Nonparametric estimation for hazard rate monotonously decreasing system

Estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric estimator is put forward. The estimator is based on the kernel function method and optimum algorithm. Numerical experiment shows that the method is accurate enough and can be used in many cases.

软件可靠性评价的Hazard Rate模型

研究软件的可靠性问题，首先要考虑如何测试与评价，作为基础的信息和数据，主要是在各开发阶段通过调试发现。介绍了一类比较简单实用的软件可靠性评价模型，并给出了解析方法。

Hazard Rate Function Estimation Using Weibull Kernel

In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.

L0 Regularization for the Estimation of Piecewise Constant Hazard Rates in Survival Analysis

In a survival analysis context, we suggest a new method to estimate the piecewise constant hazard rate model. The method provides an automatic procedure to find the number and location of cut points and to estimate the hazard on each cut interval. Estimation is performed through a penalized likelihood using an adaptive ridge procedure. A bootstrap procedure is proposed in order to derive valid statistical inference taking both into account the variability of the estimate and the variability in the choice of the cut points. The new method is applied both to simulated data and to the Mayo Clinic trial on primary biliary cirrhosis. The algorithm implementation is seen to work well and to be of practical relevance.

Characterizations on Heavy-tailed Distributions by Means of Hazard Rate

Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline F}( x )/\int_x^\infty {\overline F}( u )du $, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.

APPROACH OF FIVE-YEAR-AVERAGE HAZARD RATES FOR THE BREAST CANCER PATIENTS AND ANALYSES OF PROGNOSTIC FACTORS-AN APPLICATION OF COX REGRESSION MODEL

Objective: To compare with fiveyear survival after surgery for the 116 breast cancer patients treated at the First Teaching Hospital (FTH) and the 866 breast cancer patients at Hpital du SaintSacrement (HSS). Methods: Using Cox regression model, after eliminating the confounders, to develop the comparison of the fiveyear average hazard rates between two hospitals and among the levels of prognostic factors. Results: It has significant difference for the old patients (50 years old or more) between the two hospitals. Conclusion: Tumor size at pathology and involvement of lymph nodes were important prognostic factors.

An Adaptive Approach for Hazard Regression Modeling

Regression models for survival time data involve estimation of the hazard rate as a function of predictor variables and associated slope parameters. An adaptive approach is formulated for such hazard regression modeling. The hazard rate is modeled using fractional polynomials, that is, linear combinations of products of power transforms of time together with other available predictors. These fractional polynomial models are restricted to generating positive-valued hazard rates and decreasing survival times. Exponentially distributed survival times are a special case. Parameters are estimated using maximum likelihood estimation allowing for right censored survival times. Models are evaluated and compared using likelihood cross-validation (LCV) scores. LCV scores and tolerance parameters are used to control an adaptive search through alternative fractional polynomial hazard rate models to identify effective models for the underlying survival time data. These methods are demonstrated using two different survival time data sets including survival times for lung cancer patients and for multiple myeloma patients. For the lung cancer data, the hazard rate depends distinctly on time. However, controlling for cell type provides a distinct improvement while the hazard rate depends only on cell type and no longer on time. Furthermore, Cox regression is unable to identify a cell type effect. For the multiple myeloma data, the hazard rate also depends distinctly on time. Moreover, consideration of hemoglobin at diagnosis provides a distinct improvement, the hazard rate still depends distinctly on time, and hemoglobin distinctly moderates the effect of time on the hazard rate. These results indicate that adaptive hazard rate modeling can provide unique insights into survival time data.

Adaptive Conditional Hazard Regression Modeling of Multiple Event Times

Recurrent event time data and more general multiple event time data are commonly analyzed using extensions of Cox regression, or proportional hazards regression, as used with single event time data. These methods treat covariates, either time-invariant or time-varying, as having multiplicative effects while general dependence on time is left un-estimated. An adaptive approach is formulated for analyzing multiple event time data. Conditional hazard rates are modeled in terms of dependence on both time and covariates using fractional polynomials restricted so that the conditional hazard rates are positive-valued and so that excess time probability functions (generalizing survival functions for single event times) are decreasing. Maximum likelihood is used to estimate parameters adjusting for right censored event times. Likelihood cross-validation (LCV) scores are used to compare models. Adaptive searches through alternate conditional hazard rate models are controlled by LCV scores combined with tolerance parameters. These searches identify effective models for the underlying multiple event time data. Conditional hazard regression is demonstrated using data on times between tumor recurrence for bladder cancer patients. Analyses of theory-based models for these data using extensions of Cox regression provide conflicting results on effects to treatment group and the initial number of tumors. On the other hand, fractional polynomial analyses of these theory-based models provide consistent results identifying significant effects to treatment group and initial number of tumors using both model-based and robust empirical tests. Adaptive analyses further identify distinct moderation by group of the effect of tumor order and an additive effect to group after controlling for nonlinear effects to initial number of tumors and tumor order. Results of example analyses indicate that adaptive conditional hazard rate modeling can generate useful insights into multiple event time data.

Adaptive Conditional Hazard Regression Modeling of Multiple Event Times

Recurrent event time data and more general multiple event time data are commonly analyzed using extensions of Cox regression, or proportional hazards regression, as used with single event time data. These methods treat covariates, either time-invariant or time-varying, as having multiplicative effects while general dependence on time is left un-estimated. An adaptive approach is formulated for analyzing multiple event time data. Conditional hazard rates are modeled in terms of dependence on both time and covariates using fractional polynomials restricted so that the conditional hazard rates are positive-valued and so that excess time probability functions (generalizing survival functions for single event times) are decreasing. Maximum likelihood is used to estimate parameters adjusting for right censored event times. Likelihood cross-validation (LCV) scores are used to compare models. Adaptive searches through alternate conditional hazard rate models are controlled by LCV scores combined with tolerance parameters. These searches identify effective models for the underlying multiple event time data. Conditional hazard regression is demonstrated using data on times between tumor recurrence for bladder cancer patients. Analyses of theory-based models for these data using extensions of Cox regression provide conflicting results on effects to treatment group and the initial number of tumors. On the other hand, fractional polynomial analyses of these theory-based models provide consistent results identifying significant effects to treatment group and initial number of tumors using both model-based and robust empirical tests. Adaptive analyses further identify distinct moderation by group of the effect of tumor order and an additive effect to group after controlling for nonlinear effects to initial number of tumors and tumor order. Results of example analyses indicate that adaptive conditional hazard rate modeling can generate useful insights into multiple event time data.

THE ASYMPTOTICS OF THE INTEGRATEDSQUARE ERROR FOR THE KERNEL HAZARD RATEESTIMATORS WITH LEFT TRENCATED ANDRIGHT CENSORED DATA

A central limit theorem for the integrated square error (ISE) of the kernelhazard rate estimators is obtained based on left truncated and right censored data. Anasymptotic representation of the mean integrated square error (MISE) for the kernel hazardrate estimators is also presented.

LOCAL ASYMPTOTIC PROPERTIES OF HAZARD RATE ESTIMATORS FOR TRUNCATED AND CENSORED DATA

Functional laws of the iterated logarithm are obtained for cumulative hazard processes in the neighborhood of a fixed point when the data are subject to left truncation and right censorship. On the basis of these results the exact rates of pointwise almost sure convergence for various types of kernel hazard rate estimators are derived.

Comparison of Hazard-Rates Considering Fault Severity Levels and Imperfect Debugging for OSS

Software reliability model is the tool to measure the software reliability quantitatively. Hazard-Rate model is one of the most popular ones. The purpose of our research is to propose the hazard-rate model considering fault level for Open Source Software (OSS). Moreover, we aim to adapt our proposed model to the hazard-rate considering the imperfect debugging environment. We have analyzed the trend of fault severity level by using fault data in Bug Tracking System (BTS) and proposed our model based on the result of analysis. Also, we have shown the numerical example for evaluating the performance of our proposed model. Furthermore, we have extended our proposed model to the hazard-rate considering the imperfect debugging environment and showed numerical example for evaluating the possibility of application. As the result, we found out that performance of our proposed model is better than typical hazard-rate models. Also, we verified the possibility of application of proposed model to hazard-rate model considering imperfect debugging.

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.

泸定6.8级地震公路抢通保通方案

2022年9月5日,四川泸定发生6.8级地震,公路沿线诱发了大量的地质灾害,造成多处公路损坏或断道,极大地影响了抗震救灾工作。快速摸清震区公路网的受损情况和抢通保通难度,对震后救援至关重要。为此,对震区公路受损情况进行调查,会同地方交通部门完成公路的抢通保通任务。调查发现了507处受损点,公路灾害以崩塌滑坡为主,占总灾害的90%以上。公路灾害具有数量多、规模小、连片分布的特点,公路震害与地震烈度正相关,与断层距离、河流距离负相关。在不利因子组合下,公路震害程度明显加剧,局部位置的公路受损率可达到92.5%。在抢通保通阶段,利用龙头石及大岗山电站的库区水运资源,快速建立5处码头,建立起通往震中的生命通道,让应急队伍快速进入灾区,让伤员第一时间运送出来;灾后交通网的重建充分利用水运资源,不追求道路等级与路线指标,公路重建以提高公路的抗灾能力及韧性为目标。

基于高分辨格点数据东北水稻延迟型冷害风险评估及保险费率厘定

利用5km×5km空间分辨率3h时间分辨率的气象格点数据集,研究东北地区水稻延迟型冷害风险及其保险费率的厘定。基于东北地区1981-2010年5-9月平均温度的格点数据集和99个气象站的站点观测数据,以相关系数和均方根误差评价格点气象数据在东北地区的可用性。以日平均气温稳定通过10℃和18℃的日数作为获取水稻气候安全种植区域的指标,在水稻气候安全种植范围内,分析东北地区水稻延迟型冷害的空间分布特征,确定保险费率。结果表明,东北地区1981-2010年5-9月平均温度气象站点观测数据与格点数据的相关系数高,均方根误差小,表明格点数据在东北地区可用。水稻气候安全种植区域占东北的56.5%,主要分布在辽宁省、吉林省中西部、黑龙江省西南部和东北部、蒙东西部及东部与辽宁和吉林省接壤的区域。在水稻气候安全种植区内,水稻延迟型冷害发生频率呈南低北高,中间低东西高的分布特征,且重度延迟型冷害发生频率最高。低温冷害风险指数空间分布与之相似,内蒙古西部和东北部、黑龙江北部和吉林西部局部地区是风险指数的高值区。东北地区1981-2010年水稻延迟型冷害的天气指数保险费率在空间分布上与东北地区低温冷害风险指数的空间分布相似,呈南部低,北部高,中间低,东西高的特征,整个区域的保险费率在0.010~0.094,可为保险公司制定具体费率提供参考。

大倾角工作面飞矸冲击破碎特征研究

飞矸灾害长期威胁大倾角、急倾斜煤层长壁工作面人员和设备安全,单一飞矸迁移过程碰撞破碎衍生出大量“子矸”,其动力损害具有突发性,揭示冲击载荷作用下煤岩体破碎特征是准确掌握飞矸动力损害的重要前提。综合运用分离式霍普金森压杆试验、数值SHPB试验和物理模拟开展冲击载荷作用下煤岩体破碎特征与碎裂机制研究,得到以下主要结论:高速冲击作用下煤岩破坏模式分为相对完整、单一劈裂和完全粉碎,破碎程度随着加载应变率增加而增加,分形维数D与应变率呈对数函数关系。相同应变率水平,煤岩抗压强度越小分形破碎程度越高;煤岩分形维数D与其几何尺度负相关;圆盘和立方体煤岩分形维数D与应变率均呈对数函数关系。立方体煤岩累积碰撞作用下内部节理裂隙发育,应力波传播呈现弥散性,在边缘应力集中并诱发破坏,即不规则形状煤岩外缘易率先与主体破坏分离从而导致其球形度增加。相反,飞矸运动过程棱角处更易受到碰撞而承受直接应力冲击而产生局部崩解。研究成果可为大倾角、急倾斜煤层飞矸灾害防控实践中挡矸网形状以及网格大小的选择提供一定的科学指导。飞矸涉及材料、几何等多源不确定因素,内部层理、裂隙分布及发育程度受开采扰动影响较大,其破碎分形特征更加趋于复杂,下一步将考虑以上因素对飞矸破碎特征的影响。

基于风雨综合指数的广东省晚稻台风致灾危险性评估

利用1995—2022年登陆或影响广东省中南部16个地市的台风过程资料、气象站风雨资料以及晚稻单产数据,建立晚稻减产率测算模型和融合风、雨因子的晚稻台风致灾危险性评估模型,评估广东省中南部16个地市的晚稻台风致灾危险性。结果表明:(1)1995—2022年,每年平均有6.6个台风登陆或影响广东中南部地区,以0.8个·(10a)^(-1)的速率呈波动减少趋势。(2)晚稻减产率测算模型和台风致灾危险性评估模型可较好地反映各地市晚稻单产减产和台风致灾情况,特别是2002、2013、2017、2018年等台风重灾年表现极佳。(3)各地市晚稻生产受台风影响程度不一,其中湛江、阳江、江门、中山、珠海、汕尾是晚稻台风致灾高风险区,茂名、佛山、惠州、揭阳、汕头和潮州为中等风险区,云浮、肇庆、广州和东莞是低风险区。

钙质添加剂作用下废阴极炭还原红土镍矿脱毒机理研究

废阴极炭是铝电解工业生产过程中产生的固体废弃物,数量庞大,目前主要处理方法是堆存。废阴极炭成分主要是碳(60%~70%),还含有部分Na_(3) AlF_(6)、NaF、CaF_(2)及NaCN等,其中的氰化物和氟化物会对环境造成严重危害,属于危险废弃物。现已有利用废阴极炭替代碳质还原剂进行炼铁的研究,用来还原红土镍矿的相关研究还没有发现。本文以云南元江红土镍矿为原料,废阴极炭为还原剂,CaCO_(3)为添加剂,对废阴极炭还原红土镍矿的还原效果及固氟效果进行试验研究。试验结果表明:在废阴极炭的添加量14%、还原温度1250℃、还原时间75 min、CaCO_(3)添加量8%的较佳条件下,还原焙烧产物镍和铁品位分别为5.82%和66.23%,镍回收率为94.04%;固氟率为94.9%,此时毒性浸出溶液中F-浓度为30 mg·L^(-1),远小于100 mg·L^(-1)的排放要求;还原焙烧条件下,废阴极炭中的CN-生成CO_(2)和N_(2),F-以CaF_(2)形式留在焙烧矿中,且可作为助熔剂降低镍铁合金熔点,有利于后期焙烧矿的处理。本文研究为废阴极炭的无害化处理提供了一个新思路。

环境温度对锂离子电池爆炸参数影响

为探究在不同环境温度下锂离子电池触发热失控后的燃爆危险性,利用改进的20-L球装置测试了锂离子电池在不同初始环境温度和加热功率下触发热失控后的爆炸参数,对爆炸后的气体取样并分析气体成分。结果表明,当初始环境温度为25℃时,随着加热功率增加,电池更早发生燃爆,最大压升速率增大,电池质量损失增大,损毁更为严重;当初始环境温度为60℃时,最大压升速率由14.41 MPa/s增加至29.12 MPa/s,表明初始环境温度对爆炸参数的测试结果有显著影响;当初始环境温度为95℃时,最大压升速率基本一致,最大压力略有下降;爆炸后的气体中均存在CO和H2,其体积分数随着初始环境温度的增加而增加,表明锂离子电池热失控产物并未充分燃烧。研究结果有助于更为全面地评估锂离子电池的燃爆危险性,为锂离子电池的安全防护提供数据参考。

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

In general,simple subsystems like series or parallel are integrated to produce a complex hybrid system.The reliability of a system is determined by the reliability of its constituent components.It is often extremely difficult or impossible to get specific information about the component that caused the system to fail.Unknown failure causes are instances in which the actual cause of systemfailure is unknown.On the other side,thanks to current advanced technology based on computers,automation,and simulation,products have become incredibly dependable and trustworthy,and as a result,obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure.Therefore,because of its capacity to produce rapid and adequate failure data in a short period of time,accelerated life testing(ALT)is the most utilized approach in the field of product reliability and life testing.Based on progressively hybrid censored(PrHC)data froma three-component parallel series hybrid system that failed to owe to unknown causes,this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test(SSPALT).Failures of components are considered to follow a power linear hazard rate(PLHR),which can be used when the failure rate displays linear,decreasing,increasing or bathtub failure patterns.The Tempered random variable(TRV)model is considered to reflect the effect of the high stress level used to induce early failure data.The maximum likelihood estimation(MLE)approach is used to estimate the parameters of the PLHR distribution and the acceleration factor.A variance covariance matrix(VCM)is then obtained to construct the approximate confidence intervals(ACIs).In addition,studentized bootstrap confidence intervals(ST-B CIs)are also constructed and compared with ACIs in terms of their respective interval lengths(ILs).Moreover,a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper.Finally,real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.