可变抽样区间同时监控均值标准差的EWMA控制图

传统的EWMA控制图分别针对监控过程均值变化和监控过程标准差变化进行研究,在实际生产中,很多情形需要同时监控过程均值变化和过程标准差变化。为了提高控制图的监控效率,本文研究了同时监控均值和标准差变化时,EWMA控制图的可变抽样区间设计。其次运用马科夫链法计算可变抽样区间EWMA控制图的平均报警时间;然后与传统的EWMA控制图进行比较得出:同时监控均值和标准差时,可变抽样区间的EWMA控制图能够更快地发现过程中的异常波动,具有较短的平均报警时间,其监控效率明显优于传统的EWMA控制图。     

有偏总体的极差控制图

根据加权标准差方法建立有偏总体的极差控制图,它基于有偏总体来计算对应于正态分布的控制图常数,根据样本数据的偏度来计算上下控制限,对于总体是对称分布,该控制图退化为标准的休哈特控制图.最后,用蒙特卡洛方法给出了改进的控制图常数.     

用Bayes方法修正质量控制界限

在工序质量控制中,画控制图的传统作法是用样本均值近似代替总体的均值．由于样本的随机性,因此,估计误差在所难免．本文用Ｂａｙｅｓ方法将用样本均值χ代替总体均值μ所产生的估计误差一并计入到总体Ｘ所固有的随机性之中,从而修正了传统的质量控制界限的画法     

用Venn图表示相互独立事件及其概率

在概率论中，常用Venn图来表示事件及其概率．但尚未见用它来表示相互独立事件及其概率的报导．本文提出了一个解决这一问题的方法。     

具有可变抽样区间的EWMA标准差控制图

对指数加权滑动平均即EWM A标准差控制图进行了可变抽样区间设计,用M arkov-cha in方法给出了该控制图的平均报警时间的计算公式,并同固定抽样区间的常规EWM A标准差控制图进行比较,数据显示,所设计的控制图能较快的发现过程变化从而减少产品的不合格率.     

用Venn图表示相互独立事件及其概率

在概率论中，常用Ｖｅｎｎ图来表示事件及其概率，但尚未见用它来表示相互独立事件及其概率的报导．本文提出了一个解决这一问题的方法     

正态总体均值与标准差比在序约束下的广p-值检验

本文利用广义p-值和U-I检验法研究了多个正态总体均值与标准差比在简单半序和树序约束下的检验问题．提出了广义检验变量,得到了多个正态总体均值与标准差比在简单半序和树序约束下检验问题的广义p-值．同时运用Monte Carlo方法给出了模拟结果．     

控制图判断准则的显著性检验

徐哲，段晓江．控制图判断准则的显著性检验．数理统计与管理，１９９８，１７（３），４５～４８．利用控制图判断生产过程的状态是一种统计判断，必然犯两种错误。本文在规定“小概率事件”标准的基础上，对休哈特控制图判断准则假设检验的显著性水平进行了分析，并直观解释了各种异常情况的系统性变化特点，最后简述了计算机辅助质量控制图的应用     

有偏总体的EWMA均值控制图

基于总体分布有偏并假定总体分布未知情况下均值-极差控制图的控制限的研究结果,将其推广到EWMA均值控制图,给出总体分布有偏并假定总体分布未知情况下EWMA均值控制图的控制界限,并以质量特性值服从对数正态分布为例,给出EWMA均值控制图的控制效果的模拟分析.     

正态总体均值与标准差比在简单半序约束下的最大似然估计

本文考虑两个正态总体均值和方差是未知参数,均值与标准差的比在简单半序约束下,且样本个数不同时,计算均值和标准差的最大似然估计的问题.给出了计算均值和标准差的最大似然估计的方法.同时还给出了三个总体均值与标准差的比在简单半序约束下求均值和标准差的最大似然估计的计算方法,并给出了迭代算法的模拟结果.     

Approximating probability density functions and their convolutions using orthogonal polynomials

This paper describes and tests methods for piecewise polynomial approximation of probability density functions using orthogonal polynomials. Empirical tests indicate that the procedure described in this paper can provide very accurate estimates of probabilities and means when the probability density function cannot be integrated in closed form. Furthermore, the procedure lends itself to approximating convolutions of probability densities. Such approximations are useful in project management, inventory modeling, and reliability calculations, to name a few applications. In these applications, decision makers desire an approximation method that is robust rather than customized. Also, for these applications the most appropriate criterion for accuracy is the average percent error over the support of the density function as opposed to the conventional average absolute error or average squared error. In this paper, we develop methods for using five well-known orthogonal polynomials for approximating density functions and recommend one of them as giving the best performance overall.     

Some inequalities for strong mixing random variables with applications to density estimation

In this paper, we establish an inequality of the characteristic functions for strongly mixing random vectors, by which, an upper bound is provided for the supremum of the absolute value of the difference of two multivariate probability density functions based on strongly mixing random vectors. As its application, we consider the consistency and asymptotic normality of a kernel estimate of a density function under strong mixing. Our results generalize some known results in the literature.     

Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices

This paper explores the application of ordered weighted averaging (OWA) operators to develop water quality index, which incorporates an attitudinal dimension in the aggregation process. The major thrust behind selecting the OWA operator for aggregation of multi-criteria is its capability to encompass a range of operators bounded between minimum and maximum. A new approach for generating OWA weight distributions using probability density functions (PDFs) is proposed in this paper. The basic parameters (mean and standard deviation) of the probability density functions can be determined using the number of criteria (e.g., water quality indicators) in the aggregation process.     

Passenger grouping with risk levels in an airport security system

This is a follow-up to the recent paper by Lazar Babu et al. [V.L. Lazar Babu, R. Batta, L. Lin, Passenger grouping under constant threat probability in an airport security system, European Journal of Operational Research 168 (2006) 633–644] which investigated the benefit of classifying passengers into different groups, with the idea that the number of checks and the degree of inspection may vary for different groups. A basic assumption in that paper was that the threat probability is constant across all passengers. In this paper, we relax this assumption and consider the case where passenger risk levels are incorporated. We assume that passengers are classified into several risk classes via some passenger prescreening system, for example, Computer-Assisted Passenger Prescreening System II (CAPPS II). We consider the separate grouping of every class of passengers such that the overall false alarm probability is minimized while maintaining the overall false clear probability within specifications set by a security authority. Meanwhile, we consider the staffing needs at each check station. The problem is formulated as a mixed integer linear program. An illustrative example of the model is presented with comparisons to the model in Lazar Babu et al. (2006) using two performance measures: probability of false alarm and total number of screeners needed. Our conclusion is that incorporation of risk levels through passenger grouping strategies leads to a more efficient security check system.     

Renewal-theoretic considerations in evaluation of forecast monitoring schemes

To evaluate the performance of a scheme for monitoring forecasts that are generated by exponential smoothing, forecasters have traditionally used a simulation-based estimator of some characteristic of the associated run-length distribution. The most frequently cited performance measures are the average run length and the probability that the run length does not exceed a user-specified cut-off point. However, there is disagreement about the definition of run length that is appropriate in the context of forecasting. In this paper we use fundamental results from renewal theory to establish the precise relationships between conflicting formulations both of the average run length and of the probability density function for the run length. More generally we derive the asymptotic mean and the asymptotic distribution function of the forward recurrence time for both ordinary and delayed renewal processes whose interoccurrence distributions are arithmetic with a given span. We discuss the practical significance of these results in the context of forecasting. Our findings bear directly on the way in which simulation experiments should be designed and executed to compare alternative forecast monitoring schemes.     

Fuzzy processes

In this paper, contributions to fuzzy probability and to differential equations with fuzzy parameters are made.After an introductory section, a review of fuzzy sets and fuzzy algebra is given in Section 2. The main new results of the investigation are contained in Section 3.In Section 3, Zadeh's definition of the probability of a ‘fuzzy event’ the average value of a fuzzy function are extended into the time domain. It is then shown that not only grades of membership, but also probabilistic processes with notions of fuzziness contained, can be defined which obey ordinary, matric, or integro-differential equations. Applications are also given in Section 3.     

赌博破产概率及其随机模拟试验

讨论了赌博问题中的最终破产概率,并给出了破产概率的随机模拟计算流程和一个具体例子的数值模拟结果.计算结果表明,由此方法得到破产概率的估计值与理论值的误差很小.最后,通过随机模拟给出游戏结束的平均次数.     

基于多点报警的多元统计过程控制

本文主要研究了一种将控制图的报警准则由一点改为多点时多元控制图的构造,对于不同的多点报警准则的控制图可以通过计算平均运行长度的方法得出了不同的控制限参数。然后本文对各种报警准则下的多元控制图与Hotelling T2控制图,MCUSUM(多元累计和控制图)和MEWMA(多元指数加权移动平均控制图)进行了比较,说明这种改变报警规则的多元控制图在监测过程中出现的微小波动时具有一定的优势。     

广义非中心Wishart分布

设Z是n×m随机矩阵(n>m),它具有椭球等高分布Z～LEC_n×m(M,Σ,φ),Σ>0,其密度函数为     

关于漏失数据弥补的几点意见

漏失数据的弥补,通常采用使误差项的平方和达到最小的原则来确定,这样弥补的数据,有时会出现负值等异常情况.本文提出采用相邻小区的平均值来代替漏失数据,或用回归分析的方法分析试验结果,同样能得到最小二乘法相一致的结论,但不会出现负值.