应用威布尔过程模型统计分析中的几个问题

对威布尔过程应用中的若干问题作了进一步探讨:如威布尔过程与威布尔分布;具有切断的故障数据处理;威布尔过程的拟合优度检验;可修系统可靠性评估参数;多个同型系统参数一致性检验等.     

温度应力下的加速度计贮存寿命评定

针对加速度计长期自然贮存于不同温度应力下,试验数据为成败型不完全数据,贮存寿命无法准确评估的难题,运用极小x~2估计和拟合优度检验相结合的方法来拟合产品的失效分布,通过Matlab软件中的fminsearch函数确定了不同温度下的分布参数,采用最小二乘法求解了参数与温度之间的函数关系,提出了该类型加速度计基于不同温度的失效分布函数,并预测了正常温度下贮存寿命为16.8 a。结果表明:提出的加速度计失效分布函数更能反映加速度计在不同温度下的贮存寿命变化规律,在工程研究领域具有一定的实用价值。     

某装备系统机电产品贮存可靠性评估方法

针对某装备系统机电产品长期自然贮存环境下可靠性无法准确评估的难题,提出了一种基于极小χ2估计和拟合优度检验的贮存可靠性评估方法,并对试验数据进行了分析、计算和处理。该方法通过拟合产品的失效分布来确定其分布函数参数,并根据确定的分布函数来预测产品的贮存可靠寿命。与现有的评估方法相比,采用该方法确定的分布函数更能反映产品的可靠性变化规律,对机电产品的贮存寿命预测结果更加合理,在工程研究领域具有很好的实用价值。     

通用的雷达目标RCS统计建模方法

针对传统的雷达目标RCS起伏统计模型都是基于厘米波频段RCS建立的问题,提出了一种更为通用的基于混合正态分布的RCS统计建模方法。对典型隐身飞机的仿真数据和某型教练机的实测数据进行统计分析,拟合优度检验结果表明:混合正态分布在米波频段和厘米波频段均能实现最佳的拟合优度。研究成果可用于拓展雷达检测理论,为雷达总体设计提供理论支撑。     

基于退化量分布的某型电连接器寿命预测方法

使用基于退化量分布的方法对某型电连接器进行了寿命预测,得到了其可靠度曲线并预测出其平均寿命为398 895 h。通过对各加速应力水平下所有样品的退化量进行拟合优度检验,得出退化量在各测量时刻最优服从正态分布,进而确定了退化量均值、方差与温度应力之间的关系。为了提高估计精度,使用极大似然法进行整体统计推断获取未知参数的估计值,并基于参数值与温度的关系外推出样品在工作温度下的可靠度函数。通过可靠度曲线的比较,获知样品寿命较好地服从对数正态分布,并基于此进行了平均寿命预测。     

一种新的Weibull分布恒定应力加速寿命试验分析方法

分析了Weibull分布恒定应力加速寿命试验常用的二步分析方法存在的不足 ,建立了一种新的构造数据分析方法。考虑到分布参数的相关性 ,该方法引入了Weibull分布特征寿命参数的二次估计 ,在模型拟合优度上高于原来的二步分析方法 ,使分析精度得到了改善。同时 ,该方法避免了原来二步分析方法的查表过程 ,便于软件实现和工程实际应用。     

直升机雷达回波的动态特性分析

依据实测的直升机动态回波数据,分析了直升机机身的重点散射源及散射特征,应用Kolmogorov拟合优度检验方法及三种标准分布模型,研究了直升机动态RCS的统计特征,得到了动态RCS对各模型的拟合效果以及X2模型随视向角的半自由度分布,最后通过建立一简单的旋翼叶片散射模型并对散射中心的周期性运动调制效应进行了讨论,分析计算了直升机动态回波的谐波特征.     

探索性作战仿真实验重复次数控制研究

探索性作战仿真实验相比自然科学实验有更为复杂的不确定性和响应高阶分布特性,传统基于已知分布类型的实验重复次数控制方法不再适用,必须寻找新的非参数的控制方法.首先分析了探索性作战仿真实验的复杂特性,其次针对精确评估和优劣判断两种具体控制需求,介绍了基于Bootstrap估计和置换检验的实验重复次数控制方法,最后通过综合应用这两种方法的寻优实验实例,验证了方法的有效性.     

轻武器寿命可靠性模型研究

为轻武器寿命可靠性评定提供理论依据,运用经典的可靠性理论,将轻武器装备寿命试验归结为可修复系统的有替换定时截尾试验,通过分析某型机枪的寿命试验数据,对母体寿命可能的分布类型作出假设,选择χ2检验法对假设进行拟合优度检验,利用最小二乘法得出对应分布的线性相关系数,通过比较确定母体分布类型,建立了该型机枪寿命的可靠性数学模型,对同类轻武器装备的可靠性指标评定提供了一定的参考。     

基于叠合度的维修性多源数据融合方法

针对装备维修性试验数据样本量不足的问题,采用了数据融合方法进行扩充数据样本量,通过建立折合模型对多源先验数据进行转换,解决了与现场数据差异较大难以实现数据融合的问题,采用了改进的Bayes Bootstrap法对多源数据的分布参数进行拟合,建立基于叠合度的数据融合模型,对装备维修性多源先验数据进行融合,结合某型坦克试验数据进行算例分析,证明了该方法的可行性。     

Log‐concave and concave distributions in reliability

Nonparametric classes of life distributions are usually based on the pattern of aging in some sense. The common parametric families of life distributions also feature monotone aging. In this paper we consider the class of log‐concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log‐normal, Pareto, and Gompertz distributions) are log‐concave, while the remaining life of maintained and old units tend to have a concave distribution. The classes of concave and log‐concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operations, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 419–433, 1999     

恒定应力加速寿命试验的非参数统计方法

在恒定应力加速寿命试验 (简称恒加试验 )的统计分析中 ,非参数统计方法具有一定的实际价值 .在一定的假定下 ,文中给出了两种新估计 ,并证明了它们的优良性     

Pairwise model discrimination with applications in lifetime distributions and degradation processes

Reliability data obtained from life tests and degradation tests have been extensively used for purposes such as estimating product reliability and predicting warranty costs. When there is more than one candidate model, an important task is to discriminate between the models. In the literature, the model discrimination was often treated as a hypothesis test and a pairwise model discrimination procedure was carried out. Because the null distribution of the test statistic is unavailable in most cases, the large sample approximation and the bootstrap were frequently used to find the acceptance region of the test. Although these two methods are asymptotically accurate, their performance in terms of size and power is not satisfactory in small sample size. To enhance the small‐sample performance, we propose a new method to approximate the null distribution, which builds on the idea of generalized pivots. Conventionally, the generalized pivots were often used for interval estimation of a certain parameter or function of parameters in presence of nuisance parameters. In this study, we further extend the idea of generalized pivots to find the acceptance region of the model discrimination test. Through extensive simulations, we show that the proposed method performs better than the existing methods in discriminating between two lifetime distributions or two degradation models over a wide range of sample sizes. Two real examples are used to illustrate the proposed methods.     

正态双边可靠度的Bootstrap下限

研究了正态单元双边可靠度Bootstrap置信下限,并在小样本条件下对Bootstrap估计进行了纠偏处理,以提高区间估计的精度。进行了仿真检验,并与目前经典的使用双边容许限系数表的近似法相比较,证明该方法具有较高的精度,便于程序实现。     

The power of paired sample tests

The power of the component randomization test for the paired sample location test is compared to the power of the parametric test for paired comparisons using the sum of differences distribution. This analysis is presented in the form of operating characteristic curves for normal, exponential, uniform and absolute lambda observations over a range of small sample sizes.     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

A nonparametric approach to accelerated life testing under multiple stresses

Accelerated life testing (ALT) is concerned with subjecting items to a series of stresses at several levels higher than those experienced under normal conditions so as to obtain the lifetime distribution of items under normal levels. A parametric approach to this problem requires two assumptions. First, the lifetime of an item is assumed to have the same distribution under all stress levels, that is, a change of stress level does not change the shape of the life distribution but changes only its scale. Second, a functional relationship is assumed between the parameters of the life distribution and the accelerating stresses. A nonparametric approach, on the other hand, assumes a functional relationship between the life distribution functions at the accelerated and nonaccelerated stress levels without making any assumptions on the forms of the distribution functions. In this paper, we treat the problem nonparametrically. In particular, we extend the methods of Shaked, Zimmer, and Ball [7] and Strelec and Viertl [8] and develop a nonparametric estimation procedure for a version of the generalized Arrhenius model with two stress variables assuming a linear acceleration function. We obtain consistent estimates as well as confidence intervals of the parameters of the life distribution under normal stress level and compare our nonparametric method with parametric methods assuming exponential, Weibull and lognormal life distributions using both real life and simulated data. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 629–644, 1998     

The asymptotic sufficiency of sparse order statistics in tests of fit with nuisance parameters

In an earlier paper, it was shown that for the problem of testing that a sample comes from a completely specified distribution, a relatively small number of order statistics is asymptotically sufficient, and for all asymptotic probability calculations the joint distribution of these order statistics can be assumed to be normal. In the present paper, these results are extended to certain cases where the problem is to test the hypothesis that a sample comes from a distribution which is a member of a specified parametric family of distributions, with the parameters unspecified.     

Optimal accelerated life test designs for Burr type XII distributions under periodic inspection and type I censoring

This article develops optimal accelerated life test designs for Burr Type XII distributions under periodic inspection and Type I censoring. It is assumed that the mean lifetime (the Burr XII scale parameter) is a log-linear function of stress and that the shape parameters are independent of stress. For given shape parameters, design stress and high test stress, the test design is optimized with respect to the low test stress and the proportion of test units allocated to the low stress. The optimality criterion is the asymptotic variance of the maximum-likelihood estimator of log mean life at the design stress with the use of equally spaced inspection times. Computational results for various values of the shape parameters show that this criterion is insensitive to the number of inspection times and to misspecification of imputed failure probabilities at the design and high test stresses. Procedures for planning an accelerated life test, including selection of sample size, are also discussed. It is shown that optimal designs previously obtained for exponential and Weibull distributions are similar to those obtained here for the appropriate special cases of the Burr XII distribution. Thus the Burr XII distribution is a useful and widely applicable family of reliability models for ALT design. © 1996 John Wiley & Sons, Inc.     

加速寿命试验下复合失效产品的可靠性评估

产品往往受随机失效和耗损失效两种模式的双重影响,通过构建复合寿命分布模型来表征这类产品失效规律。在加速寿命试验下,基于极大似然估计构造了该类产品寿命参数估计的数值算法;为了验证该寿命分布是否真服从假定的复合分布,构建了常应力等效失效数据的柯尔莫哥诺夫分布检验法;最后,以电连接器这一典型产品为例进行了工程仿真试验并进行数据评估,从而验证了评估方法的正确性。