## 5 Conclusions  
In order to examine the extent of degradation in oil debris, online condition monitoring technology is commonly used to provide real-time information on the oil state and equipment wear state without disassembling the equipment. We documented in this study that there has been limited research on state-based oil degradation modeling initiatives in the past. The key contribution of work lies in introducing a multistate modeling approach to lubrication degradation trajectory, citing the complexity and inability to trace the trajectory with a stochastic model [31]. The proposed work can effectively classify the multiple states. The probabilistic progression of the wear state under frequent oil replenishments and oil changes is also provided by a state-based prognostic model. While the hidden Markov model (HMM) with a prior preassigned state count (\(N\)) is widely used for multistate modeling to quantify the probabilistic changes in the degradation parameters. This estimate of state count is purely based on experience and assumption, limiting its application for complex systems with nonmonotonic and singular (spiky) degradation traces with frequent external intentional or unintentional interferences into the system. With this scenario in mind and with the limitations of HMM and HDP-HMM, the sticky HDP-HMM appears to be an elegant Bayesian model for an infinite number of states [32]. We presented the hierarchical Dirichlet process-hidden Markov model (HDP-HMM) framework with its nonparametric properties to infer the system's unknown state space size based purely on the degradation time series data. The sticky HDP-HMM helped further refine the data learning capability of the model, where the degradation data (i.e., wear debris concentration in oil) was simulated for the system considering multiple oil replenishments and oil changes. The remaining useful life (RUL) is indirectly evaluated in terms of the CRF and MRL to estimate the time for an oil change. Our analysis proves that the experience and assumption-based states' classification is not effective for real-time oil diagnosis and prognosis. The state-based Dirichlet process for lubrication condition monitoring still needs more intense research explorations in the near future. The HDP-HMM can improve state-based DP for various industrial systems. In the future, though the sticky HDP-HMM follows a state persistence approach, our work needs to be extended by considering the HDP-hidden semi-Markov model (HSMM) to learn nongeometric state durations with natural priors over state duration. A comparative analysis for estimated state space, state evolution over time, and estimated RUL will need to be carried out with the HDP-HMM, HDP-HSMM, and HDP-Hierarchical hidden Markov model (HHMM) for the same WDC time series data set. Various sampling algorithms in parallel with the sticky algorithm will also be explored in the context of their state estimation capability. While the present work estimates the instantaneous wear state space based on current WDC data, the work will also be extended to investigate cumulative wear state-space estimation to detect system wear state. The RUL will be predicted using CRF and MRL for comparative analysis with another nonparametric Bayesian approach, i.e., MO-GPR. Conceptualization, M.T. and N.R. ; methodology, M.T. ; software, M.T. ; validation, M.T., N.R., and H.P. ; formal analysis, M.T. ; investigation, M.T. and N.R. ; resources, M.T., N.R., and H.P. ; data curation, M.T. ; writing--original draft preparation, M.T. ; writing--review and editing, N.R. and H.P. ; visualization, N.R. and H.P. ; supervision, N.R. ; project administration, N.R. ; funding acquisition, N.R. All authors have read and agreed to the published version of the manuscript. This research was funded by the Ministry of Education (MOE), Singapore Academic Research Fund (AcRF) under the Tier-2 Grant Call No. MOE-2017-T2-1-115. The corresponding author additionally acknowledges the support of Industry Postgraduate Fund Grant No.