be useful in forecasting future claims, making warranty policies, which defines the period and price of warranty. Conventionally, researchers assumes that warranty claims from products of a manufacturer are statistically independent, based on which they optimise warranty policies. Nevertheless, a manufacturer normally produces more than one product and some common subsystems may be installed in different products. As a result, warranty claims are statistically dependent. This paper optimises warranty policies of a collection of products with the value-at-risk method, a well known and established risk management method in modern portfolio theory in finance.
Luo, M. & Wu, S. (2018) A mean-variance optimisation approach to collectively pricing warranty policies, International Journal of Production Economics,196, 101-112
This paper has a similar background but optimises warranty policies with the mean-variance method, which is another well known and established risk management method in modern portfolio theory in finance.
Wu, S. (2011) Warranty claim analysis considering human factors, Reliability Engineering and System Safety, 96 (1), pp. 131-138.
The behaviours of product users play an important role in warranty management. For instance, they may not be bothered to claim warranty on failed product items or they may claim warranty on product items that are not failed or their failures are not due to the manufacturer. This paper proposes methods to estimate warranty claims under such scenarios.
Wu, S. (2005) Joint importance of multistate systems, Computers and Industrial Engineering, 49 (1), pp. 63-75.
Component importance is useful in ranking the importance of components in a physical system. Joint importance measures the interaction of two components in a system interact in contributing to system reliability. This paper proposes joint importance measures of states in a multistate system.
Wu, S. (1994) Reliability analysis of a repairable system without being repaired as good as new, Microelectronics Reliability, 34 (2), pp. 357-360.
This paper analyses the reliability of a system using the geometric process. It is the first paper that is published in an international journal and that applies the geometric process to analyse system reliability.
Energy consumption analysis
Zeng, S., Li, T., Wu, S., Gao, W., Gen Li, (2024) Does green technology progress have a significant impact on carbon dioxide emissions? Energy Economics, 133, 107524
Structural, economic, and technological factors shape carbon dioxide (CO2) emissions under the environmental Kuznets curve hypothesis. Since curbing economic growth and structural adjustments are limited in reducing emissions, green technology progress (GTP) emerges as a key pathway for carbon reduction. This study addresses gaps in existing research by applying a spatial Durbin model to panel data from 30 Chinese provinces between 2008 and 2020. Results reveal that GTP produces a clear “technological dividend,” significantly lowering local CO2 emissions, though its spatial spillover effect remains weak. Three transmission channels—industrial structure, energy structure, and energy efficiency—mediate the influence of GTP on emissions. Regional disparities are evident, with eastern provinces benefiting more from GTP than central and western regions. The innovation environment, particularly human capital and technology market development, enhances GTP’s effectiveness, while government support shows limited impact. These findings provide important insights for advancing low‑carbon economic development and achieving carbon neutrality goals.
Zeng, S., Li, G., Wu, S., Dong Z. (2022) The impact of green technology innovation on carbon emissions in the context of carbon neutrality in China: Evidence from spatial spillover and nonlinear effect analysis, International Journal of Environmental Research and Public Health, 19 (2), 73
This paper aims to analyze the levels of GTI (green technology innovation) in 30 provinces in mainland China between 2001 and 2019. It uses the spatial econometric models and panel threshold models along with the slack based measure and Global Malmquist-Luenberger index to analyze the spatial spillover and nonlinear effects of GTI on regional carbon emissions. The results show that GTI achieves growth every year, but the innovation efficiency was low. China’s total carbon dioxide emissions were increasing at a marginal rate, but the carbon emission intensity was declining year by year.
Wu, S. & Noy, P. (2011) A conceptual design of a wireless sensor actuator system for optimizing energy and well-being in buildings, Intelligent Buildings International, 2 (1), pp. 41-56.
Saving energy consumption of a building and maximising occupant comfort in the building is an increasing pursuit in building design. This paper designs a new device aiming to optimise energy consumption in buildings and meanwhile maximising occupant comfort.
Risk analysis
Wu, S., Hrudey, S., French, S., Bedford, T., Soane, E., Pollard, S. (2009) A role for human reliability analysis (HRA) in preventing drinking water incidents and securing safe drinking water, Water Research, 43 (13), pp. 3227-3238.
Drinking water incidents occur from time to time in different countries. Human factors play a role in preventing drinking water incidents. This paper is the first paper that analyses drinking water incidents from a human reliability analysis viewpoint.