指数分布场合下竞争失效产品加速寿命试验的Bayes估计

在指数分布场合下，本文给出了竞争失效产品加速寿命试验（恒加试验，步加试验）一种新的Bayes估计，这种估计方法能充分利用产品各失效机理在正常应力水平下的先验信息．最后利用Monte－Carlo方法对这种估计作了模拟比较．     

竞争失效产品定时截尾的简单恒加寿命试验的优化设计

本文在指数分布场合下研究了具有竞争失效机理产品的简单恒加试验的优化设计问题,得出了一系列与简单步加试验相对应的结果．这里最优性是指正常应力水平下各失效机理的对数平均寿命的极大似然估计（MLE）的渐进方差之和的极小化．     

具有竞争失效机理产品的简单步如寿命试验统计分析

本文在指数分布场合下讨论了具有竞争失效机理产品的简单步加寿命试验的统计分析，并且研究了失效机理对正常应力下平均寿命估计的影响，最后，我们通过Ｍｏｎｔｅ－Ｃａｒｌｏ试验说明本文方法的可行性。     

指数分布场合下竞争失效产品的恒定应力加速寿命试验的统计分析

本文在指数分布场合下讨论了竞争失效产品的恒加试验的统计分析，研究了失效机理对产品在正常应力水平下平均寿命估计的影响，最后给出了一实际例子。     

竞争失效产品定量截尾的简单恒加寿命试验的优化设计

本文在指数分布场合下研究了具有竞争失效机理产品的简单恒加试验的优化设计问题，得出了一系列与简单步加试验相对应的结果，这里最优性是指正常应力水平下各失效机理的对数平均寿命的极大似然估计（ＭＬＥ）的渐进方差之和的极小化。     

竞争失效产品步进应力加速寿命试验的优化设计

本文在一般ｋ个未知参数的加速寿命方程下,以各失效机理的对数平均寿命的ＭＬＥ的渐进方差之和最小为准则,解决了指数分布场合下具有ｐ（ｐ≥１）个竞争失效机理的产品,ｋ个应力情况下的步加试验的优化设计问题．本文既可以看成是Ｄ．Ｓ．Ｂａｉ,Ｙ．Ｒ．Ｃｈｕｎ（１９９１）的推广,又可以看成是程依明（１９９４）的推广．     

竞争失效产品恒定应力加速寿命试验的优化设计

本文在一般k个未知参数的加速寿命方程下，以各失效机理的对数平衡寿命的MLE的渐近方差之和最小为准则，解决了指数分布场合下具有p（p≥1）个竞争机理的产品，k个应力情况下的桓加试验的优化设计问题，对它的结论从不同侧面特殊化，得到一系列推论，并与D．S．Bai,Y.R.C(1991),D.S.Bai,M.S.Kim,S.H.Lee(1989），R.Miller,W.B.Nelson(1983），程依明（1994）等步加试验优化设计所得结论比较，可知所有结论都是对应的且有些结论是完全一致的。     

一个贝叶斯离散可靠性增长模型(英)

本文提出了一个贝叶斯离散可靠性增长模型．假设一个产品的开发过程由m个阶段组成．在每一个阶段中，都进行一个成败型寿命试验．在试验结束后，再分析其结果，然后对产品进行修改或重新设计，以期提高产品的可靠性．如果产品的失效可分为不可修复的以及可修复的两种．假定产品的不可修复失效概率在各个阶段中保持相同，而可修复失效概率随着试验阶段的增加而减少．     

电容器加速寿命试验数据的统计分析

一、引言某厂生产的电容器是高可靠产品,在额定条件下寿命很长,难以获得失效数据,为了分析此产品的失效机理,测定其可靠性指标,安排了五组恒定双应力加速寿命试验(恒双加试验),进行了18000小时试验,除在第一组,第二组分别有6个和4个失效外,其余三组均无失效,数据见表1。这种情况给数据的统计分析带来困难,进而考虑对后三组样品继续进行电压步进应     

步进应力加速寿命试验方法初探

加速寿命试验就是在不改变元器件失效机理的前提下,提高可能引起元器件失效的那些应力促使元器件加速失效,从而可以在较短的时间内测出失效率,找出寿命与温度或电压的关系(加速系数)再用外推法来预计实际使用条件下的失效率,以达到加速估计元器件的可靠性的目的。加速寿命试验按照施加应力方式的不同分为恒定应力加速寿命试验,步进应力加速寿命试验,序进应力加速寿命试验三种类型.其中恒定应力加速寿命试验方法更为成熟已形     

竞争失效产品加速寿命试验的统计分析

本文讨论了指数分布场合竞争失效产品恒定应力加速寿命试验和步进应力加速寿命试验的参数估计。对常用的最大似然估计作了改进，并用大样本结果和模拟比较说明了改进的有效性。     

竞争失效产品加速寿命试验的参数估计

讨论了指数分布场合竞争失效产品加速寿命试验的参数估计,对常用极大似然估计作了一些改进,从而使改进后的参数估计在均方误差意义下更优.     

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在已有讨论竞争失效数据统计分析的文献中, 大多数都假设失效机理之间相互独立. 本文使用copula作为连接函数来考查加速寿命试验中的竞争失效模型. 通过模拟, 把失效机理相关时得到的结果与失效机理独立时得到的结果做了比较. 最后分析了文献中的一个实际数据.     

Dependent competing risks: Cause elimination and its impact on survival

The dependent competing risks model of human mortality is considered, assuming that the dependence between lifetimes is modelled by a multivariate copula function. The effect on the overall survival of removing one or more causes of death is explored under two alternative definitions of removal, ignoring the causes and eliminating them. Under the two definitions of removal, expressions for the overall survival functions in terms of the specified copula (density) and the net (marginal) survival functions are given. The net survival functions are obtained as a solution to a system of non-linear differential equations, which relates them through the specified copula (derivatives) to the crude (sub-) survival functions, estimated from data. The overall survival functions in a model with four competing risks, cancer, cardiovascular diseases, respiratory diseases and all other causes grouped together, have been implemented and evaluated, based on cause-specific mortality data for England and Wales published by the Office for National Statistics, for the year 2007. We show that the two alternative definitions of removal of a cause of death have different effects on the overall survival and in particular on the life expectancy at birth and at age 65, when one, two or three of the competing causes are removed. An important conclusion is that the eliminating definition is better suited for practical use in competing risks’ applications, since it is more intuitive, and it suffices to consider only positive dependence between the lifetimes which is not the case under the alternative ignoring definition.     

Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues

Cure rate models offer a convenient way to model time-to-event data by allowing a proportion of individuals in the population to be completely cured so that they never face the event of interest (say, death). The most studied cure rate models can be defined through a competing cause scenario in which the random variables corresponding to the time-to-event for each competing causes are conditionally independent and identically distributed while the actual number of competing causes is a latent discrete random variable. The main interest is then in the estimation of the cured proportion as well as in developing inference about failure times of the susceptibles. The existing literature consists of parametric and non/semi-parametric approaches, while the expectation maximization (EM) algorithm offers an efficient tool for the estimation of the model parameters due to the presence of right censoring in the data. In this paper, we study the cases wherein the number of competing causes is either a binary or Poisson random variable and a piecewise linear function is used for modeling the hazard function of the time-to-event. Exact likelihood inference is then developed based on the EM algorithm and the inverse of the observed information matrix is used for developing asymptotic confidence intervals. The Monte Carlo simulation study demonstrates the accuracy of the proposed non-parametric approach compared to the results attained from the true correct parametric model. The proposed model and the inferential method is finally illustrated with a data set on cutaneous melanoma.     

Reliability modeling for mutually dependent competing failure processes due to degradation and random shocks

Many systems are subject to two mutually dependent competing risks namely degradation and random shocks, and they can fail due to two competing modes of failure, soft and hard failure. Soft failure occurs when the total degradation performance, including continuous degradation and sudden degradation increments caused by random shocks, exceeds a certain critical threshold level. Hard failure occurs when the magnitude of any shock (extreme shock model) or the accumulated damage of shocks (cumulative shock model) is beyond some strength threshold level, which is affected by the temporal degradation performance. From viewpoints of Stress-Strength models and Cumulative damage/shock model, a realistic reliability model is developed in this article for mutually dependent competing failure processes due to degradation and random shocks. Finally, a numerical example of Micro-Electro-Mechanical System (MEMS) is conducted to illustrate the implementation and effectiveness of the proposed model.     

Reliability evaluation based on a dependent two-stage failure process with competing failures

This paper evaluates system reliability performance based on a dependent two-stage failure process with competing failures. The failure process of the system can be divided into two stages, i.e., the defect initialization stage, and the defect development stage. Dependence between these two stages is reflected in the fact that they share the same shock process modeled by a nonhomogeneous Poisson process. The impact of shock damage on system failure behavior is characterized by random hazard rate increments of the two stages. Based on practical failure behavior of industrial systems, we consider two typical and competing failure modes, defect-based failure and duration-based failure. Defect-based failure occurs when a defect reaches the damage threshold and duration-based failure is triggered when the duration in defective state is larger than a time threshold. We derive some results on system reliability and show that, with different parameter settings, our model reduces to several classic competing risk models. Finally, a detailed illustrative example of an oil pipeline system is given to demonstrate the applicability of the proposed model.     

A U-statistic test in competing risk models

We consider a situation in which systems are subject to failure from competing risks or could be censored from an independent censoring process. A procedure, based on a U-statistic, is proposed for testing the equality of two failure rates in the competing risks set. Under independence assumptions, the asymptotic distribution of the statistic is given and used to construct the test. To cite this article: N. Molinari, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Modelling the joint distribution of competing risks survival times using copula functions

The problem of modelling the joint distribution of survival times in a competing risks model, using copula functions, is considered. In order to evaluate this joint distribution and the related overall survival function, a system of non-linear differential equations is solved, which relates the crude and net survival functions of the modelled competing risks, through the copula. A similar approach to modelling dependent multiple decrements was applied by Carriere [Carriere, J., 1994. Dependent decrement theory. Transactions, Society of Actuaries XLVI, 45-65] who used a Gaussian copula applied to an incomplete double-decrement model which makes it difficult to calculate any actuarial functions and draw relevant conclusions. Here, we extend this methodology by studying the effect of complete and partial elimination of up to four competing risks on the overall survival function, the life expectancy and life annuity values. We further investigate how different choices of the copula function affect the resulting joint distribution of survival times and in particular the actuarial functions which are of importance in pricing life insurance and annuity products. For illustrative purposes, we have used a real data set and used extrapolation to prepare a complete multiple-decrement model up to age 120. Extensive numerical results illustrate the sensitivity of the model with respect to the choice of copula and its parameter(s).     

Conditional laplace transforms for bayesian nonparametric inference in reliabity theory

In order to apply nonparametric meyhods to reliability problems, it is desibrable to have available priors over a broad class of survival distributions.In the paper, this is achieved by taking the failure rate function to be the sum oof a nonnegative stochastic process with increasing sample patjhs and a process with decreasing sample paths. This approach produces a prior which chooses an absolutely survival distribution that can have an IFR, DFR, or U-shapped failure rate. Posterior Laplace transforms of the failure rate are obtained based on survival data allows censoring. Bayes estimates of the failure rate as well as the lifetime distribution are then calculated from these posterior Laplace transforms. This approach is also applied to a competing risks model and the proportional hazards model of Cox.