A GA-based solution approach for balancing printed circuit board assembly lines

Printed circuit board (PCB) assembly lines consist of a number of different machines for mounting electronic components onto PCBs. While high-speed placement machines are employed to assemble standard components, so-called fine-pitch placement machines are used to mount complex electronic components with high precision and by use of specific nozzles. In this paper, we investigate a typical mass production environment where a single type of PCB is assembled in a line comprising high-speed as well as high-precision placement machines. The PCB assembly line balancing problem consists of assigning component feeders, each holding a specific electronic component type, and the corresponding placement operations to machines in the line so as to minimize the assembly cycle time. To solve this problem, a two-stage solution procedure based on genetic algorithm (GA) is proposed. In the first stage, component feeders are assigned to the placement machines with the objective of balancing the workload within the assembly line. A number of candidate solutions are then transmitted to the second stage, where specific machine optimization algorithms are applied to determine the feeder-slot assignment in the component magazine of the machines and the placement sequence of the various components. As a result, fine-tuned placement operation times are achieved which reflect the individual operation mode and the actual component setup of the placement machines. Finally, from the candidate solutions the one which minimizes the actual PCB assembly time is selected.     

A mathematical model for loading the sequencers in a printed circuit pack manufacturing environment

A sequencing machine is a piece of equipment used in the electronics industry to produce sequenced reel-packaged tapes of axial leaded components for different types of printed circuit packs (PCPs). Due to the limited number of dispensing heads available on the sequencing machines, the relatively large number of component types competing for these heads, and the diversity of the component type requirements of different types of PCPs, efficient scheduling of these machines is usually not a simple task. In this paper we discuss a structured approach to the problem of scheduling the sequencers, and present a mathematical model, as well as a heuristic procedure, that can be used to resolve some of the difficulties involved.     

A closed form solution for the G/M/r machine interference model

This paper solves the machine interference problem in which N different machines are looked after by a team of r operatives. The run time of each machine is assumed to have a general distribution, different for each machine and the repair times are assumed to have a negative exponential distribution with different means for the different machines. An explicit expression for the probability that a particular group of machines is found running in the steady state is derived. From this other useful measures for the system can be obtained. It is shown that these depend on the run time distributions only through the means of those distributions.     

基于小波包和进化支持向量机的齿轮早期诊断研究

针对齿轮早期故障的特征不明显，提出了一种基于小波包和进化支持向量机的齿轮故障诊断方法，该方法既充分利用了小波包优良的时频局部化特性，又利用了支持向量机在小样本情况下出色的学习性能和良好的推广特性，以及遗传算法的全局优化能力。在齿轮试验台上的应用结果表明，经过特征提取和参数优化后，提高了支持向量机的分类能力。     

A stochastic model of an unreliable kanban production system

We analyze a stochastic model of a production line withk stations (machines) in series. There are finitecapacity buffers between the machines and at the end of the line. The movement of the workpieces through the line is demand-driven, i.e. we deal with a pull (kanban) production system. Processing times are assumed to be deterministic and constant. There are two sources of randomness in the model: Demand for workpieces from outside is stochastic, and the machines may break down (and then be repaired) with a given probability. A demand from outside is lost if the final buffer is empty. This system is described by a discrete-time Markov chain. The steadystate distribution is given for k=1. This is the basis of a decomposition algorithm which approximates the throughput of the line and the percentage of satisfied demand for arbitraryk. A comparison with simulation results shows that this algorithm is very accurate.     

A part-and-tool assignment method for the workload-balance between machines and the minimisation of tool-shortage occurrences in an FMS

In this paper, we look into the loading problem of a flexible manufacturing system (FMS) that is made up of several identical flexible manufacturing machines (CMMs). These machines are capable of different operations as long as the required tools are provided to them. The loading problem studied in this paper is a pre-release problem that deals with the pre-assignment of parts and tools before the process of an FMS begins. There are two objectives that one would like to achieve. They include minimising the number of tool-shortage occurrences and balancing the workload between machines. Since one cannot directly minimise the number of tool-shortage occurrences at the current pre-release stage, a surrogate objective of minimising the total tool-capacity shortage (TTCS) is adopted. Furthermore, because of the ‘tool movement policy’ assumption, our loading problem only involves assigning parts and tools to each machine. In this paper, we propose a part-and-tool assignment method that combines fuzzy c-means, SA (simulated annealing), and an optimal tool-assignment algorithm. The proposed part-and-tool assignment method is designed to be interactive. Because of this interactive nature, human designers can experiment with different evaluation criteria or reset the parameters of SA to look for alternative solutions. An example is given which illustrates the proposed part-and-tool assignment method. From the example, one can see that the proposed method is very efficient and effective in finding good-quality solutions.     

JOB ASSIGNMENT ALGORITHMS ON UNIFORM PARALLEL MACHINES

Uniform parallel machine scheduling problems with a makespan measure cannot generally be solved within polynomial time complexity. This paper considers special problems with a single type of job on the uniform parallel machines, where each machine is available at a given ready time. Also the machine can be restricted on the number of jobs to be processed. The objective is to develop job assignment or batching algorithms which minimize makespan. When all the machines are available at time zero and have no restriction on the number of assignable jobs, a lower bound and optimal solution properties are derived. Based upon these properties, a polynomial algorithm is suggested to find the optimal job assignment on each machine. Three generalized problems are considered under the following situations: (1) some machines have capacity restrictions on the production batch, (2) each machine has its ready time, and (3) the jobs require series-parallel operations. The generalized problems arc also characterized and polynomial algorithms are developed for the same aim of optimal job assignment, except for the case of series-parallel operations. A heuristic algorithm is suggested with numerical tests for the series-parallel operations problem     

A bi-objective parallel machine problem with eligibility,release dates and delivery times of the jobs

The scheduling of parallel machines is a well-known problem in many companies. Nevertheless, not always all the jobs can be manufactured in any machine and the eligibility appears. Based on a real-life problem, we present a model which has m parallel machines with different level of quality from the highest level for the first machine till the lowest level for the last machine. The set of jobs to be scheduled on these m parallel machines are also distributed among these m levels: one job from a level can be manufactured in a machine of the same or higher level but a penalty, depending on the level, appears when a job is manufactured in a machine different from the highest level i.e. different from the first machine. Besides, there are release dates and delivery times associated to each job. The tackled problem is bi-objective with the criteria: minimisation of the final date – i.e. the maximum for all the jobs of their completion time plus the delivery time – and the minimisation of the total penalty generated by the jobs. In a first step, we analyse the sub-problem of minimisation of the final date on a single machine for jobs with release dates and delivery times. Four heuristics and an improvement algorithm are proposed and compared on didactic examples and on a large set of instances. In a second step an algorithm is proposed to approximate the set of efficient solutions and the Pareto front of the bi-objective problem. This algorithm contains two phases: the first is a depth search phase and the second is a backtracking phase. The procedure is illustrated in detail on an instance with 20 jobs and 3 machines. Then extensive numerical experiments are realised on two different sets of instances, with 20, 30 and 50 jobs, 3 or 4 machines and various values of penalties. Except for the case of 50 jobs, the results are compared with the exact Pareto front.     

Data transformation in SPC for semiconductor machinery control: A case of monitoring particles

Yield is an important indicator of productivity in semiconductor manufacturing. In the complex manufacturing process, the particles on wafers inevitably cause defects, which may result in chip failure and thus reduce yield. Semiconductor manufacturers initially use wafer testing to control the machine for the number of particles. This machinery control procedure aims to detect any unusual condition of machines, reduce defects in actual wafer production and thus improve yield. In practice, the distribution of particles does not usually follow a Poisson distribution, which causes an overly high rate of false alarms in applying the c-chart. Consequently, the semiconductor machinery cannot be appropriately controlled by the number of particles on machines. This paper primarily combines data transformation with the control chart based on a Neyman type-A distribution to develop a machinery control procedure applicable to semiconductor machinery. The proposed approach monitors the number of particles on the testing wafer of machines. A semiconductor company in Taiwan in the Hsinchu Science Based Industrial Park demonstrated the feasibility of the proposed method through the implementation of several machines. The implementation results indicated that the occurrence of false alarms declined extensively from 20% to 4%.     

真空洗衣机工作原理的探讨

真空洗衣机是真空技术在家用电器领域方面的一个新应用.根据真空洗衣机的洗涤原理,设计了一套简易洗涤系统,并在所设计的系统中进行了洗涤实验.在此基础上对真空洗衣机的洗净原理、结构设计作了一些思考,对真空洗衣机的可行性提出了自己的看法.     

FRACTURE MECHANICS ANALYSIS BASED ON A LOCAL SIMULATION PRINCIPLE

Abstract— A local simulation principle is presented which allows the transfer of geometry-dependent fracture parameters from a specimen to a component if the local constraint conditions of the crack tip in the component are simulated by the specimen. This can be achieved by adapting the specimen to the component with respect to the ligament length, the ligament width, the crack length and the loading geometry. If these requirements are met, then the relationship between the load and the driving force in the component can be estimated from the specimen by a simple scaling procedure. The application of the local simulation principle is illustrated by an example.     

盾构在掘进过程中的力学分析与载荷预估

该文分析了盾构在掘进过程中的总载荷,将其分为基准载荷与掘进载荷,提出一种基于力学分析的可有效描述地质参数、操作参数及结构参数影响规律的盾构载荷计算方法。在计算掘进载荷时,建立了反映盾构刀盘与土体在掘进界面上耦合作用的刀盘接触载荷近似计算模型。通过天津地铁工程的载荷实测数据与基于该文提出方法得到的载荷计算结果比对表明:该方法可用于估算盾构掘进过程中的总载荷,并可用于近似描述地质条件、操作状态及刀盘结构等重要工程参数对载荷的影响,为盾构设计及施工提供了一种可行的工程载荷计算手段。     

A linear programming approach to capacity estimation of automated production lines with finite buffers

This paper considers a highly automated manufacturing line which consists of a sequence of workstations. Relatively small buffers are assigned between workstations in order to guarantee a small manufacturing interval and quick feedback in the event of process failure to make acceptable product. These small buffers could lead to a noticeable loss of line capacity due to the phenomenon of blocking and starvation. We show by means of simple examples how the buffer sizes and the mix and loading sequence of different types of jobs could significantly affect the production rate of the line. A linear programming based method is then developed to estimate the line capacity for a given configuration of machines and buffers sizes and for a given job mix and sequence. This method also gives the expected machine utilizations, the time machines are blocked/starved and, more importantly, the reason for this lost production capacity. By judiciously interpreting this information, one or more of the following steps can be taken to improve the production rate: (a) change the loading sequence, (b) increase the buffer space selectively, (c) make the products in smaller or larger batches, and (d) add new machines.     

铁矿球团抗压强度自动试验机计量校准的探讨

由于铁矿球团自动抗压强度试验机的计量校准目前尚无国际,国家标准可依,因此就新引进的一台铁矿球团自动抗压强度试验机的计量校准,性能测试,来探测该类仪器计量校准方法的制订。     

单缸发动机偏心滑块平衡机构的研究与应用

单缸发动机广泛应用于摩托车、园林作业机等机械,由发动机引起的振动是影响机器性能的一个主要因素。文章运用运动学和动力学知识对一种新型的单缸发动机平衡机构——偏心滑块平衡机构进行理论分析,推导出不平衡惯性力和惯性力矩与设计参数间的关系,并提出了偏心滑块平衡机构的设计准则,研究成果应用于某园林发动机上,实验验证了理论分析和设计的正确性。     

A hybrid electromagnetism-like algorithm for two-stage assembly flow shop scheduling problem

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation.     

A geometric process repair model for a repairable cold standby system with priority in use and repair

In this paper, a deteriorating cold standby repairable system consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy N based on the number of repairs of component 1 under which the system is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N^* such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit equation of the average cost rate of the system is derived and the corresponding optimal replacement policy N^* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.     

Workload planning in small lot printed circuit board assembly

The problem of workload planning in small lot printed circuit board (PCB) assembly concerns the determination of the daily mix of production orders to be released into the production system. When switching from one production order (board type) to another, a considerable set-up time is incurred based on the number of component feeders to be replaced in the component magazine of the assembly machines. To support the order-mix decision faced by a major electronics manufacturer, two versions of a linear programming model are developed. The models differ primarily in their degree of aggregation and their computational effort. In order to reduce the aggregational error incurred, a fuzzy approach is developed to estimate the number of component set-ups at automatic SMD placement machines. Our numerical investigation reveals that sufficiently accurate solutions may be obtained from a highly aggregate fuzzy LP-model and this is achieved with considerably less computational effort than with a more detailed LP-model. We also demonstrate the potential suitability of the fuzzy LP-model for implementation within an interactive decision support system.     

ON THE USE OF BUFFER INVENTORIES TO MINIMIZE COSTS WITH AN UNRELIABLE MACHINE

In this paper, we discuss the problem of quality control with an unreliable machine which produces defects at a rate of Λ₀, per unit when in-control and a rate of Lambda; ₁, when out-of-control (where Λ₁ Λ ₀). Every h time periods, we sample n units, count the number of defects, and (using a process based on a Shewart c-chart) test the hypothesis that the machine is in control by comparing the total number of defects to an upper control limit (UCL). More important, we introduce the concept that a buffer inventory which immediately follows the unreliable machine may reduce expected total costs. This buffer serves to delay the movement of items from the unreliable machine to the next stage of the production process. In this way, we can isolate and repair most defective items before they are embedded in a product downstream or sold to customers where repair is more costly. To search for the optimal control policy, we find bounds for n, h, and UCL; given values for these variables, we show how the optimal buffer size can be determined directly. Numerical results illustrate the magnitude of potential savings.