Control Policy for a Manufacturing System with Random Yield and Rework

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.     

On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.     

Linear and Nonlinear Optical Properties Of Racemic (±)2-(α-Methylbenzylamino)-5-Nitropyridine Single Crystals

Linear and nonlinear optical properties of racemic (±)2-(α-methylbenzylamino)-5-nitropyridine ((±)MBANP) single crystals have been comprehensively investigated and compared with those of the enantiomorph (–)2-(α-methylbenzylamino)-5-nitropyridine ((–)MBANP) crystals. (±)MBANP crystal exhibits very high chemical and physical stability, but relatively small nonlinear optical coefficients (d₃₁ = 6.8 pm/V, d₃₂ = 4.7 pm/V, d₃₃ = 0.84 pm/V). A comparison between the nonlinear optical coefficients of (±)MBANP and (–)MBANP demonstrates the validity of the oriented-gas model in molecular crystals that neglects all the contributions from intermolecular interaction.     

Assessing the Error Probability of the Model Selection Test

The asymptotic error probability of Linhart's model selection test isevaluated, and compared with the nominal significance level. We examine thecase where the expected discrepancies of the candidate models from the truemodel are asymptotically equal. The local alternatives method is employed inthe limiting operation of the asymptotic evaluation. Although the errorprobability under the null hypothesis is actually shown to be equal to orless than the level for most situations, intolerable violations of the errorcontrol are observed for nested models: It is often erroneously concludedthat the smaller model is significantly better than the larger model. Toprevent this violation, a modification of Linhart's test statistic isproposed. The effectiveness of the proposed test is confirmed throughtheoretical analysis and numerical simulations.     

非线性系统两变量控制下的分枝特性

采用分枝理论推导非线性系统两变量P和PI控制下的分枝特性,所导得的几个定理阐明了简单分枝点和Hopf分枝点的位置和性质。一个简化精馏塔模型用于演示这一过程,展示出精馏塔系统在闭环时,可能出现多态和极限环。     

CNC系统中任意三维椭圆弧的高速插补新方法

本文根据两步递归插补的思想,导出了任意三维椭圆弧高速插补的公式和算法.它是空间圆弧高速插补方法在三维椭圆弧的情况下进一步推广应用.本文最后还对插补算法进行了稳定性分析和误差分析.     

On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

一个改进的Hardy-Hilbert不等式

通过建立权系数的不等式,得到一个改进的Hardy-Hilbert不等式.