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。

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.

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.

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.

Effect of flow rates of gases flowing through a coal bed during coal heating and cooling on concentrations of gases emitted and fire hazard assessment

The flow velocity of gases in gobs directly influences the kinetics and intensity of gaseous components release during heating and cooling of coal.The assessment of fire hazard is performed on the basis of concentrations of particular gases in a mine air.These concentrations differ in coal heating and cooling phase which was proven in the study.This paper presented the results of the experimental study on temperature distribution in a simulated coal bed in heating(50–250°C)and cooling(250–35°C)phases as well as its correlation to variations in concentration of gases released in these phases and flow rates of gases flowing through the coal bed.The research was performed on twenty-two samples of bituminous coals acquired from various coal beds of Polish coal mines.Considerable differences were observed between heating and cooling phases in terms of the concentrations of gases taken into account in calculations of self-combustion index.In the heating phase temperature increase resulted in the decrease of concentrations ratios of ethane,ethylene,propane,propylene and acetylene,while in the cooling phase these ratios increased systemically.The effect of air(in heating phase)and nitrogen(in cooling phase)flow rate on the self-ignition index CO/CO2 was also determined.

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.

基于锥形量热仪的氧化煤燃烧特性研究

为了研究氧化煤的燃烧特性,以朱集西煤矿1/3焦煤为研究对象,在不同预氧化温度(80℃、140℃、200℃)下对煤样进行氧化处理10 h,并以原煤为对照,利用锥形量热仪测试煤样的点燃时间、热释放速率、总热释放量等主要燃烧特征参数。结果表明:随着预氧化温度的提高,煤样点燃时间I_(TT)、CO气体变化呈现先减小后增大的趋势,热释放速率峰值P_(HRR)、总热释放量T_(HR)、CO_(2)气体变化、质量损失速率R_(ML)峰值呈现先增大后减小的趋势。结合测试数据,并计算出火灾增长指数G_(FI)和火灾性能指数P_(FI),得出氧化煤与原煤的火灾危险性程度大小关系为140℃氧化煤样>80℃氧化煤样>原煤>200℃氧化煤样。

Comparing rockfall hazard and risk assessment procedures along roads for different planning purposes

Hazard and risk assessment procedures of different types of rockfall were analyzed to compare their outcomes when they are applied to the same case study.Although numerous methodologies are available in literature,rockfall hazard and risk analyses are often limited to standard estimations,affected by a margin of uncertainty,especially when relevant engineering projects are about to be realized.Based on the design purpose,different types of approaches can be chosen among the qualitative and quantitative ones available in literature,which allow different levels of analysis.One of the main criticisms related to rockfall events is the risk affecting linear structures,such as road or railways,due both to their strategic relevance for trade and communications and to the great entity of the exposed value(traffic units)traveling along them.In this perspective,a comparison between the qualitative method known as Evolving Rockfall Hazard Assessment(EHRA),the semi-quantitative modified Rockfall Hazard Rating System(RHRS)and the quantitative Rockfall Risk Management(RoMa)approach is herein commented according to a practical application to a case study.It is the case of the rockfall threat along slopes crossed by a strategic road connecting two of the most known spots of eastern Sicily(Italy),at the Taormina tourist complex.Data were retrieved from both recent literature and technical surveys on field.Achieved results highlight how the approaches are affected by a different level of detail and uncertainty,arising also by some necessary assumption that must be taken into account,especially when mitigation measures or territory planning have to be designed.Achieved results can be also taken into account for similar studies worldwide,in order to choose the most suitable procedure based on the design purpose.This is indeed crucial in the perspective of the optimization of time and economic resources in the territorial planning practice.

Development of an aftershock occurrence model calibrated for Turkey and the resulting likelihoods

This paper presents the calibration of Omori’s aftershock occurrence rate model for Turkey and the resulting likelihoods. Aftershock occurrence rate models are used for estimating the probability of an aftershock that exceeds a specific magnitude threshold within a time interval after the mainshock. Critical decisions on the post-earthquake safety of structures directly depend on the aftershock hazard estimated using the occurrence model. It is customary to calibrate models in a region-specific manner. These models depend on rate parameters(a, b, c and p) related to the seismicity characteristics of the investigated region. In this study, the available well-recorded aftershock sequences for a set of Mw ≥ 5.9 mainshock events that were observed in Turkey until 2012 are considered to develop the aftershock occurrence model. Mean estimates of the model parameters identified for Turkey are a =-1.90, b = 1.11, c = 0.05 and p = 1.20. Based on the developed model, aftershock likelihoods are computed for a range of different time intervals and mainshock magnitudes. Also, the sensitivity of aftershock probabilities to the model parameters is investigated. Aftershock occurrence probabilities estimated using the model are expected to be useful for post-earthquake safety evaluations in Turkey.

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.

Studies on the flame propagation characteristic and thermal hazard of the premixed N2O/fuel mixtures

An experimental study was carried out to investigate the flame propagation and thermal hazard of the premixed N2O/fuel mixtures,including NH3,C3H8 and C2H4.The study provided the high speed video images and data about the flame locations,propagation patterns,overpressures and the quenching diameters during the course of combustion in different channels to elucidate the dynamics of various combustion processes.The onset decomposition temperature was determined using high-performance adiabatic calorimetry.It was shown that the order of the flame acceleration rate and thermal hazard was N2O/C2H4>N2O/C3H8>N2O/NH3.

Landslide Hazard Zonation Mapping in Ghat Road Section of Kolli Hills, India

Landslides are the most common natural disaster in hilly terrain which causes changes in landscape and damage to life and property. The main objective of the present study was to carry out landslide hazard zonation mapping on 1:50,000 scale along ghat road section of Kolli hills using a Landslide Hazard Evaluation Factor(LHEF) rating scheme. The landslide hazard zonation map has been prepared by overlaying the terrain evaluation maps with facet map of the study area. The terrain evaluation maps include lithology, structure, slope morphometry, relative relief, land use and land cover and hydrogeological condition. The LHEF rating scheme and the Total Estimated Hazard(TEHD) were calculated as per the Bureau of Indian Standard(BIS) guidelines(IS: 14496(Part-2) 1998) for the purpose of preparation of Landslide Hazard Zonation(LHZ) map in mountainous terrains. The correction due to triggering factors such as seismicity, rainfall and anthropogenic activities were also incorporated with Total Estimated Hazard to get final corrected TEHD. The landslide hazard zonation map was classified as the high, moderate and low hazard zones along the ghat road section based on corrected TEHD.

Landslide Hazard Mapping of Nagadhunga-Naubise Section of the Tribhuvan Highway in Nepal with GIS Application

The aim of this project was to prepare and study a hazard map of Nagadhunga-Naubise section of the Tribhuvan highway. This section lies in the Middle Mountain region of Nepal. For the preparation of the hazard map of the corridor three steps, initial study, field investigation, and data analysis and presentation were carried out. In the initial study, the collection of available data and review of the literature were done. The base map was then prepared from the topographical map. In the field investigation step, all information and maps prepared earlier in the initial study were verified by field check. In the final step, prepared and verified data were then analyzed for the hazard mapping. Topography (gradient, slope shape and slope aspect), geology, drainage and land-use were considered to be the major influencing factors in the slope stability. Pre-assigned hazard rating method was used for hazard mapping of the study area. The area was divided into equal facets. Then ratings of responsible factors to the hazard were assigned to each facet and overlaid based upon a predetermined rating scheme. Total estimated hazard was the sum of these ratings for each overlay. Hazard map was prepared by using three categories as low hazard, medium hazard and high hazard. The Geographic Information System (GIS) was the main tool for the data input, analysis, and preparing of the final hazard map. The hazard map showed the areas of different hazard potential classes of;“low” with 32% portion, “Medium” with 51%, and “high” with 17% portion.

Rockfall hazard assessment in a natural and historical site: The case of ancient Kilistra settlement(Konya), Turkey

The ancient Kilistra settlement is a natural,historical and cultural heritage site in Central Anatolia(Turkey), which makes it an attractive destination for tourists. However, the settlement located on a hill with steep hillsides has suffered from rockfall events,causing the destruction of some historical buildings.The rockfall risk in the region continues to create a serious danger today for land users and visitors during uncontrolled tourist visits. This paper offers an assessment of rockfall hazard for the ancient Kilistra settlement based on experimental investigation and numerical analyses. For the study, comprehensive field studies were carried out, including the identification of slope profiles, scanline surveys on discontinuities and stability analysis of the slopes. The location and size of the fallen, detached and hanging blocks were also identified. Geomechanical properties of the geological units were determined, and also the rockfall risk rating method was applied for the evaluation of the rockfall hazard risk. Runout distance, bounce height, kinetic energy as well as the velocity of the detached and hanging blocks were determined by using twodimensional rockfall analyses. Based on the results from the rockfall analyses, possible rockfall-based danger zones have been defined for the ancient Kilistra settlement and its close vicinity. The results of this study point at an immediate necessity for the installation of support systems. Findings of the study also offer preliminary data for the description of risk administration strategies and also provide scientific contribution to the study of the hazard and risk resulting from rockfall phenomena.

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.

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.