Classification analysis for simulation of the duration of machine breakdowns

Machine failure can have a significant impact on the throughput of manufacturing systems, therefore accurate modelling of breakdowns in manufacturing simulation models is essential. Finite mixture distributions have been successfully used by Ford Motor Company to model machine breakdown durations in simulation models of engine assembly lines. These models can be very complex, with a large number of machines. To simplify the modelling we propose a method of grouping machines with similar distributions of breakdown durations, which we call the Arrows Classification Method, where the Two-Sample Cramér-von-Mises statistic is used to measure the similarity of two sets of the data. We evaluate the classification procedure by comparing the throughput of a simulation model when run with mixture models fitted to individual machine breakdown durations; mixture models fitted to group breakdown durations; and raw data. Details of the methods and results of the classification will be presented, and demonstrated using an example.     

Modeling and analysis of multi‐stage transfer lines with unreliable machines and finite buffers

This paper models and analyzes multistage transfer lines with unreliable machines and finite buffers. The machines have exponential operation, failure, and repair processes. First, a mixed vector–scalar Markov process model is presented based on some notations of mixed vector–scalar operations. Then, several steadystate system properties are deduced from this model. These include the reversibility and duality of transfer lines, conservation of flow, and the flow rate–idle time relationship. Finally, a fourstage transfer line case is used to compare and evaluate the accuracy of some approximation methods presented in the literature with the exact numerical solutions this model can provide. The properties and their proofs in this paper lay the theoretic foundation for some widely held assumptions in decomposition techniques of long transfer lines in the area of manufacturing systems engineering.     

Analysis of flexible manufacturing systems with priority scheduling: PMVA

A new methodology for performance analysis of flexible manufacturing systems (FMSs) with priority scheduling is presented. The analytic model developed extends the mean value analysis of closed networks of queues with multiple product types, various non-preemptive priority service disciplines, and with parallel machine stations. Performance measures derived include the expected throughput per product and per station, utilization of machines and transporters, queuing times and queue length measures for various configurations. Extensive numerical calculations have shown that the algorithm used for solving the problem converges rapidly and retains numerical stability for large models. The paper also illustrates the application of the model to a system with a mixture of FCFS and HOL disciplines which gives insights into various priority assignment policies in FMSs. Special attention was given to the problem of scheduling the robot carriers (transporters).     

Waiting times in queueing networks with a single shared server

We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems, and robotics. Special cases of the introduced network include well-known polling models, tandem queues, systems with a waiting room, multi-stage models with parallel queues, and many others. A complicating factor of this model is that the internally rerouted customers do not arrive at the various queues according to a Poisson process, causing standard techniques to find waiting-time distributions to fail. In this paper, we develop a new method to obtain exact expressions for the Laplace–Stieltjes transforms of the steady-state waiting-time distributions. This method can be applied to a wide variety of models which lacked an analysis of the waiting-time distribution until now.     

Exact analysis of a two-workstation one-buffer flow line with parallel unreliable machines

This paper examines a model of a serial flow line with two workstations and an intermediate buffer. Each workstation consists of multiple unreliable parallel machines which are not necessarily identical, viz., the processing times, failure times and repair times of the parallel machines at each workstation are assumed to be exponentially distributed with non-identical mean rates. The system under consideration is solved via exact Markovian analysis. More specifically, a recursive algorithm that generates the transition matrix for any value of the intermediate buffer capacity is developed and all possible transition equations are derived and solved analytically. Once the transition equations are solved the performance measures of the model under consideration can be easily evaluated. This model may be used as a decomposition block for solving larger flow lines with parallel unreliable machines at each workstation.     

Efficiency and production rate of a transfer line with two machines and a finite storage buffer

A markov model for a transfer line with two unreliable machines separated by a finite storage size buffer is introduced. Service time distribution for the two machines is Erlang whereas failure and repair times are assumed to be exponential random variables. The paper presents an efficient method to solve analytically the steady state probabilities of the system. This method is independent of the buffer size. We also include in the paper a study of the behavior of some systems performance measures such as the efficiency of the two machines and the production rate of the system.     

Modelling and analysis of Markovian continuous flow systems with a finite buffer

In this study, a Markovian fluid flow system with two stages separated by a finite buffer is considered. Fluid flow models have been analyzed extensively to evaluate the performance of production, computer, and telecommunication systems. Recently, we developed a methodology to analyze general Markovian continuous flow systems with a finite buffer. The flexibility of this methodology allows us to analyze a wide range of systems by specifying the transition rates and the flow rates associated with each state of each stage. In this study, in order to demonstrate the applicability of our methodology, we model and analyze a range of models studied in the literature. The examples we analyze as special cases of our general model include systems with phase-type failure and repair-time distributions, systems with machines that have multiple up and down states, and systems with multiple unreliable machines in series or parallel in each stage. For each case, the Markovian model is developed, the transition and flow rates are determined, and representative numerical results are obtained by using our methodology.     

A dispatching rule-based approach to production scheduling in a printed circuit board manufacturing system

This paper focuses on a production-scheduling problem in a printed circuit board (PCB) manufacturing system that produces multiple product types with different due dates and different manufacturing processes. In the PCB manufacturing system, there is a number of serial workstations, and there are multiple parallel machines at each workstation. Also, setup operations are required at certain workstations or machines, and some product types have re-entrant flows. We develop new dispatching rules for scheduling at each workstation, considering the special features of PCB manufacturing. With the dispatching rules, we determine not only the start time of each lot at a machine but also the batch size of each product at each machine. Simulation experiments are carried out to test the performance of the production-scheduling method and dispatching rules devised in this study. Results show that the production-scheduling method suggested in this study performs better than methods with well-known dispatching rules and heuristic algorithms for lot sizing in terms of the total tardiness of orders.     

Geometric decay in level-expanding QBD models

Level-expanding quasi-birth-and-death (QBD) processes have been shown to be an efficient modeling tool for studying multi-dimensional systems, especially two-dimensional ones. Computationally, it changes the more challenging problem of dealing with algorithms for two-dimensional systems to a less challenging one for block-structured transition matrices of QBD type with varying finite block sizes. In this paper, we focus on tail asymptotics in the stationary distribution of a level-expanding QBD process. Specifically, we provide sufficient conditions for geometric tail asymptotics for the level-expanding QBD process, and then apply the result to an interesting two-dimensional system, an inventory queue model.     

Analysis of a Fork/Join Synchronization Station with Inputs from Coxian Servers in a Closed Queuing Network

Fork/join stations are commonly used to model the synchronization constraints in queuing models of computer networks, fabrication/assembly systems and material control strategies for manufacturing systems. This paper presents an exact analysis of a fork/join station in a closed queuing network with inputs from servers with two-phase Coxian service distributions, which models a wide range of variability in the input processes. The underlying queue length and departure processes are analyzed to determine performance measures such as throughput, distributions of the queue length and inter-departure times from the fork/join station. The results show that, for certain parameter settings, variability in the arrival processes has a significant impact on system performance. The model is also used to study the sensitivity of performance measures such as throughput, mean queue lengths, and variability of inter-departure times for a wide range of input parameters and network populations.     

Complexity of Buffer Capacity Allocation Problems for Production Lines with Unreliable Machines

Buffer capacity allocation problems for flow-line manufacturing systems with unreliable machines are studied. These problems arise in a wide range of manufacturing systems and concern determining buffer capacities with respect to a given optimality criterion which can depend on the average production rate of the line, buffer cost, inventory cost, etc. Here, this problem is proven to be NP-hard for a tandem production line and oracle representation of the revenue and cost functions, and NP-hard for a series-parallel line and stepwise revenue function.     

A New Decomposition Approach for Non-Cyclic Continuous Material Flow Lines with a Merging Flow of Material

We extend the decomposition approaches for flow lines with unreliable machines and limited buffer capacity as proposed by Gershwin and refined by Dallery, David, and Xie and by Burman by incorporating a new building block in the decomposition. This new building block is a three-machine, one buffer system which models a merging flow of material. While previous decomposition approaches led to a decomposition of the original network into virtual two-machine lines, we now use both virtual two- and three-machine lines. This requires a new set of decomposition equations for the virtual machines of the two-machine lines that surround the new building block modelling the merge. We present these equations, show how to solve them in an algorithm and present numerical results for non-cyclic networks in order to determine production rate and inventory level estimates.     

Decomposition of unreliable assembly/disassembly networks with limited buffer capacity and random processing times

An assembly/disassembly (A/D) network is a manufacturing system in which machines perform assembly and/or disassembly operations. We consider tree-structured systems of unreliable machines that produce discrete parts. Processing times, times to failure and times to repair in the inhomogeneous system are assumed to be stochastic and machine-dependent. Machines are separated by buffers of limited capacity. We develop Markov process models for discrete time and continuous time systems and derive approximate decomposition equations to determine performance measures such as production rate and average buffer levels in an iterative algorithm. An improved parameter updating procedure leads to a dramatic improvement with respect to convergence reliability. Numerical results demonstrate that the methods are quite accurate.     

Sensitivity analysis of machine repair problems in manufacturing systems with service interruptions

This paper models a manufacturing system consisting of M operating machines and S spare machines under the supervision of a group of technicians in a repair facility. Machines fail according to a Poisson process, and the repair (service) process of a failed machine may require more than one phase. In each phase, service times are assumed to be exponentially distributed but may be interrupted when the repair facility encounters unpredictable breakdowns. Two models of manufacturing systems are considered. In the first model, technicians repair failed machines at different rates in each phase. In the second model, a two-phase service system with differing numbers of technicians is considered. Profit functions are developed for both models and optimized by a suitable allocation of the number of machines, spares, and technicians in the system. Finally, a sensitivity analysis (see Cao [X.R. Cao, Realization Probabilities: The Dynamics of Queuing Systems, Springer-Verlag: London, 1994; X.R. Cao, The relations among potentials, perturbation analysis, and Markov decision processes, Discrete Event Dynam. Syst.: Theory Applicat. 8 (1998) 71–87]) is performed to provide an approach that quantifies the impact of changes in the parameters on the profit models.     

Performance evaluation of transfer lines with general repair times and multiple failure modes

The paper proposes a decomposition method for evaluating the performance of transfer lines where machines can fail in multiple modes and can be repaired with non-exponential times. Indeed, while times to machine failure can be often modeled using exponential distributions with acceptable accuracy, times to repair are very rarely observed to be exponentially distributed in actual systems. This feature limits the applicability of existing approximate analytical methods to real production lines. In this paper, the discrete acyclic phase-type distribution is used to model the repair process, for each failure mode of the machines composing the system. The exact analysis of the two-machine system is used as a building block for the decomposition method, proposed to study multi-stage lines. Numerical results show the high accuracy of the developed method in estimating the average throughput and buffer levels.     

Development of a model for a two-station serial transfer line subject to machine and buffer failure

In modern automated production lines, it is common to connect pairs of machines with mechanical storage devices in order to provide buffering between processing stations. Since these devices are mechanical, they are prone to failure. Previous research concerning the analytical modeling of a class of production lines, the serial transfer line, assumes that these buffers are completely reliable. The concept of an unreliable buffer is introduced and an analytic model of a two machine line with an unreliable buffer is developed. It is proposed that this model will form the foundation for an analytic model of the more complex K > 2 machine serial transfer line with unreliable buffers.     

Production variability in manufacturing systems: Bernoulli reliability case

The problem of production variability in serial manufacturing lines with unreliable machines is addressed. Bernoulli statistics of machine reliability are assumed. Three problems are considered: the problem of production variance, the problem of constant demand satisfaction, and the problem of random demand satisfaction generated by another (unreliable) production line. For all three problems, bounds on the respective variability measures are derived. These bounds show that long lines smooth out the production and reduce the variability. More precisely, these bounds state that the production variability of a line with many machines is smaller than that of a single machine system with production volume and reliability characteristics similar to those of the longer line. Since all the variability measures for a single machine line can be calculated relatively easily, these bounds provide analytical tools for analysis and design of serial production lines from the point of view of the customer demand satisfaction.     

Genetic algorithm-based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops

In this paper, we consider a modified shifting bottleneck heuristic for complex job shops. The considered job shop environment contains parallel batching machines, machines with sequence-dependent setup times and reentrant process flows. Semiconductor wafer fabrication facilities (Wafer Fabs) are typical examples for manufacturing systems with these characteristics. Our primary performance measure is total weighted tardiness (TWT). The shifting bottleneck heuristic uses a disjunctive graph to decompose the overall scheduling into scheduling problems for single tool groups. The scheduling algorithms for these scheduling problems are called subproblem solution procedures (SSPs). In previous research, only subproblem solution procedures based on dispatching rules have been considered. In this paper, we are interested in how much we can gain in terms of TWT if we apply more sophisticated subproblem solution procedures like genetic algorithms for parallel machine scheduling. We conduct simulation experiments in a dynamic job shop environment in order to assess the performance of the suggested subproblem solution procedures. It turns out that using near to optimal subproblem solution procedures leads in many situations to improved results compared to dispatching-based subproblem solution procedures.     

Representation and analysis of transfer lines with machines that have different processing rates

A transfer line is a tandem production system, i.e. a series of machines separated by buffers. Material flows from outside the system to the first machine, then to the first buffer, then to the second machine, the second buffer, and so forth. In some earlier models, buffers are finite, machines are unreliable, and the times that parts spend being processed at machines are equal at all machines. In this paper, a method is provided to extend a decomposition method to large systems in which machines are allowed to take different lengths of time performing operations on parts. Numerical and simulation results are provided.     

Solving a multi-objective simulation model using a hybrid response surface method and lexicographical goal programming approach—a case study on integrated circuit ink-marking machines

In an integrated circuit (IC) packaging plant, the ink-marking machine has a significantly higher throughput than the other processing machines. When periodic demand surges result in backlog orders or in lost customers, there is a need to increase system throughput. To resolve this problem, the purchase of a new machine often results in excess capacity in addition to added operation and acquisition costs. Therefore, the productivity improvement effort has priority over the machine purchase decision. This paper seeks to optimize both throughput and cycle time performance for IC ink-marking machines. While throughput increase is the primary objective, there is an acceptable cycle time limit for a feasible solution. It is a multi-objective problem. The proposed solution methodology constructed a simulation metamodel for the ink-marking operation by using a fractional factorial experimental design and regression analysis. It is then solved by a hybrid response surface method and lexicographical goal programming approach. Solution results illustrated a successful application.