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.     

Joint optimization of preventive maintenance and inventory control in a production line using simulation

This paper proposes an integrated method for preventive maintenance and inventory control of a production line, composed of n machines (n?≥?1) without intermediate buffers. The machines are subject to failures and an age-dependent preventive maintenance policy is used. Approximate analytical results are proposed for the one machine case. Simulation software is used to model and simulate the behaviour of the production line of n machines under various maintenance and inventory control strategies. A methodology combining the simulation and genetic algorithms is proposed jointly to optimize maintenance and inventory control policies. Results are compared with the analytical solutions.     

Reducing energy consumption in serial production lines with Bernoulli reliability machines

This paper is devoted to developing an integrated model to minimise energy consumption while maintaining desired productivity in Bernoulli serial lines with unreliable machines and finite buffers. For small systems, such as three- and four-machine lines with small buffers, exact analysis to optimally allocate production capacity is introduced. For medium size systems (e.g. three- and four-machine lines with larger buffers, or five-machine lines with small buffers), an aggregation procedure to evaluate line production rate is introduced. Using it, optimal allocation of machine efficiency is searched to minimise energy consumption. Insights and allocation principles are obtained through the analyses. Finally, for larger systems, a fast and accurate heuristic algorithm is presented and validated through extensive numerical experiments to obtain optimal allocation of production capacity to minimise energy consumption while maintaining desired productivity.     

Queuing network analysis approach for estimating the sizes of the time buffers in Theory of Constraints-controlled production systems

The present paper describes an open queuing network modelling approach to estimate the size of the time buffers in production systems controlled by the Theory of Constraints philosophy. Workstations in the production network are modelled as GI/G/m queues and a queuing network analysis multiproduct open queuing network modelling method is used to estimate the average flow time to the time buffer origin and the standard deviation of flow time. Using these two values together with an assumption of normally distributed flow times and a chosen service level, the final time buffer length is determined. The queuing network analysis method has been modified to enable the modelling of production networks with machine failures, batch service and varying transfer batch sizes. The modelling approach has also been incorporated in a computerized tool that uses product specific information such as bill-of-material and routing data, and production network information such as resource data to estimate the sizes and location of the necessary time buffers for each product. Simulation experiments indicate that the procedure is sufficiently accurate to provide an initial quick estimate of the needed time buffer lengths at the design stage of the line.     

Buffers and backup machines in automatic transfer lines

Buffer storage of the work-in-process inventory, decouples successive stages of automatic transfer production lines, assuring partial operability under machine failure. Certain special features such as secondary (standby) machines, special maintenance and diagnostic systems can lengtben the uptime or shorten the downtime of individual stages. When special features for K stages and spaces for M buffers are available, it is of great interest to system designers to know which stages should have the special features and where the buffer spaces should be inserted to maximize the line output rate. This paper addresses itself to such design problems. A bivariate dynamic programming procedure is developed which provides a layout for the buffers and an allocation of special features, maximizing the line output rate as defined by Buzacott (1967, 1968). The Buzacott formula is based on a heuristic argument which provides, in general, an upper bound on the true system output rate.     

Scheduling manufacturing systems with work-in-process inventory control: Reentrant systems

In this paper, we propose a procedure for production flow control in reentrant manufacturing systems. The system under study consists ofN machines and producesM product types simultaneously. Each part goes through the system following a predefined process and may visit a machine many times. All machines are subject to random failures and need random repair times. The scheduling objectives are to keep the production close to demand and to keep the WIP inventory level and cycle times at low values. The model is motivated by semiconductor fabrication production. A three-level hierarchical controller is constructed to regulate the production. At the top level of this hierarchy, we perform capacity planning by selecting the desirable buffer sizes and the target production level for each operation. A production flow rate controller is at the middle level which recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. Comparison with alternative control is made through simulation and it shows that the control policy performs well.     

Throughput centered prioritization of machines in transfer lines

In an environment of scarce resources and complex production systems, prioritizing is key to confront the challenge of managing physical assets. In the literature, there exist a number of techniques to prioritize maintenance decisions that consider safety, technical and business perspectives. However, the effect of risk mitigating elements—such as intermediate buffers in production lines—on prioritization has not yet been investigated in depth. In this line, the work proposes a user-friendly graphical technique called the system efficiency influence diagram (SEID). Asset managers may use SEID to identify machines that have a greater impact on the system throughput, and thus set prioritized maintenance policies and/or redesign of buffers capacities. The tool provides insight to the analyst as it decomposes the influence of a given machine on the system throughput as a product of two elements: (1) system influence efficiency factor and (2) machine unavailability factor. We illustrate its applicability using three case studies: a four-machine transfer line, a vehicle assembly line, and an open-pit mining conveyor system. The results confirm that the machines with greater unavailability factors are not necessarily the most important for the efficiency of the production line, as it is the case when no intermediate buffers exist. As a decision aid tool, SEID emphasizes the need to move from a maintenance vision focused on machine availability, to a systems engineering perspective.     

Improved preventive maintenance in the framework of forecasting problem under subcontractor constraint

The paper presents a new improved preventive maintenance strategy for a forecasting problem of production and maintenance optimisation under subcontractor constraint. In order to satisfy the customer, the manufacturing system consists of a principal machine M₁ and called upon subcontractor machine M_s. Knowing that both machines are subjected to random failures, failure rate of main machine increases with time and according to production rates. An improved preventive maintenance strategy is used for control of the machine M₁, whereas subcontractor machine M_s is uncontrollable from preventive maintenance point of view. An analytic formulation of problem has been proposed in order to determine the economical production plans for M₁ and M_s. An improved maintenance strategy (IMS) is developed in order to minimise the total production loss, when the subcontractor machine is unavailable. It consists of determining the best time to perform preventive maintenance actions taking into account production rates, history of M₁ and the state of subcontractor machine M_s. Numerical results and sensitivity analysis are presented to highlight the performance measure and the usefulness of the IMS.     

Preventive maintenance of manufacturing systems under environmental constraints

The paper describes a new preventive maintenance approach for manufacturing systems under environment constraints. The manufacturing system under consideration consists of a machine M₁ that produces a single product in a Just-in-Time context. To satisfy a constant demand d, the system called upon another machine M₂ (the subcontractor), comprising the so-called environment, which produces at a certain rate the same type of product as M₁. Both machines are subjected to random failures. Whereas machine M₂ is uncontrollable from the maintenance point of view, an age-limit policy is used for preventive maintenance of machine M₁. It is proved that the best age to perform preventive maintenance depends on the history of machine M₁ and the state of M₂. A numerical example is used to illustrate the proposed approach.     

The modelling of degraded and critical failures for components with dormant failures

The failures reported in reliability data bases are often classified into sseverity classes, e.g., as critical or degraded failures. This paper presents models for the failure mechanism causing the degraded and critical failures, and estimators for the failure intensities of the models are provided. The discussions mainly focus on dormant (hidden) failures of a standby component. The suggested models are based on exponentially distributed random variables, but they give non-exponential (phase-type) distributions for the time to failure, and thus provide alternatives to the more common Weibull model. The main model is adapted to the information available in modern reliability data bases. Using this model it is also possible to quantify the reduction in the rate of critical failures, achieved by repairing degraded failures. In particular the so-called ‘naked failure rate’ (defined as the rate of critical failures that would be observed if no repair of degraded failures was carried out) is derived. Further, the safety unavailability (Mean Fractional Deadtime) of a dormant system is obtained for the new model.     

Scheduling manufacturing systems with work-in-process inventory control: single-part-type systems

A real-time algorithm is developed for scheduling single-part-type production lines with work-in-process inventory buffers. We consider three classes of activities: operations, failures and repairs, and starvation and blockage. The scheduling objectives are to keep the actual production close to the demand, the work-in-process (WIP) inventory level low, and the cycle time short. A three-level hierardhical controller is constructed to regulate the production. At the top level, we determine the desirable buffer sizes and the target production level for each operation. At the middle level is a production flow rate controller that recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. The production scheduling algorithm is evaluated by using computer simulations for a variety of cases. Compared with a transfer line policy, a significant improvement in system performance is observed.     

基于数据驱动仿真的两设备系统元模型

半导体封装测试系统等复杂制造系统的性能分析是项非常困难的任务。利用仿真模型构建两设备系统元模型,并以元模型为基石构建面向大规模复杂系统的近似解析方法是分析复杂制造系统的有效手段。为了快速准确地构建两设备系统元模型,提出了一种基于数据驱动仿真技术及人工神经网络的元模型构建方法。该方法以考虑缓存输送时间的两设备制造系统为研究对象,采用AREAN的二次开发技术实现仿真模型的自动配置、运行、统计,以生成人工神经网络所需案例,并通过比较分析BP、RBF和Chebyshev这3类典型的函数逼近神经网络确定最优的人工神经网络模型。实验结果表明径向基函数密度为120的RBF神经网络模型表现最优,其结果误差最小,能够成为大规模复杂制造系统近似解析方法的基石。     

Forecasting and maintenance problem under subcontracting constraint with transportation delay

In this paper, a forecasting production/maintenance optimization problem has been proposed with a random demand and single machine M₁ on a finite horizon. The function rate of the machine M₁ is depending on the production rate for each period of the forecasting horizon. In order to satisfy the customer, a subcontracting assures the rest of the production through machine M₂ with transportation delay. An analytic formulation of the problem has been proposed using a sequential computation of the optimal production plan for which an optimal preventive maintenance policy has been calculated based on minimal repair. Firstly, we find, the optimal production plans of principal and subcontracting machines, which minimises the total production and inventory cost for the cases without and with returned products under service level and subcontracting transportation delay. Secondly, we determine a joint effective maintenance policy with the optimal production plan, which integrates the various constraints for the production rates, the transportation delay and the returned production deadline. Numerical results are presented to highlight the application of the developed approach and sensitivity analysis shows the robustness of the model.     

Investigation of ablation studies of EPS pattern produced by rapid prototyping

Expanded Polystyrene (EPS) patterns are used in Evaporative Pattern Casting (EPC). The cost of EPS pattern-making through moulding cannot be justified for small batch production. As 3D printing or Additive Manufacturing (AM) is suitable for small volumes, several efforts have been made to develop these machines for EPS including Segmented Object Manufacturing (SOM) of the authors. EPS is typically processed through ablation or traditional machining, the former using hot tools in the form of profiled axisymmetric shapes, blades or wire. The efficacy of SOM machine relies on the performance of the individual sub-systems, so in the present work, the ablation studies of hot wire slicing of the machine is performed. The kerfwidth and surface roughness determine the quality of the pattern produced by ablation. The objective of the paper is to investigate the ablation process by introducing novel mathematical model to predict the kerfwidth for different power inputs and feedrates, which is further validated with experimental data. Subsequently, an empirical relationship is established to predict the surface roughness (R_a) of the sliced surface by performing regression analysis of collected experimental data. The different cutting zones have also been classified, which gives an overall understanding of slicing mechanism. The average error in surface roughness prediction is found to be around ±10%. With the help of these models, the SOM machine can produce better quality EPS patterns in terms of kerfwidth and R_a value, which finally depicts the quality of final casting produced by EPC process.     

Reliability analysis for dynamic configurations of systems with three failure modes

Analytical models for computing the reliability of dynamic configurations of systems, such as majority and k-out-of-n, assuming that units and systems are subject to three types of failures: stuck-at-0, stuck-at-1, and stuck-at-x are presented in this paper. Formulas for determining the optimal design policies that maximize the reliability of dynamic k-out-of-n configurations subject to three types of failures are defined. The comparisons of the reliability modeling functions are also obtained. The optimum system size and threshold value k that minimize the expected cost of dynamic k-out-of-n configurations are also determined.     

An improved decomposition method for evaluating the performance of transfer lines with unreliable machines and finite buffers

In this paper, we consider transfer lines consisting of a series of machines separated by finite buffers. The processing time of each machine is deterministic and may be not identical. All machines are prone to operation-dependent failures, and the times between failures and the times to repair are assumed to be exponentially distributed. Many analytical methods have been developed to evaluate the performance of such lines. In general, these methods provide fairly accurate results. However, in some real cases where the orders of magnitude of machines’ reliability parameters (mean times between failures and mean times to repair) are not at the same level, the accuracy of these existing methods may not be good enough. The purpose of this paper is to propose an improved decomposition method that performs well even in the situation above. We use generalised exponential distributions instead of exponential distributions to approximate the repair-time distributions of the fictitious machines, and a new ADDX algorithm is developed to calculate the performance parameters such as the production rate and the average buffer levels. Numerical results indicate that the improved decomposition method provides more accurate results and converges in most cases. It is feasible and valid to evaluate the performance of transfer lines with unreliable machines and finite buffers.     

Modeling the bathtub shape hazard rate function in terms of reliability

In this paper, a general form of bathtub shape hazard rate function is proposed in terms of reliability. The degradation of system reliability comes from different failure mechanisms, in particular those related to (1) random failures, (2) cumulative damage, (3) man–machine interference, and (4) adaptation. The first item is referred to the modeling of unpredictable failures in a Poisson process, i.e. it is shown by a constant. Cumulative damage emphasizes the failures owing to strength deterioration and therefore the possibility of system sustaining the normal operation load decreases with time. It depends on the failure probability, 1−R. This representation denotes the memory characteristics of the second failure cause. Man–machine interference may lead to a positive effect in the failure rate due to learning and correction, or negative from the consequence of human inappropriate habit in system operations, etc. It is suggested that this item is correlated to the reliability, R, as well as the failure probability. Adaptation concerns with continuous adjusting between the mating subsystems. When a new system is set on duty, some hidden defects are explored and disappeared eventually. Therefore, the reliability decays combined with decreasing failure rate, which is expressed as a power of reliability. Each of these phenomena brings about the failures independently and is described by an additive term in the hazard rate function h(R), thus the overall failure behavior governed by a number of parameters is found by fitting the evidence data. The proposed model is meaningful in capturing the physical phenomena occurring during the system lifetime and provides for simpler and more effective parameter fitting than the usually adopted ‘bathtub’ procedures. Five examples of different type of failure mechanisms are taken in the validation of the proposed model. Satisfactory results are found from the comparisons.     

Modeling and Analysis of Assembly Systems with Unreliable Machines and Finite Buffers

An assembly line is a tree-structured manufacturing system in which some machines perform assembly operations. In this paper, we consider assembly lines with the following features: every operation is performed in a fixed amount of time, machines are unreliable, and buffers have finite capacity. Usually, the times to failures of machines are much larger than the processing times. This allows us to approximate the behavior of these systems by a continuous flow model. The behavior of this model is then analyzed using a decomposition technique which is an extension of an earlier technique proposed in the case of transfer lines. An efficient algorithm for calculating performance measures such as production rate and average buffer levels is derived. Experimental results are provided showing mat this approximate method is quite accurate.     

A Modeling Approach to Maintenance Decisions Using Statistical Quality Control and Optimization

Maintenance concerns impact systems in every industry and effective maintenance policies are important tools. We present a methodology for maintenance decision making for deteriorating systems under conditions of uncertainty that integrates statistical quality control (SQC) and partially observable Markov decision processes (POMDPs). We use simulation to develop realistic maintenance policies for real‐world environments. Specifically, we use SQC techniques to sample and represent real‐world systems. These techniques help define the observation distributions and structure for a POMDP. We propose a simulation methodology for integrating SQC and POMDPs in order to develop and valuate optimal maintenance policies as a function of process characteristics, system operating and maintenance costs. A two‐state machine replacement problem is used as an example of how the method can be applied. A simulation program developed using Visual Basic for Excel yields results on the optimal probability threshold and on the accuracy of the decisions as a function of the initial belief about the condition of the machine. This work lays a foundation for future research that will help bring maintenance decision models into practice. Copyright © 2005 John Wiley & Sons, Ltd.     

An efficient analytical method for performance evaluation of transfer lines with unreliable machines and finite transfer-delay buffers

Buffers are widely adopted in transfer lines to reduce the fluctuations caused by the imbalances of systems or machine failures. This paper presents an efficient analytical method to evaluate the performance of transfer lines with unreliable machines and finite transfer-delay buffers. Firstly, the buffers with transfer delays are transformed equivalently into a series of perfect machines and buffers without transfer delays. Correspondingly, the initial transfer line is replaced by an equivalent transfer line with more machines and zero-transfer-delay buffers. Since in the equivalent transfer line the orders of magnitude of machines’ reliability parameters (mean times between failures and mean times to repair) are not at the same level, an advanced decomposition method is introduced to analyse the equivalent transfer line, using the general-exponential distributions instead of the exponential distributions to approximate the repair time distributions of the fictitious machines. Finally, extensive simulation and numerical cases are carried out to verify the performance of the developed method.