Technical note: An improved range chart for normal and long‐tailed symmetrical distributions

The distribution of the range of a sample, even in the case of a normal distribution, is not symmetric. Shewhart's control chart for range and other approximations for range from skewed distributions and long‐tailed (leptokurtic) symmetrical distributions assume the distribution of range as symmetric and provide 3 sigma control limits. We provide accurate approximations for the R‐chart control limits for the leptokurtic symmetrical distributions, using a range quantile approximation (RQA) method and illustrate the use of the RQA method with a numerical example. As special cases, we provide constants for the R‐chart for the normal, logistic, and Laplace distributions. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue

We use the matrix‐geometric method to study the MAP/PH/1 general preemptive priority queue with a multiple class of jobs. A procedure for obtaining the block matrices representing the transition matrix P is presented. We show that the special upper triangular structure of the matrix R obtained by Miller [Computation of steady‐state probabilities for M/M/1 priority queues, Oper Res 29(5) (1981), 945–958] can be extended to an upper triangular block structure. Moreover, the subblock matrices of matrix R also have such a structure. With this special structure, we develop a procedure to compute the matrix R. After obtaining the stationary distribution of the system, we study two primary performance indices, namely, the distributions of the number of jobs of each type in the system and their waiting times. Although most of our analysis is carried out for the case of K = 3, the developed approach is general enough to study the other cases (K ≥ 4). © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 662–682, 2003.     

幂函数型完全非线性函数原像分布的特征

完全非线性函数是特征为奇数的有限域上抗差分密码攻击最优的函数,目前已有的六类完全非线性函数都是2-1的。当Π(x)为Fqm上的Dembowski-Ostrom函数或者Coulter-Matthews函数时,从Fqm到Fq的完全非线性函数tr(aΠ(x))的原像分布恰有两种取值,其中一种取值对应Fqm所有平方剩余元,另一种取值对应Fqm所有非平方剩余元。该结论在文中得到了证明。     

Approximations for heavily loaded G/GI/n + GI queues

Motivated by applications to service systems, we develop simple engineering approximation formulas for the steady‐state performance of heavily loaded G/GI/n+GI multiserver queues, which can have non‐Poisson and nonrenewal arrivals and non‐exponential service‐time and patience‐time distributions. The formulas are based on recently established Gaussian many‐server heavy‐traffic limits in the efficiency‐driven (ED) regime, where the traffic intensity is fixed at ρ > 1, but the approximations also apply to systems in the quality‐and‐ED regime, where ρ > 1 but ρ is close to 1. Good performance across a wide range of parameters is obtained by making heuristic refinements, the main one being truncation of the queue length and waiting time approximations to nonnegative values. Simulation experiments show that the proposed approximations are effective for large‐scale queuing systems for a significant range of the traffic intensity ρ and the abandonment rate θ, roughly for ρ > 1.02 and θ > 2.0. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 187–217, 2016     

Equivalent accelerated life testing plans for log‐location‐scale distributions

Accelerated life testing (ALT) is widely used to determine the failure time distribution of a product and the associated life‐stress relationship in order to predict the product's reliability under normal operating conditions. Many types of stress loadings such as constant‐stress, step‐stress and cyclic‐stress can be utilized when conducting ALT. Extensive research has been conducted on the analysis of ALT data obtained under a specified stress loading. However, the equivalency of ALT experiments involving different stress loadings has not been investigated. In this article, a log‐location‐scale distribution under Type I censoring is considered in planning ALT. An idea is provided for the equivalency of various ALT plans involving different stress loadings. Based on this idea, general equivalent ALT plans and some special types of equivalent ALT plans are explored. For demonstration, a constant‐stress ALT and a ramp‐stress ALT for miniature lamps are presented and their equivalency is investigated. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue

If the number of customers in a queueing system as a function of time has a proper limiting steady‐state distribution, then that steady‐state distribution can be estimated from system data by fitting a general stationary birth‐and‐death (BD) process model to the data and solving for its steady‐state distribution using the familiar local‐balance steady‐state equation for BD processes, even if the actual process is not a BD process. We show that this indirect way to estimate the steady‐state distribution can be effective for periodic queues, because the fitted birth and death rates often have special structure allowing them to be estimated efficiently by fitting parametric functions with only a few parameters, for example, 2. We focus on the multiserver M_t/GI/s queue with a nonhomogeneous Poisson arrival process having a periodic time‐varying rate function. We establish properties of its steady‐state distribution and fitted BD rates. We also show that the fitted BD rates can be a useful diagnostic tool to see if an M_t/GI/s model is appropriate for a complex queueing system. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 664–685, 2015     

空时频域中欠定混合条件下的波达方向估计

波达方向估计是阵列信号处理领域的热点问题,但经典的波达方向估计方法通常要求阵元数大于源信号个数,即满足超定条件,而在实际中往往面临的是源信号个数大于阵元数的欠定条件。基于此,提出了一种基于空间时频分布的多重信号分类扩展算法,通过将空间时频分布矩阵进行扩展,实现了欠定条件下的波达方向估计。相比时频多重信号分类算法,所提算法能同时适应超定和欠定条件;相比已有的欠定波达方向估计方法,其不但保证了波达方向估计的精度,而且放宽了对源信号稀疏性的要求,同时还降低了对快拍数的要求。仿真实验结果证明了该方法的有效性。     

完全非线性函数的原像分布特征

完全非线性函数在密码设计与分析中具有十分重要的作用.利用代数数论的方法,研究一般有限Abel群上完全非线性函数的原像分布特征,给出了一般有限Abel群上完全非线性函数存在的一个必要条件,证明了某些群上不存在完全非线性函数,得到了素数域上完全非线性函数的原像分布.     

基于任意分布随机Petri网的装备维修保障建模与分析

通过将任意分布随机Petri网的基本理论和算法应用到装备维修保障的建模与分析,建立了维修保障系统的任意随机Petri网模型,实现了随机Petri网中变换概率服从指数分布的限制.根据实际系统中相关数据的统计分析和经验估计,以便为利用矩姆函数分析方法对维修保障系统的性能进行分析,为维修保障决策层提供参考,获得了一些有价值的性能指标信息.