Subjective estimation of the delay time distribution in maintenance modelling

In this paper, the problems in the current method for obtaining a subjective estimate of the delay time distribution used in maintenance modelling are discussed and a brief literature survey on assessing subjective probability and expert judgment in decision making is presented. Based upon the results of the survey and experience in conducting a subjective estimating procedure for the delay time distribution, a revised procedure and method for obtaining the subjective delay time estimate is proposed, and the models for combining experts' opinions and updating the delay time distribution are also discussed. Case examples are given in the paper to demonstrate the methodology.     

Estimation and status prediction in a discrete mover‐stayer model with covariate effects on stayer's probability

A discrete‐time mover‐stayer (MS) model is an extension of a discrete‐time Markov chain, which assumes a simple form of population heterogeneity. The individuals in the population are either stayers, who never leave their initial states or movers who move according to a Markov chain. We, in turn, propose an extension of the MS model by specifying the stayer's probability as a logistic function of an individual's covariates. Such extension has been recently discussed for a continuous time MS but has not been considered before for a discrete time one. This extension allows for an in‐sample classification of subjects who never left their initial states into stayers or movers. The parameters of an extended MS model are estimated using the expectation‐maximization algorithm. A novel bootstrap procedure is proposed for out of sample validation of the in‐sample classification. The bootstrap procedure is also applied to validate the in‐sample classification with respect to a more general dichotomy than the MS one. The developed methods are illustrated with the data set on installment loans. But they can be applied more broadly in credit risk area, where prediction of creditworthiness of a loan borrower or lessee is of major interest.     

Bayesian analysis of hybrid life tests with exponential failure times

Summary A hybrid life test procedure is discussed from the Bayesian viewpoint. A total ofn items is placed on test, failed items are either not replaced or are replaced, and the test is terminated either when a pre-chosen number,K, of items have failed, or when a pre-determined time on test has been reached. Posterior and predictive distributions are obtained under the assumption of an exponential failure distribution, and point and interval estimates are given for the mean life and the life of an untested item. The results are applied to a numerical example.     

Ranking assignments in order of increasing completion time

Bottleneck Assignment Problem has already been solved by Gross [5], Gar-Finkel [3] and Bhatia [1]. Starting with an assignment yielding minimum completion time, the present paper presents two procedures for ranking various assignments in order of increasing completion time. In the first, closed circuits satisfying certain conditions are found. Non-existence of such circuits at a particular time imply no assignment yielding that completion time. In the second procedure a cost minimizing assignment problem is solved to get an assignment yielding next best time, Murty's [8] cost ranking procedure has been suitably modified for time ranking and is discussed in a note in this paper.     

Algorithm of orbit determination using one or two GPS satellites

The problem of orbit determination using one or two GPS satellites is discussed. Methods of getting initial values based on linear translation is presented; the Secant method and the descend Newton iterative procedure and the continuation algorithm are used synthetically to solve the nonlinear equations. Computer simulation shows that this algorithm can give preliminary state of satellite orbit with a certain precision in short time.     

一类时变需求且存货影响销售率的EOQ模型

从实际背景出发,在R AM P型需求和存货影响销售率条件下,讨论了一类以缺货开始的变质性物品的EOQ模型.给出了模型的求解方案及单位时间内平均利润最大化的两个充分条件,并用数值算例进行了验证.     

Controlling Production Processes Which are Subject to Linear Trends

Industrial processes must often be reset when a critical dimension of the product approaches or exceeds a specified value. This control procedure ensures that specifications remain between predetermined limits, but the resetting operation may be costly and involve loss of production time. Optimal resetting policies are examined for processes which exhibit a linear trend of a variable dimension produced by the process with a known distribution. Optimal policies are discussed for two criteria: (a) maximum rate of production and (b) minimum cost per unit.     

Estimation of Travel Times in Multiple Mode Systems<Superscript>†</Superscript>

This paper describes a procedure for generating estimates of the minimum travel times (shortest distances, least cost routes) between pairs of points on a standard map. The procedure exhibits substantial improvements in accuracy over the traditional generation methods involving simple orthogonal and vector-directed distance metrics. These improvements are achieved by combining the traditional methods with algorithms which find shortest routes in networks. The new procedure is particularly appropriate to the analysis of transportation or distribution systems which entail "multiple-mode travel", e.g. surface road vs. expressway travel, or railway vs. air travel. The advantages of the procedure are illustrated with empirical evidence from a simulation study of travel times in a large urban area. Finally, the generality of this procedure to a wide class of problems is discussed.     

Option pricing in incomplete discrete markets

Various methods of option pricing in discrete time models are discussed. The classical risk minimization method often results in negative prices and a natural modification is proposed. Another method of risk minimization using an inductive procedure as in the Cox-Ross-Rubinstein model is also proposed. The definition of the risk interpreted as the maximum of possible loss is discussed.     

The inverted complex Wishart distribution and its application to spectral estimation

The inverted complex Wishart distribution and its use for the construction of spectral estimates are studied. The density, some marginals of the distribution, and the first- and second-order moments are given. For a vector-valued time series, estimation of the spectral density at a collection of frequencies and estimation of the increments of the spectral distribution function in each of a set of frequency bands are considered. A formal procedure applies Bayes theorem, where the complex Wishart is used to represent the distribution of an average of adjacent periodogram values. A conjugate prior distribution for each parameter is an inverted complex Wishart distribution. Use of the procedure for estimation of a 2 × 2 spectral density matrix is discussed.     

Time-Dependent Marginal Energy Costs in Power Systems with Forced Outages

Marginal pricing of electricity calls for the determination of marginal energy costs over time. The purpose of this paper is to provide a computationally efficient procedure for computing the time-dependent probability, under merit order operation and forced outages of units, that any given plant will be the last plant used in a given multi-plant power system. This then allows a straightforward calculation of expected marginal energy cost for the given-power system over time. Other performance measures are derived as a by-product at relatively little extra computational effort. The method is applied to a realistic system and numerical results are presented and discussed.     

抛物型界面问题的变网格有限元方法

本文针对抛物型界面问题,提出了一种线性三角形变网格有限元方法.其主要思路是针对空间变量采用有限元离散,对时间变量采用差分离散,但是不同时刻的有限元剖分网格可以不同.在不引入Ritz投影这一传统分析工具的情况下,得到了最优误差估计结果,使得证明过程更加简洁.给出的数值算例验证了理论分析的正确性.     

Pulsreflektometrische Bestimmung eines Transistor-Ersatzschaltbildes

Summary A transistor equivalent circuit has been determined by means of time domain reflectometry. The described method yields a procedure requiring one measurement per equivalent circuit element only. The influences of the transistor package and finite rise time of test pulse are discussed and included in the analysis. The validity of this measurement technique for ultra high speed transistors is demonstrated by the rise time prediction of various pulse amplifier configurations down to below 0.5 nsec.     

Time–accurate Modular CFD‐CSD Coupling for Aeroelastic Rotor Simulations

This paper addresses the timewise accuracy of different coupling approaches applied to instationary aeroelastic simulations of rotors in forward flight. Two different approaches which are widely discussed in literature are examined: the tight or strong coupling, and the fully integrated or monolithic coupling. Strong coupling means an exchange of fluid loads and structural deformations at each time step which is effectuated in a fully modular manner. We will address aspects of conservativity and time‐accuracy, and will present results for a helicopter forward flight scenario. However, objections concerning the correct solution of the global non‐linear three field problem – structure, grid deformation, aerodynamics – remain. These objections are normally rejected by the monolithic approach. Here, a common set of partial differential equations is derived and solved in a single code. However, a truly monolithic system of equations is only needed for stability analysis, and it can be decomposed in a three field problem respecting appropriate boundary conditions for each domain. Thus, modularity can be maintained, conceiving a quasi‐monolithic procedure, when both domains are simultaneously solved in a common non‐linear iteration loop on a per time‐step basis. First results will be shown for a 2D flutter testcase.     

Converging Branch Multi-Stage Production Schedules with Finite Production Rates and Start-up Delays

This article considers scheduling production in a multi-stage system with converging branches and assumes an infinite time horizon, deterministic parameters, finite production rates, and constant lot sizes at each stage. The objective is the minimization of total time-averaged setup-shutdown and holding cost.The interdependence of successive stages is accounted for by delaying the initial startup at one stage relative to that at its immediate predecessors, to prevent shortages between the stages. Analytical expressions are found for such delay times and written under an "integer multiple" assumption on the cycle times at adjacent stages. Total cost is then minimized for a given set of integer multiples, and a heuristic search procedure for finding the optimal integer multiple values is described. Extensions of this procedure are then discussed.     

Stepwise selection of variables in data envelopment analysis: Procedures and managerial perspectives

One of the most important steps in the application of modeling using data envelopment analysis (DEA) is the choice of input and output variables. In this paper, we develop a formal procedure for a “stepwise” approach to variable selection that involves sequentially maximizing (or minimizing) the average change in the efficiencies as variables are added or dropped from the analysis. After developing the stepwise procedure, applications from classic DEA studies are presented and the new managerial insights gained from the stepwise procedure are discussed. We discuss how this easy to understand and intuitively sound method yields useful managerial results and assists in identifying DEA models that include variables with the largest impact on the DEA results.     

一组水动力学方程组的分步流线差分解法

这篇文章针对一组平面二维水动力学方程组提出了分步流线差分法。用破开算子法将其分成两部分,在空间上用三角形单元的分片线性插值来逼近,在时间步上用沿流线的差分来逼近。并给出了该方法的误差估计和稳定性分析。     

Hybrid procedures for solving linear systems

Summary. In this paper, we introduce the notion of hybrid procedures for solving a system of linear equations. A hybrid procedure consists in a combination of two arbitrary approximate solutions with coefficients summing up to one. Thus the combination only depends on one parameter whose value is chosen in order to minimize the Euclidean norm of the residual vector obtained by the hybrid procedure. Properties of such procedures are studied in detail. The two approximate solutions which are combined in a hybrid procedure are usually obtained by two iterative methods. Several strategies for combining these two methods together or with the previous iterate of the hybrid procedure itself are discussed and their properties are analyzed. Numerical experiments illustrate the various procedures. Received October 21, 1992/Revised version received May 28, 1993     

The two-machine total completion time flow shop problem

In this paper we study the NP-hard scheduling problem of minimizing total completion time in a two-machine flow shop. Five known lower bounds are discussed and two new ones are presented. A new dominance criterion is also proposed. Several versions of a branch and bound method are derived by applying, both individually and combined, these lower bounds. A heuristic procedure is also presented that uses a constructive O(n²) time method, which computes a good starting solution, together with a neighborhood search based on pairwise interchanges. Computational results show that the exact method can handle problems of up to 30 jobs in size within a reasonable amount of time and that the heuristic procedure has an average error of less than 0.5% from the optimal value and less than 2.7% from the lower bound.     

Heuristic Solution Methods for Two Location Problems with Unreliable Facilities

In this paper, the p-median and p-centre problems are generalized by considering the possibility that one or more of the facilities may become inactive. The unreliable p-median problem is defined by introducing the probability that a facility becomes inactive. The (p, q)-centre problem is defined when p facilities need to be located but up to q of them may become unavailable at the same time. An heuristic procedure is presented for each problem. A rigorous procedure is discussed for the (p, q)-centre problem. Computational results are presented.