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.

Accelerated proportional degradation hazards-odds model in accelerated degradation test

An accelerated proportional degradation hazards-odds model is proposed. It is a non-parametric model and thus has pathfree and distribution-free properties, avoiding the errors caused by faulty assumptions of degradation paths or distribution of degradation measurements. It is established based on a link function which combines the degradation cumulative hazard rate function and the degradation odds function through a transformation parameter, and this makes the accelerated proportional degradation hazards model and the accelerated proportional degradation odds model special cases of it. Hypothesis tests are discussed, and the proposed model is applicable when some model assumptions are satisfied. This model is utilized to estimate the reliability of miniature bulbs under low stress levels based on the degradation data obtained under high stress levels to validate the effectiveness of this model.

Clinical Study on the Impact of Long-term Survival Quality in 204 Postoperative Patients with Breast Cancer by Cox Proportional Hazard Models

The aim of study was to evaluate clinical characteristics, social support and the association with the prognosis of breast cancer patients. A total of 204 participants were followed from 2003 until the end of 2008. Information about patients with breast cancer was submitted by investigators. Data were analyzed by Cox’s proportional hazard model. The clinical staging of breast cancer we used was the TNM classification. A 'T' score is based upon the size and/or extent of invasion. The 'N' score indicates the extent of lymph node involvement. Age at diagnose was associated with protective factors (HR=0.972;95%CI (0.834-1.130)), T staging (HR=2.075;95%CI (1.424-3.022)), N staging (HR=1.513;95%CI (1.066-2.148)), were associated with risk factor. Two survival graphs of nodes with negative effects by histology and nodes with positive effects by histology was analyzed by log-rank test, there was statistically significant relationship between two survival graphs (χ2 =136.8467, p <.0001). Age at diagnoses, Clinical stage tumor and node could contribute to the development of breast cancer and disease free survival in Chinese women.

A Cox Proportional Hazard Model Approach to Age at First Sexual Intercourse in Nigeria

Early age at first sexual intercourse comes with many negative sexual outcomes namely: having unprotected sex on first sexual intercourse, condom misuse, high rate of sexually transmitted infections (STIs), teenage pregnancy, increased number of sexual partners, etc. In this paper, we considered some socio-demographic and cultural factors and their relationship with age at first sexual intercourse so as to reduce the numerous negative sexual outcomes of early age at first sexual intercourse using the 2018 Nigerian Demographic and Health Survey data. The analysis was made using the Cox proportional hazard model and the Kaplan-Meier plot. The result shows that some respondents started having their first sexual intercourse at the age of 8 years and about 54.4% of the respondents had their first sexual intercourse before age 17 years. The median age of first sexual intercourse is 16 years which implies that about 50% of the respondents had their first sexual intercourse on or before their 16th birthday. Education, religion, region and residence significantly affects the age of first sexual intercourse while circumcision has no significant effect.

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.Numerical 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.

A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis

The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.

Comparison of Cox proportional hazards model,Cox proportional hazards with time-varying coefficients model,and lognormal accelerated failure time model:Application in time to event analysis of melioidosis patients

Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

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.

基于迭代融合优化算法和WPHM的牵引电机轴承可靠性评估

为了评估列车牵引电机轴承的运行可靠性,提出一种基于反向指数鲸鱼群(OEWOA)与粒子群(PSO)迭代融合的优化算法和威布尔比例故障率模型(WPHM)的评估方法。提取振动信号的时域、频域特征指标,利用主成分分析法(PCA)进行特征信息的融合,将融合后的特征指标作为WPHM的响应协变量进行可靠性评估。针对模型中多个参数直接求解困难的问题,利用反向学习策略(OBL)和指数收敛因子提高鲸鱼算法(WOA)的搜索能力,迭代融合PSO算法良好的收敛能力;通过OEWOA的探索指导PSO的迭代,避免PSO陷入局部最优,从而彻底探索搜索空间,同时使用PSO限制OEWOA的搜索,以便更快地将解收敛到全局最优值。应用该优化算法对WPHM中多个参数进行求解,实现牵引电机轴承运行可靠性的评估。结果表明,该方法与PSO、WOA等优化算法比较,具有更快的收敛速度和寻优能力。

基于WPHM的动车组牵引传动系统可靠性分析

提出了一种考虑天气因素的威布尔比例故障率模型(WPHM),采用威布尔分布的基准故障率函数,构建能够反映动车组外部运行环境的天气因素协变量,建立牵引传动系统的部件WPHM,利用遗传算法进行模型参数估计,依据所估计参数得出正常天气状态和恶劣天气状态下各部件的故障率和可靠度。实例研究表明,当牵引传动系统各部件均处于耗损失效期,部件均不同程度受天气因素影响,其中影响程度较大的部件有M2S车牵引电机及冷却风机,TP车主断路器,TPB车主断路器,MH车牵引电机及冷却风机等;不同天气状态下系统各部件的故障率和可靠度随服役时间推移均有明显变化,尤其恶劣天气状态下部件故障率更高,可靠度更低。因此,模型能有效地度量天气因素对部件可靠性的影响,为运用维修决策提供理论依据。

糖尿病肾脏疾病预后影响因素的COX比例风险回归模型分析

目的基于COX比例风险回归模型分析糖尿病肾脏疾病(diabetic kidney disease,DKD)预后的影响因素,为临床早期评估和防治DKD提供科学的依据。方法收集多中心(河南中医药大学第一附属医院、河南中医药大学第三附属医院、河南省中医院及郑州市人民医院)2010—2021年就诊治疗的DKD患者资料,包括一般资料、实验室指标、中医辨证分型及中医药治疗,以肾小球滤过率(eGFR)下降≥50%、血肌酐(Scr)翻倍、DKD 5期、死亡为结局指标,随访其发生时间及情况,利用COX比例风险回归模型分析筛选DKD预后影响因素。结果本研究最终纳入1947例患者,随访时间为4.65(4.557~4.746)年,发生复合终点事件305例(15.67%)。单因素COX回归分析结果表明,不同年龄、DKD病程≥4年、饮酒史、吸烟史、高血压、冠心病、脑血管病、糖尿病足、糖尿病眼病、糖化血红蛋白(HbA1c)、血尿酸(SUA)、Scr、24 h尿蛋白定量(24 h-UTP)、eGFR、湿热血瘀证、脾肾气虚兼湿聚血瘀证、脾肾阳虚兼血瘀证、中药熏洗、服用中药患者DKD预后情况比较,差异有统计学意义(P<0.05)。多因素COX回归分析结果表明,年龄[HR(95%CI)=2.52(1.92,3.30)]、DKD病程[HR(95%CI)=1.62(1.09,2.42)]、吸烟史[HR(95%CI)=1.61(1.13,2.29)]、饮酒史[HR(95%CI)=1.41(1.01,1.95)]、脑血管病[HR(95%CI)=1.33(1.01,1.75)]、糖尿病眼病[HR(95%CI)=1.43(1.13,1.82)]、SUA[HR(95%CI)=1.72(1.26,2.33)]、24 h-UTP[HR(95%CI)=1.48(1.14,1.91)]、脾肾气虚兼湿聚血瘀证[HR(95%CI)=2.22(1.44,3.43)]与DKD发生终点事件的风险关系密切(P<0.05),服用中药[HR(95%CI)=2.57(2.00,3.31)]能够减少终点事件的发生(P<0.05)。结论年龄、DKD病程、吸烟史、饮酒史、脑血管病、糖尿病眼病、SUA、24 h-UTP、脾肾气虚兼湿聚血瘀证是影响DKD患者预后的危险因素,而服用中药治疗为其保护因素。

激素治疗慢性肾脏病进展高风险IgA肾病患者的预后分析——一项回顾性研究

背景IgA肾病(IgAN)是世界范围内常见的原发性肾小球肾炎之一,目前糖皮质激素是否能改善慢性肾脏病(CKD)进展高风险IgAN患者肾脏预后尚无明确结论。目的本研究旨在探讨激素治疗对CKD进展高风险IgAN患者的治疗反应及肾脏预后的影响。方法回顾性纳入2017年1月—2021年10月于郑州大学第一附属医院就诊的CKD进展高风险IgAN患者。根据是否进行激素治疗将患者分为激素治疗组和支持治疗组,采用倾向匹配法按照性别、年龄、24 h尿蛋白定量、估算肾小球滤过率(eGFR)对患者进行1∶1匹配筛选病例,收集患者的临床及病理资料,记录患者治疗1年内疾病缓解情况及不良反应发生情况。以开始支持治疗的日期作为随访起点,随访至2022-10-31,主要终点事件定义为:进展为终末期肾脏病(ESRD)或接受透析治疗。复合终点事件定义为:eGFR较基线持续下降超过30%或进入ESRD或接受透析或患者死亡;运用Kaplan-Meier法绘制生存曲线,并采用Log-rank检验比较两组患者主要/复合终点事件累积发生率的差异。运用Cox比例风险回归分析探究影响CKD进展高风险IgAN患者预后的可能因素。结果共有236例原发性IgAN患者符合纳入标准,经过1∶1匹配,激素治疗组97例与支持治疗组97患者匹配成功,两组基线数据匹配均衡。激素治疗组患者完全缓解率、部分缓解率均高于支持治疗组(χ^(2)=6.171,P=0.013;χ^(2)=3.973,P=0.046)。中位随访时间为18.00(9.75,28.00)个月。Kaplan-Meier生存分析结果显示,激素治疗组的主要终点事件累积发生率低于支持治疗组(χ^(2)=4.495,P=0.034);激素治疗组的复合终点事件累积发生率低于支持治疗组(χ^(2)=4.419,P=0.036)。符合纳入标准的236例患者中有177例中等量蛋白尿患者,采用倾向匹配法按照性别、年龄、24 h尿蛋白定量、eGFR对激素治疗和支持治疗的177例患者进行1∶1匹配后,激素治疗中等量蛋白尿者和支持治疗中等量蛋白尿者各有76例患者匹配成功。Kaplan-Meier生存曲线结果显示,激素治疗中等量蛋白尿者的主要终点事件累积发生率低于支持治疗中等量蛋白尿者(χ^(2)=4.127,P=0.042);激素治疗中等量蛋白尿者的复合终点事件累积发生率低于支持治疗中等量蛋白尿者(χ^(2)=4.934,P=0.026)。多因素Cox比例风险回归分析结果显示血红蛋白(HR=0.982)、血肌酐(HR=1.019)、eGFR(HR=1.020)、24 h尿蛋白定量(HR=1.205)是影响CKD进展高风险IgAN患者发生主要终点事件的影响因素(P<0.05)。激素治疗组感染发生率高于支持治疗组(P<0.05)。结论在CKD进展高风险IgAN肾病患者中,与单纯支持治疗相比,激素治疗可以显著提升肾脏缓解率,降低肾功能下降、肾衰竭风;但仍需警惕其不良反应的发生。

基于KPCA和WPHM的滚动轴承可靠性评估与寿命预测

为了评估滚动轴承的可靠性和预测剩余使用寿命,选取能够反映性能退化过程的特征参数作为寿命预测模型的输入参数,提出一种基于核主元分析(kernel principal component analysis,简称KPCA)和威布尔比例故障率模型(Weibull proportional hazards model,简称WPHM)的方法。首先,提取滚动轴承全寿命周期的时域、频域及时频域等多特征参数,从中筛选出有效的特征参数,构建高维相对特征集;其次,进行核主元分析,选取能够反映轴承全寿命周期性能退化过程的核主元,进而作为WPHM的协变量来进行可靠性评估和剩余寿命预测。通过滚动轴承全寿命试验,验证了该方法能够对轴承进行准确的可靠性评估和剩余寿命预测,以提供及时的维修决策。同时,由于提取的是相对特征,降低了同种轴承间在制造、安装及工况的差异,增强了该方法的适用性和稳定性。

基于比例风险模型的飞机部件剩余寿命预测

为准确预测飞机部件的剩余寿命,在对某航空公司最近4年的163架波音B737 NG型号飞机的维修数据进行分析的基础上,提出基于比例风险模型的飞机部件剩余寿命预测方法。通过估计部件装拆间隔飞行时间对应的寿命分布,计算部件在当前时刻对应的可靠度;对部件的维修数据进行分析,筛选出影响部件寿命的主要因素;据此预测部件的剩余寿命。通过实例分析,部件的累计飞行时间、飞机的机龄以及飞机的运行环境等均为影响部件寿命的重要因素。实验结果表明,基于比例风险模型的预测结果较其它预测模型在3个评价指标上均取得了最好效果。

一种基于PHM考虑老化和设备状态的油浸式变压器故障率模型

比例故障率模型(Proportional hazard model,PHM)中的故障率函数包含基准故障率函数和连接函数,前者表征设备的一般老化,后者描述设备状态的影响,对不同影响因素(协变量)进行量化。基于PHM提出了一种综合考虑老化和设备状态的油浸变压器故障率模型,基准故障率函数采用常用的温升老化模型,连接函数中的协变量选择了能够全面客观反映设备状况的油中溶解气体信息。推导了故障前时间的概率密度分布并给出了使用极大似然估计拟合参数的方法。算例证明了拟合方法的正确性,结果分析表明提出的模型具有正确合理表征故障率的能力,并且能有效表征变压器维护操作对故障率的影响。

基于生命八要素的心血管健康评分与新发心房颤动的关联研究:大样本长期随访研究

背景近年来全球心房颤动(以下简称房颤)的患病率持续升高,房颤增加了卒中、心力衰竭、心肌梗死、慢性肾病等疾病的发病风险。研究证实高血压、糖尿病、吸烟、阻塞性睡眠呼吸暂停、肥胖和久坐等是房颤发生的危险因素。而这些因素多数是美国心脏协会提出的“生命八要素”(LE8)的范畴。目的探讨基于LE8的心血管健康(CVH)评分与房颤的关联。方法选取2006年6月—2007年10月河北省唐山市开滦集团职工健康体检人群91131名为研究对象。LE8评分根据美国心脏协会制订的算法评估,结合开滦研究实际情况形成LE8开滦研究版本,包括4个健康行为(饮食、体育活动、烟草暴露和睡眠)和4个健康因素(BMI、血脂、血糖和血压)。依据LE8评分将研究对象分为3组:LE8评分<50分为低CVH组(8407名),50分≤LE8评分<80分为中CVH组(73493名),LE8评分≥80分为高CVH组(9231名)。以研究对象首次参加开滦体检时间为随访起点,每年随访1次,以发生房颤为终点事件,随访终点时间为发生房颤或随访结束时间(2020-12-31)。采用Kaplan-Meier生存曲线分析不同组新发房颤累积发病率,并进行Log-rank检验比较组间差异;采用Cox比例风险回归分析探讨不同LE8评分分组及单个因素评分对新发房颤发病风险的影响。结果3组研究对象年龄、性别、受教育程度、家庭人均月收入、饮酒史以及LE8评分比较,差异均有统计学意义(P<0.001)。随访中新发房颤1088例,其中低CVH组新发房颤133例(1.58%),中CVH组新发房颤883例(1.20%),高CVH组新发房颤72例(0.78%);中位随访时间15.0(14.7,15.2)年;3组研究对象新发房颤累积发病率比较,差异有统计学意义(P<0.0001)。校正年龄、性别、受教育程度、家庭人均月收入、饮酒史后进行Cox比例风险回归分析结果显示,与低CVH组相比,中CVH组(HR=0.697,95%CI=0.579~0.841,P<0.001)、高CVH组(HR=0.609,95%CI=0.454~0.816,P=0.001)均可降低新发房颤的发病风险;LE8评分升高可降低新发房颤的发病风险(HR=0.859,95%CI=0.804~0.918,P<0.001);LE8单个因素BMI评分(HR=0.762,95%CI=0.717~0.809,P<0.001)、血压评分(HR=0.824,95%CI=0.776~0.876,P<0.001)与新发房颤发病风险呈负相关。结论CVH的LE8评分与新发房颤的发病风险呈负相关,且LE8单个因素BMI评分、血压评分与新发房颤发病风险均呈负相关。

基于PHM的发动机旋转部件状态维修决策研究

发动机旋转部件是发动机的关键部件,部队中经常出现由于发动机旋转部件故障而导致的重大飞行事故。详细介绍了威布尔比例风险模型,在参数估计时采用了极大似然估计方法估计出模型中的参数。然后以可靠度为要求,预测装备的剩余寿命,从而指导实施维修决策。最后选择发动机某类轴承为例,利用比例风险模型对其进行了维修决策研究。

高血压人群年龄及体重指数对癌症发病共同作用的回顾性队列研究

目的在上海市闵行区高血压人群中,探究年龄和体重指数(body mass index,BMI)对癌症发生的共同作用。方法研究对象为2007—2015年进入上海市闵行区电子健康信息系统的未患癌症的212394名高血压患者。将年龄、BMI以平滑函数形式纳入广义加性Cox比例风险模型,用双变量响应模型构建曲面图使结果可视化,全面分析两者对癌症发生的联合效应。结果截至2018年12月31日,累计22141名高血压患者新发癌症。年龄与癌症发生风险整体呈线性趋势,而BMI与癌症发生风险整体呈“U”型,BMI在26 kg/m^(2)左右时癌症发生风险最低。不同BMI下,随着年龄增大,癌症发生风险均增加;不同年龄下,BMI与癌症发生风险的关联不同:青年人群(20~44岁)中BMI与癌症发生风险无明显关联,中老年人群(≥45岁)中BMI与癌症发生风险呈“U”型关联,BMI在26 kg/m^(2)左右时癌症发生风险最低。结论建议高血压人群控制BMI在合理范围内,特别是中老年人群,以减少癌症发生。