Reliability estimation and remaining useful lifetime prediction for bearing based on proportional hazard model

As the central component of rotating machine,the performance reliability assessment and remaining useful lifetime prediction of bearing are of crucial importance in condition-based maintenance to reduce the maintenance cost and improve the reliability.A prognostic algorithm to assess the reliability and forecast the remaining useful lifetime(RUL) of bearings was proposed,consisting of three phases.Online vibration and temperature signals of bearings in normal state were measured during the manufacturing process and the most useful time-dependent features of vibration signals were extracted based on correlation analysis(feature selection step).Time series analysis based on neural network,as an identification model,was used to predict the features of bearing vibration signals at any horizons(feature prediction step).Furthermore,according to the features,degradation factor was defined.The proportional hazard model was generated to estimate the survival function and forecast the RUL of the bearing(RUL prediction step).The positive results show that the plausibility and effectiveness of the proposed approach can facilitate bearing reliability estimation and RUL prediction.

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

Cox Proportional Hazard Model for Survival Time of Neonatal Mortality in Neonatal Intensive Care Unit of Hospitals in River Nile State-Sudan

Cox Proportional Hazard model is a popular statistical technique for exploring the relationship between the survival time of neonates and several explanatory variables. It provides an estimate of the study variables’ effect on survival after adjustment for other explanatory variables, and allows us to estimate the hazard (or risk) of death of newborn in NICU of hospitals in River Nile State-Sudan for the period (2018-2020). Study Data represented (neonate gender, mode of delivery, birth type, neonate weight, resident type, gestational age, and survival time). Kaplan-Meier method is used to estimate survival and hazard function for survival times of newborns that have not completed their first month. Of 700 neonates in the study area, 25% of them died during 2018-2020. Variables of interest that had a significant effect on neonatal death by Cox Proportional Hazard Model analysis were neonate weight, resident type, and gestational age. In Cox Proportional Hazard Model analysis all the variables of interest had an effect on neonatal death, but the variables with a significant effect included, weight of neonate, resident type and gestational age.

A Software Reliability Model for OSS Including Various Fault Data Based on Proportional Hazard-Rate Model

The software reliability model is the stochastic model to measure the software reliability quantitatively. A Hazard-Rate Model is the well-known one as the typical software reliability model. We propose Hazard-Rate Models Considering Fault Severity Levels (CFSL) for Open Source Software (OSS). The purpose of this research is to make the Hazard-Rate Model considering CFSL adapt to baseline hazard function and 2 kinds of faults data in Bug Tracking System (BTS), i.e., we use the covariate vectors in Cox proportional Hazard-Rate Model. Also, we show the numerical examples by evaluating the performance of our proposed model. As the result, we compare the performance of our model with the Hazard-Rate Model CFSL.

Influence of donor age on liver transplantation outcomes: A multivariate analysis and comparative study

BACKGROUND The growing disparity between the rising demand for liver transplantation(LT)and the limited availability of donor organs has prompted a greater reliance on older liver grafts.Traditionally,utilizing livers from elderly donors has been associated with outcomes inferior to those achieved with grafts from younger donors.By accounting for additional risk factors,we hypothesize that the utili-zation of older liver grafts has a relatively minor impact on both patient survival and graft viability.AIM To evaluate the impact of donor age on LT outcomes using multivariate analysis and comparing young and elderly donor groups.METHODS In the period from April 2013 to December 2018,656 adult liver transplants were performed at the University Hospital Merkur.Several multivariate Cox propor-tional hazards models were developed to independently assess the significance of donor age.Donor age was treated as a continuous variable.The approach involved univariate and multivariate analysis,including variable selection and assessment of interactions and transformations.Additionally,to exemplify the similarity of using young and old donor liver grafts,the group of 87 recipients of elderly donor liver grafts(≥75 years)was compared to a group of 124 recipients of young liver grafts(≤45 years)from the dataset.Survival rates of the two groups were estimated using the Kaplan-Meier method and the log-rank test was used to test the differences between groups.RESULTS Using multivariate Cox analysis,we found no statistical significance in the role of donor age within the constructed models.Even when retained during the entire model development,the donor age's impact on survival remained insignificant and transformations and interactions yielded no substantial effects on survival.Consistent insigni-ficance and low coefficient values suggest that donor age does not impact patient survival in our dataset.Notably,there was no statistical evidence that the five developed models did not adhere to the proportional hazards assumption.When comparing donor age groups,transplantation using elderly grafts showed similar early graft function,similar graft(P=0.92),and patient survival rates(P=0.86),and no significant difference in the incidence of postoperative complications.CONCLUSION Our center's experience indicates that donor age does not play a significant role in patient survival,with elderly livers performing comparably to younger grafts when accounting for other risk factors.

Storage reliability assessment model based on competition failure of multi-components in missile

The degradation data of multi-components in missile is derived by periodical testing. How to use these data to assess the storage reliability (SR) of the whole missile is a difficult problem in current research. An SR assessment model based on competition failure of multi-components in missile is proposed. By analyzing the missile life profile and its storage failure feature, the key components in missile are obtained and the characteristics voltage is assumed to be its key performance parameter. When the voltage testing data of key components in missile are available, a state space model (SSM) is applied to obtain the whole missile degradation state, which is defined as the missile degradation degree (DD). A Wiener process with the time-scale model (TSM) is applied to build the degradation failure model with individual variability and nonlinearity. The Weibull distribution and proportional risk model are applied to build an outburst failure model with performance degradation effect. Furthermore, a competition failure model with the correlation between degradation failure and outburst failure is proposed. A numerical example with a set of missiles in storage is analyzed to demonstrate the accuracy and superiority of the proposed model.

Prediction models for development of hepatocellular carcinoma in chronic hepatitis B patients

Chronic hepatitis B(CHB)-related hepatocellular carcinoma(HCC)is a major health problem in Asian-Pacific regions.Antiviral therapy reduces,but does not completely prevent,HCC development.Thus,there is a need for accurate risk prediction to assist prognostication and decisions on the need for antiviral therapy and HCC surveillance.A few risk scores have been developed to predict the occurrence of HCC in CHB patients.Initially,the scores were derived from untreated CHB patients.With the development and extensive clinical application of nucleos(t)ide analog(s)(NA),the number of risk scores based on treated CHB patients has increased gradually.The components included in risk scores may be categorized into host factors and hepatitis B virus factors.Hepatitis activities,hepatitis B virus factors,and even liver fibrosis or cirrhosis are relatively controlled by antiviral therapy.Therefore,variables that are more dynamic during antiviral therapy have since been included in risk scores.However,host factors are more difficult to modify.Most existing scores derived from Asian populations have been confirmed to be accurate in predicting HCC development in CHB patients from Asia,while these scores have not offered excellent predictability in Caucasian patients.These findings support that more relevant variables should be considered to provide individualized predictions that are easily applied to CHB patients of different ethnicities.CHB patients should receive different intensities of HCC surveillance according to their risk category.

Simulation and Experiment Research on the Proportional Pressure Control of Water-assisted Injection Molding

Water-assisted injection molding（WAIM）,a newly developed fluid-assisted injection molding technology has drawn more and more attentions for the energy saving,short cooling circle time and high quality of products.Existing research for the process of WAIM has shown that the pressure control of the injecting water is mostly important for the WAIM.However,the proportional pressure control for the WAIM system is quite complex due to the existence of nonlinearities in the water hydraulic system.In order to achieve better pressure control performance of the injecting water to meet the requirements of the WAIM,the proportional pressure control of the WAIM system is investigated both numerically and experimentally.A newly designed water hydraulic system for WAIM is first modeled in AMEsim environment,the load characteristics and the nonlinearities of water hydraulic system are both considered,then the main factors affecting the injecting pressure and load flow rate are extensively studied.Meanwhile,an open-loop model-based compensation control strategy is employed to regulate the water injection pressure and a feedback proportional integrator controller is further adopted to achieve better control performance.In order to verify the AMEsim simulation results WAIM experiment for particular Acrylonitrile Butadiene Styrene（ABS） parts is implemented and the measured experimental data including injecting pressure and flow rate results are compared with the simulation.The good coincidence between experiment and simulation shows that the AMEsim model is accurate,and the tracking performance of the load pressure indicates that the proposed control strategy is effective for the proportional pressure control of the nonlinear WAIM system.The proposed proportional pressure control strategy and the conclusions drawn from simulation and experiment contribute to the application of water hydraulic proportional control and WAIM technology.

Risk prediction model for cutaneous squamous cell carcinoma in adult cardiac allograft recipients

BACKGROUND Heart transplant recipients are at higher risk of developing skin cancer than the general population due to the long-term immunosuppression treatment.Cancer has been reported as one of the major causes of morbidity and mortality for patients after heart transplantation.Among different types of skin cancers,cutaneous squamous cell carcinoma(cSCC)is the most common one,which requires timely screening and better management.AIM To identify risk factors and predict the incidence of cSCC for heart transplant recipients.METHODS We retrospectively analyzed adult heart transplant recipients between 2000 and 2015 extracted from the United Network for Organ Sharing registry.The whole dataset was randomly divided into a derivation set(80%)and a validation set(20%).Uni-and multivariate Cox regression were done to identify significant risk factors associated with the development of cSCC.Receiver operating characteristics curves were generated and area under the curve(AUC)was calculated to assess the accuracy of the prediction model.Based on the selected risk factors,a risk scoring system was developed to stratify patients into different risk groups.A cumulative cSCC-free survival curve was generated using the Kaplan-Meier method for each group,and the log-rank test was done to compare the intergroup cSCC rates.RESULTS There were 23736 heart-transplant recipients during the study period,and 1827 of them have been reported with cSCC.Significant predictors of post-transplant cSCC were older age,male sex,white race,recipient and donor human leukocyte antigen(HLA)mismatch level,malignancy at listing,diagnosis with restrictive myopathy or hypertrophic myopathy,heart re-transplant,and induction therapy with OKT3 or daclizumab.The multivariate model was used to predict the 5-,8-and 10-year incidence of cSCC and respectively provided AUC of 0.79,0.78 and 0.77 in the derivation set and 0.80,0.78 and 0.77 in the validation set.The risk scoring system assigned each patient with a risk score within the range of 0-11,based on which they were stratified into 4 different risk groups.The predicted and observed 5-year probability of developing cSCC match well among different risk groups.In addition,the log-rank test indicated significantly different cSCCfree survival across different groups.CONCLUSION A risk prediction model for cSCC among heart-transplant recipients has been generated for the first time.It offers a c-statistic of≥0.77 in both derivation and validation sets.

Analysis of Length of Stay (LOS) Data from the Medical Records of Tertiary Care Hospital in Saudi Arabia for Five Diagnosis Related Groups: Application of Cox Prediction Model

Background: One of the main objectives of hospital managements is to control the length of stay (LOS). Successful control of LOS of inpatients will result in reduction in the cost of care, decrease in nosocomial infections, medication side effects, and better management of the limited number of available patients’ beds. The length of stay (LOS) is an important indicator of the efficiency of hospital management by improving the quality of treatment, and increased hospital profit with more efficient bed management. The purpose of this study was to model the distribution of LOS as a function of patient’s age, and the Diagnosis Related Groups (DRG), based on electronic medical records of a large tertiary care hospital. Materials and Methods: Information related to the research subjects were retrieved from a database of patients admitted to King Faisal Specialist Hospital and Research Center hospital in Riyadh, Saudi Arabia between January 2014 and December 2016. Subjects’ confidential information was masked from the investigators. The data analyses were reported visually, descriptively, and analytically using Cox proportional hazard regression model to predict the risk of long-stay when patients’ age and the DRG are considered as antecedent risk factors. Results: Predicting the risk of long stay depends significantly on the age at admission, and the DRG to which a patient belongs to. We demonstrated the validity of the Cox regression model for the available data as the proportionality assumption is shown to be satisfied. Two examples were presented to demonstrate the utility of the Cox model in this regard.

Transformation Models for Survival Data Analysis with Applications

When the event of interest never occurs for a proportion of subjects during the study period, survival models with a cure fraction are more appropriate in analyzing this type of data. Considering the non-linear relationship between response variable and covariates, we propose a class of generalized transformation models motivated by Zeng et al. [1] transformed proportional time cure model, in which fractional polynomials are used instead of the simple linear combination of the covariates. Statistical properties of the proposed models are investigated, including identifiability of the parameters, asymptotic consistency, and asymptotic normality of the estimated regression coefficients. A simulation study is carried out to examine the performance of the power selection procedure. The generalized transformation cure rate models are applied to the First National Health and Nutrition Examination Survey Epidemiologic Follow-up Study (NHANES1) for the purpose of examining the relationship between survival time of patients and several risk factors.

Fibrinogen-to-albumin ratio predicts overall survival of hepatocellular carcinoma

BACKGROUND Fibrinogen-to-albumin ratio(FAR)has been found to be of prognostic significance for several types of malignant tumors.However,less is known about the association between FAR and survival outcomes in hepatocellular carcinoma(HCC)patients.AIM To explore the association between FAR and prognosis and survival in patients with HCC.METHODS A total of 366 histologically confirmed HCC patients diagnosed between 2013 and 2018 in a provincial cancer hospital in southwestern China were retrospectively selected.Relevant data were extracted from the hospital information system.The optimal cutoff for baseline serum FAR measured upon disease diagnosis was established using the receiver operating characteristic(ROC)curve.Univariate and multivariate Cox proportional hazards models were used to determine the crude and adjusted associations between FAR and the overall survival(OS)of the HCC patients while controlling for various covariates.The restricted cubic spline(RCS)was applied to estimate the dose-response trend in the FAR-OS association.RESULTS The optimal cutoff value for baseline FAR determined by the ROC was 0.081.Multivariate Cox proportional hazards model revealed that a lower baseline serum FAR level was associated with an adjusted hazard ratio of 2.43(95%confidence interval:1.87–3.15)in the OS of HCC patients,with identifiable dose-response trend in the RCS.Subgroup analysis showed that this FAR-OS association was more prominent in HCC patients with a lower baseline serum aspartate aminotransferase or carbohydrate antigen 125 level.CONCLUSION Serum FAR is a prominent prognostic indicator for HCC.Intervention measures aimed at reducing FAR might result in survival benefit for HCC patients.

SICA for Cox's Proportional Hazards Model with a Diverging Number of Parameters

The smooth integration of counting and absolute deviation （SICA） penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan （2009）. In this article, we extend their idea to Cox＇s proportional hazards （PH） model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-Newton （SQN） algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.

Health evaluation method for degrading systems subject to dependent competing risks

This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determined by a non-stationary Gamma process and the soft failure is encountered when it exceeds a predefined critical level. For the hard failure, a Cox’s proportional hazard model is applied to describe the hazard rate of the time to system failure. The dependent relationship is modeled by incorporating the degradation process as a time-varying covariate into the Cox’s proportional hazard model. To facilitate the health characteristics evaluation, a discretization technique is applied both to the degradation process and the monitoring time.All health characteristics can be obtained in the explicit form using the transition probability matrix, which is computationally attractive for practical applications. Finally, a numerical analysis is carried out to show the effectiveness and the performance of the proposed health evaluation method.

Optimal Generalized Case-Cohort Analysis with Cox's Proportional Hazards Model

Generalized case-cohort design has been proved to be a cost-effective way to enhance the efficiency of large epidemiological cohort. In this article, we propose an inference procedure for estimating the unknown parameters in Cox＇s proportional hazards model in generalized case-cohort design and establish an optimal sample size allocation to achieve the maximum power at a given budget. The finite sample performance of the proposed method is evaluated through simulation studies. The proposed method is applied to a real data set from the National Wilm＇s Tumor Study Group.

Prediction Approach to Life on Wing for Civil Aeroengine

To reduce engine maintenance cost and support safe operation, a prediction method of engine life on wing was proposed. This method is a kind of regression model which is a function of the condition monitoring and failure data. Key causes of engine removals were analyzed, and the life limit due to performance deterioration was predicted by proportional hazards model. Then the scheduled removal causes were considered as constraints of engine life to predicte the finai life on wing. Application of the proposed prediction method to the case of CF6-80C2A5 engine fleet in an airline proved its effectiveness.

Partial proportional odds model for analyzing pedestrian crashes,threshold heterogeneity by scale and proportional odds factor

Despite low traffic in Wyoming,pedestrian crash severity accounts for a high number of fatalities in the state.Thus this study was conducted to highlights factors contributing to those crashes.The results highlighted that drivers under influence,type of vehicle,location of crashes,estimated speed of vehicles,driving over the recommended speed are some of factors contributing to the severity of crashes.In this study,we used proportional odds model which assumes that the impact of each attribute is consistent or proportional across various threshold values.However,it has been argued that this assumption might be unrealistic,especially at the presence of extreme values.Thus,the assumption was relaxed in this study by shifting the thresholds based on some explanatory attributes,or proportional odds effects.In addition,we accounted for the spread rate,or scale,of the model’s latent distribution of pedestrian crashes.The results highlighted that the partial proportional odds model through proportional odds factor and scale effects result in a significant improvement in model fit compared with the standard proportional odds model.Comparisons were also made across standard normal,simple partial ordinal model,and partial ordinal accounting for scale heterogeneity.In addition,various potential threshold structures such as symmetric and flexible were considered,but similar goodness of fits were observed across all those models.Extensive discussion has been made regarding the formulation of the implemented methodology,and its implications.

Prognostic Factors in Patients with Pancreatic Carcinoma

Objective: To evaluate the major prognostic factors in patients with pancreatic carcinoma. Methods:113 cases of a particular disease were retrospectively analysed and 9 factors for prognosis were studied by multivaritate analysis with Cox proportional hazards survival model.Survival rate was calculated by Kaplan-Meier estimation. Results:In this group,survival time was 0.1 to 82 months,and the median survival time was 3 months.Overall survival rates at month 6,12,18,36 were 35.6%,20.3%,15.9% and 6.2%,respectively.Multivariate analyses revealed significant prognostic factors as follows:jaundice,metastasis,therapy method and synthetic therapy. Conclusion: The prognosis of pancreatic carcinoma is determined by various factors.Jaundice and metastasis are independent predictors of poor survival.Radical operation and synthetic therapy will improve the prognosis.

Maximum Likelihood Estimator for the Proportional Hazards Model with Incomplete Information

Right randomly censored data with incomplete infor-mation are frequently met in practice.Although much study about right randomly censored data has been seen in the proportional hazards model,relatively little is known about the inference of regression parameters for right randomly censored data with in-complete information in such model.In particular,theoretical properties of the maximum likelihood estimator of the regression parameters have not been proven yet in that model.In this paper,we show the consistency and asymptotic normality of the maxi-mum likelihood estimator of unknown regression parameters.

The Proportional Hazards Model for Multiple Type Recurrent Gap Times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies,and often more than one type of recurrent events is of interest.In this paper,we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covaxiates on the censored event processes of interest.An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions.We examine asymptotic properties of the proposed estimators.Finite sample properties of these estimators are demonstrated by simulations.