Predicting remaining useful life of an individual unit using proportional hazards model and logistic regression model

2006 ◽  
Author(s):  
Haitao Liao ◽  
Wenbiao Zhao ◽  
Huairui Guo
Keyword(s):  
Logistic Regression ◽  
Regression Model ◽  
Logistic Regression Model ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Remaining Useful Life ◽  
Hazards Model ◽  
Individual Unit ◽  
Useful Life

scholarly journals An Inference-based Prognostic Framework for Health Management of Automotive Systems

2020 ◽  
Vol 7 (2) ◽  
Author(s):  
Chaitanya Sankavaram ◽  
Anuradha Kodali ◽  
Krishna Pattipati ◽  
Satnam Singh ◽  
Yilu Zhang ◽  
...  
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Failure Time ◽  
Remaining Useful Life ◽  
Survival Functions ◽  
Time Data ◽  
Automotive Systems ◽  
Multiple Fault Diagnosis ◽  
Hazards Model ◽  
Useful Life

This paper presents a unified data-driven prognostic framework that combines failure time data, static parameter data and dynamic time-series data. The framework employs proportional hazards model and a soft dynamic multiple fault diagnosis algorithm for inferring the degraded state trajectories of components and to estimate their remaining useful life times. The framework takes into account the cross-subsystem fault propagation, a case prevalent in any networked and embedded system. The key idea is to use Cox proportional hazards model to estimate the survival functions of error codes and symptoms (probabilistic test outcomes/prognostic indicators) from failure time data and static parameter data, and use them to infer the survival functions of components via soft dynamic multiple fault diagnosis algorithm. The average remaining useful life and its higher-order central moments (e.g., variance, skewness, kurtosis) can be estimated from these component survival functions. The framework is demonstrated on datasets derived from two automotive systems, namely hybrid electric vehicle regenerative braking system, and an electronic throttle control subsystem simulator. Although the proposed framework is validated on automotive systems, it has the potential to be applicable to a wide variety of systems, ranging from aerospace systems to buildings to power grids.

Remaining useful life prediction of rolling bearings based on the three-parameter Weibull distribution proportional hazards model

2020 ◽  
Vol 62 (12) ◽  
pp. 710-718
Author(s):  
Ye Wang ◽  
Zhixiong Chen ◽  
Yang Zhang ◽  
Xin Li ◽  
Zhixiong Li
Keyword(s):  
Weibull Distribution ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Remaining Useful Life ◽  
Rolling Bearings ◽  
Time Frequency ◽  
Intelligent Maintenance ◽  
Hazards Model ◽  
Useful Life ◽  
Essential Knowledge

In order to accurately predict the remaining useful life (RUL) of rolling bearings, a novel method based on the threeparameter Weibull distribution proportional hazards model (WPHM) is proposed in this paper. In this new method, degradation features of the bearing vibration signals were calculated in the time, frequency and time-frequency domains and treated as the input covariates of the predictive WPHM. Essential knowledge of the bearing degradation dynamics was learnt from the input features to build an effective three-parameter WPHM for bearing RUL prediction. Experimental data acquired from the run-to-failure bearing tests of the intelligent maintenance system (IMS) was used to evaluate the proposed method. The analysis results demonstrate that the proposed model is able to produce accurate RUL prediction for the tested bearings and outperforms the popular two-parameter WPHM.

Remaining useful life prediction of lubricating oil with dynamic principal component analysis and proportional hazards model

2019 ◽  
Vol 234 (6) ◽  
pp. 964-971
Author(s):  
Ying Du ◽  
Tonghai Wu ◽  
Shengxi Zhou ◽  
Viliam Makis
Keyword(s):  
Condition Monitoring ◽  
Life Prediction ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Principal Component ◽  
Remaining Useful Life ◽  
Lubricating Oil ◽  
Hazards Model ◽  
Dynamic Principal Component Analysis ◽  
Useful Life

Lubricating oil contains a lot of tribological information of the machine and plays an important role in machine health. Oil degrades with serving time and causes severe wear afterwards, which is a complex dynamic process, and difficult to be accurately described by a single property. Therefore, the main purpose of deterioration prediction is to estimate the remaining useful life that the oil can still fulfill its functions by analyzing oil condition monitoring data. With a large amount of oil condition monitoring data collected, a vector autoregressive model is applied to the original oil data to describe the dynamic deterioration process. Then dynamic principal component analysis, an effective dimensionality reduction method, is employed to obtain the principal components capturing the most information of the oil data. The proportional hazards model is then built to calculate the failure risk of the lubricating oil based on the condition monitoring information, where its baseline function represents the aging process assuming to follow the Weibull distribution and its positive link function represents the influence of covariates (the principal components) on the failure risk. Finally, the remaining useful life prediction of lubricating oil can be obtained by explicit formulas of the characteristics such as the conditional reliability function and the mean residual life function. This work provides an approach to assess the health of lubricating oil, and a guidance for oil maintenance strategy.

A Predictive Tool for Remaining Useful Life Estimation of Rotating Machinery Components

2005 ◽  
Author(s):  
Haitao Liao ◽  
Hai Qiu ◽  
Jay Lee ◽  
Daming Lin ◽  
Dragan Banjevic ◽  
...  
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Remaining Useful Life ◽  
Model Parameters ◽  
Predictive Tool ◽  
Hazards Model ◽  
On Line ◽  
Likelihood Approach ◽  
Useful Life ◽  
The Mean

This paper introduces a model for multiple degradation features of an individual component. The maximum likelihood approach is employed to estimate the model parameters. Afterwards, a proportional hazards model is presented, which considers hard failures and multiple degradation features simultaneously. The integrated model enables us to predict the mean remaining useful life of a component based on on-line degradation information. An example for bearing prognostic is provided to demonstrate the proposed models in practical use.

A censored quantile regression approach for the analysis of time to event data

2016 ◽  
Vol 27 (3) ◽  
pp. 955-965 ◽  
Author(s):  
Xiaonan Xue ◽  
Xianhong Xie ◽  
Howard D Strickler
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Time To Event ◽  
Censored Quantile Regression ◽  
Quantile Regression Model ◽  
Hazards Model

The commonly used statistical model for studying time to event data, the Cox proportional hazards model, is limited by the assumption of a constant hazard ratio over time (i.e., proportionality), and the fact that it models the hazard rate rather than the survival time directly. The censored quantile regression model, defined on the quantiles of time to event, provides an alternative that is more flexible and interpretable. However, the censored quantile regression model has not been widely adopted in clinical research, due to the complexity involved in interpreting its results properly and consequently the difficulty to appreciate its advantages over the Cox proportional hazards model, as well as the absence of adequate validation procedure. In this paper, we addressed these limitations by (1) using both simulated examples and data from National Wilms’ Tumor clinical trials to illustrate proper interpretation of the censored quantile regression model and the differences and the advantages of the model compared to the Cox proportional hazards model; and (2) developing a validation procedure for the predictive censored quantile regression model. The performance of this procedure was examined using simulation studies. Overall, we recommend the use of censored quantile regression model, which permits a more sensitive analysis of time to event data together with the Cox proportional hazards model.

Metabolic activity to predict clinical response and prognosis in esophageal adenocarcinoma patients treated with bimodality.

2018 ◽  
Vol 36 (4_suppl) ◽  
pp. 127-127
Author(s):  
Kazuto Harada ◽  
Carol C Wu ◽  
Xuemei Wang ◽  
Dilsa Mizrak Kaya ◽  
Fatemeh Ghazanfari Amlashi ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Regression Model ◽  
Esophageal Adenocarcinoma ◽  
Metabolic Activity ◽  
Logistic Regression Model ◽  
Proportional Hazards ◽  
Clinical Stage ◽  
Standardized Uptake Value ◽  
Cox Proportional Hazards ◽  
Multivariate Logistic Regression Model

127 Background: Patients with localized esophageal adenocarcinoma (L-EAC) who are not suitable for surgery receive definitive chemoradiation. However, there are no biomarkers or imaging variables to predict clinical complete response (cCR; negative bx and physiologic PET post chemoradiation) or prognosticate favorable overall survival (OS). We analyzed tumor metabolic activity by standardized uptake value (SUV) or total lesion glycolysis (TLG). Methods: 266 patients with L-EAC, who declined or were unsuitable for surgery, were analyzed. Cox proportional hazards regression model for OS was analyzed using categorized SUV (low; < 6.5, moderate; 6.5-12.9, or high; ≥12.9) or TLG (low; < 24.2, moderate; 24.2-82.6, or high; ≥82.6). Logistic regression model for cCR was analyzed using categorized SUV (low; < 5.4 or high; ≥5.4) or TLG (low; < 27.0 or high; ≥27.0). Results: Mean SUV and TLG were 12.8 ± 10.7 and 209 ± 376.8, respectively. Both SUV and TLG were significantly associated with the length of the tumor (p < 0.0001) and clinical stage (p < 0.0001). Higher SUV and TLG were significantly associated with shorter OS than low SUV and TLG (moderate SUV; HR 1.79, CI 1.19-2.69, high SUV; HR 2.82, 1.90-4.18, moderate TLG; HR 1.82, 1.14-2.90, high TLG; 3.16, 2.11-4.74). 68 patients (28%) achieved cCR and remained free of recurrence. In the multivariate logistic regression model, low SUV and low TLG highly predicted cCR without recurrence (low SUV; OR 3.15, 1.38–7.19, low TLG; OR 4.79, 2.28-10.08). Conclusions: Tumor metabolic activity is highly associated with prognosis and response to chemoradiation in patients with L-EAC not undergoing surgery. Further refinements (addition of biomarkers) could allow personalized care of these patients.

Methods for displaying and calibration of Cox proportional hazards models

2017 ◽  
Vol 232 (1) ◽  
pp. 105-115
Author(s):  
Chrianna I Bharat ◽  
Kevin Murray ◽  
Edward Cripps ◽  
Melinda R Hodkiewicz
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Explanatory Power ◽  
Cox Proportional Hazards ◽  
Remaining Useful Life ◽  
Cox Proportional Hazards Model ◽  
Data Set ◽  
Proportional Hazards Models ◽  
Hazards Model ◽  
Cox Proportional Hazards Models

Cox proportional hazards modelling is a widely used technique for determining relationships between observed data and the risk of asset failure when model performance is satisfactory. Cox proportional hazards models possess good explanatory power and are used by asset managers to gain insight into factors influencing asset life. However, validation of Cox proportional hazards models is not straightforward and is seldom considered in the maintenance literature. A comprehensive validation process is a necessary foundation to build trust in the failure models that underpin remaining useful life prediction. This article describes data splitting, model discrimination, misspecification and fit methods necessary to build trust in the ability of a Cox proportional hazards model to predict failures on out-of-sample assets. Specifically, we consider (1) Prognostic Index comparison for training and test sets, (2) Kaplan–Meier curves for different risk bands, (3) hazard ratios across different risk bands and (4) calibration of predictions using cross-validation. A Cox proportional hazards model on an industry data set of water pipe assets is used for illustrative purposes. Furthermore, because we are dealing with a non-statistical managerial audience, we demonstrate how graphical techniques, such as forest plots and nomograms, can be used to present prediction results in an easy to interpret way.

A Note on Standard Errors for Survival Curves in Discrete-Time Survival Analysis

2005 ◽  
Vol 30 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Rebecca Zwick ◽  
Jeffrey C. Sklar
Keyword(s):  
Logistic Regression ◽  
Discrete Time ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Standard Errors ◽  
Survival Functions ◽  
Hazards Model ◽  
Time Period ◽  
Flexible Form ◽  
Ordinary Logistic Regression

Cox (1972) proposed a discrete-time survival model that is somewhat analogous to the proportional hazards model for continuous time. Efron (1988) showed that this model can be estimated using ordinary logistic regression software, and Singer and Willett (1993) provided a detailed illustration of a particularly flexible form of the model that includes one parameter per time period. This work has been expanded to show how logistic regression output can also be used to estimate the standard errors of the survival functions. This is particularly simple under the model described by Singer and Willett, when there are no predictors other than time.

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