# Bayesian Joint Model of Multi-Sensor and Failure Event Data for Multi-Mode Failure Prediction

arXiv: https://arxiv.org/abs/2506.17036 · HTML: https://mlsanity.com/paper/2506.17036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Builds on (most cited first, 8 of 8)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Variational Inference of Joint Models using Multivariate Gaussian Convolution Processes](https://mlsanity.com/paper/1903.03867/) (2019)
- [Modularized Bayesian analyses and cutting feedback in likelihood-free inference](https://mlsanity.com/paper/2203.09782/) (2022)
- [Joint Models with Multiple Longitudinal Outcomes and a Time-to-Event Outcome: a Corrected Two-Stage Approach](https://mlsanity.com/paper/1808.07719/) (2018)
- [Weakly-supervised Multi-output Regression via Correlated Gaussian Processes](https://mlsanity.com/paper/2002.08412/) (2020)

## Abstract (arXiv)

Modern industrial systems are often subject to multiple failure modes, and their conditions are monitored by multiple sensors, generating multiple time-series signals. Additionally, time-to-failure data are commonly available. Accurately predicting a system's remaining useful life (RUL) requires effectively leveraging multi-sensor time-series data alongside multi-mode failure event data. In most existing models, failure modes and RUL prediction are performed independently, ignoring the inherent relationship between these two tasks. Some models integrate multiple failure modes and event prediction using black-box machine learning approaches, which lack statistical rigor and cannot characterize the inherent uncertainty in the model and data. This paper introduces a unified approach to jointly model the multi-sensor time-series data and failure time concerning multiple failure modes. This proposed model integrate a Cox proportional hazards model, a Convolved Multi-output Gaussian Process, and multinomial failure mode distributions in a hierarchical Bayesian framework with corresponding priors, enabling accurate prediction with robust uncertainty quantification. Posterior distributions are effectively obtained by Variational Bayes, and prediction is performed with Monte Carlo sampling. The advantages of the proposed model is validated through extensive numerical and case studies with jet-engine dataset.