Rework Operation Research Articles

Exact analysis of production lines with Coxian-2-distributed processing times and parallel machines

This study considers production lines where each station has parallel machines with 2-phase Coxian processing times. The setting in this paper is designed specifically for scrutiny of the replenishment of raw materials and finished goods inventories with intermediate buffers in-between stations. Each buffer has a limit of capacity. Raw material supply and demand for finished goods are generated according to independent stationary Poisson processes. Coxian-2 processing times can be utilized to model failure-prone machines with exponential service times, times to failure, and repair times. The second phase of Coxian-2 can also be considered as a rework operation visited with a predefined probability. We model the line as a continuous-time Markov chain and propose recursive algorithms to generate the transition rate matrix. Although the general recursive form is specific to 3-station 4-buffer lines, routines for calculating the number of states and generating the states work for any M−station (M + 1)-buffer systems. The developed model allows obtaining steady-state distribution and performance metrics such as throughput, the average number of items in the buffers, and average system cost consisting of production, holding, and shortage costs. Furthermore, we enrich our study with numerical experiments and analyze the impacts of buffer capacities, processing rates of the machines and the number of parallel machines on the system performance. Moreover, the exact analysis provided in this paper can also be used as the decomposition block for the performance analysis of longer lines.

A Single-Stage Manufacturing Model with Imperfect Items, Inspections, Rework, and Planned Backorders

Each industry prefers to sell perfect products in order to maintain its brand image. However, due to a long-run single-stage production system, the industry generally obtains obstacles. To solve this issue, a single-stage manufacturing model is formulated to make a perfect production system without defective items. For this, the industry decides to stop selling any products until whole products are ready to fulfill the order quantity. Furthermore, manufacturing managers prefer product qualification from the inspection station especially when processes are imperfect. The purpose of the proposed manufacturing model considers that the customer demands are not fulfilled during the production phase due to imperfection in the process, however customers are satisfied either at the end of the inspection process or after reworking the imperfect products. Rework operation, inspection process, and planned backordering are incorporated in the proposed model. An analytical approach is utilized to optimize the lot size and planned backorder quantities based on the minimum average cost. Numerical examples are used to illustrate and compare the proposed model with previously developed models. The proposed model is considered more beneficial in comparison with the existing models as it incorporates imperfection, rework, inspection rate, and planned backorders.

“Digital Twins” for Highly Customized Electronic Devices – Case Study on a Rework Operation

The ongoing changes in manufacturing require that new information models for industrial computer systems be developed and applied. This paper describes a concept for the material model as a “digital twin” for producing highly customised, smart electronic devices. The scope of the research is the transformation of the models that are typical for the currently used automation pyramid approach to Reference Architecture Models for Industry 4.0 (RAMI4.0). The ISA95 standard is used as the modelling tool and Open Production Connectivity Unified Architecture (OPC UA) as the communication middleware. The presented use case focuses on a rework operation that is performed during the short series production of highly customised electronic devices that are produced by the Aiut company. The paper focuses on the transformation from the static architecture of Manufacturing Execution Systems to flexible and dynamic information models.

The effects of rework on the shopfloor control in wafer fabrication

The purpose of this paper is to study the effect of rework operations on the shopfloor control’s strategies, including order release and dispatching. An attempt is made to determine the performance of various production control strategies on the system performance indicators under different levels of rework rate. Also the interaction of order release and dispatching strategies under different rework operations is investigated. Some representative shopfloor control (SFC) strategies are considered in our simulation model. It was found that the effect of rework operation on the system performance is significant. The order release and dispatching strategies’ performance is affected by the rework operation. The performance is improved dramatically if a suitable combination of order release and dispatching strategies is adopted. Under different rework rates and performance indicators a suitable combination of SFC strategies is suggested in this paper.

CAPP for Electronics Manufacturing Case Study: Fine Pitch SMT Laser Soldering

The trend to high-density packaging in surface mount assembly has highlighted inherent difficulties in the assembly line of these very fine pitch devices. A variety of defects is still common in printed circuit board assembly (PCBA) technology despite all the improvements made, and rework of PCBA is inevitable and performed manually in PCBA manufacturing floors since the cost of each component and PCB itself may be hundreds of dollars. In the last few years, the number of rework stations available on the market has grown considerably including the automated ones, but there has still been no significant reduction in the number of the defects. In electronics manufacturing, rework is defined as the activity that replaces defective components with those that are acceptable such that the populated board performs to the specifications. Increasing product complexity, decreasing component size, and using double sided boards have made rework more difficult and the economic reworking of PCBAs is one of the main problems facing PCB manufacturers. PCBA manufacturing has been relatively improved with fully automated, accurate assembly machines and the use of robots. Although significant improvement in automated rework has also been made by the author, it has been shown that the outcomes of the automated rework line have not produced a high enough level of the reliable yield percentage. The objective of this research project is to make a contribution towards this surface mount rework by creating a Computer Aided Process Planning (CAPP) system of circuit board defects so that the defects that necessitate rework operation can be detected through the electronics manufacturing assembly line. With the development of CAPP tool, the rework will be removed from the PCBA line and PCBA process parameters which cause joint level reliability problems will be troubleshot with the help of the developed system.

Modelling the cost of poor quality in a five-state part manufacturing operation: a case study

The quality history of individual parts from a critical operation can be modeled by a five-state Markov chain involving factory rework operation, customer inspection and field test, parts scrapped, parts defective but used-as-is by concession or re-graded for alternative applications, and defect-free parts satisfying customer requirements. We estimate total failure cost by a five-state Markov chain model and present a case study to demonstrate relationship of the total failure cost to appraisal and prevention costs.

Experimental Investigation of Thermoelastic Deformation in Turbojet-Engine Bearings Under Maintenance Inspection

The present investigation examined the vertical and horizontal thermoelastic changes in the outside diameter of a turbojet-engine roller bearing. Thermal loads were imparted to the bearing by the hands of a bearing technician during a rework operation. A worst-case analysis was examined by assuming a three-minute dwell time and diametrically symmetric thermal loading. Contact temperature was experimentally determined and used in conjunction with a numerical model to simulate thermal propagation throughout the bearing outer ring. Diametric deflection data, obtained using the contact temperature in conjunction with analytic and finite elements, have been shown for comparative purposes. Experimental diametric expansions of the bearing outer ring were determined and compared with the predicted results. Assuming a worst-case scenario, this investigation yielded vertical expansions in the bearing outer ring’s diameter, which would be problematic for some bearings during the rework operation; appropriate corrective action was discussed.

Optimal Operating Policy for a Bottleneck with Random Rework

This paper presents a model of a bottleneck facility that performs two distinct types of operations: “regular” and “rework.” Each job is subjected to a test after completing the regular operation at the bottleneck. If the job passes the test, then it continues its process downstream. Otherwise, the job will cycle back to the bottleneck stage for rework operation. Upon the completion of a batch of regular jobs, the decision maker observes the amount of rework and decides on whether to switch over to process the reworks or continue to process another batch of regular jobs. It is assumed that both switch-over time and cost are incurred when the facility switches from performing one type of operation to a different type. The goal of the analysis is to characterize the optimal operating policy for the bottleneck so that the average operating cost is minimized. In order to characterize the optimal operating policy, we first formulate the problem as a semi-Markov decision process. Then we show that there exists an optimal “threshold” operating policy that can be described as follows: upon completion of a batch of regular jobs, switch over to process the reworks only if the number of reworks exceeds a critical value. In addition, we develop a simple procedure to compute the critical value that specifies the optimal threshold policy. Moreover, we evaluate the impact of batch sizes, yield, and switch-over time on the optimal threshold policy.

THERMAL DEFORMATIONS IN THIN CIRCULAR RINGS SUBJECTED TO LOCALIZED HEATING

This investigation examined the vertical and horizontal thermoelastic deformations of the outside diameter of a turbojet-engine roller bearing. During a rework operation, thermal loads were imparted to the bearing by the hands of a bearing technician. A worst case analysis was employed by assuming a three-minute dwell time and diametrically symmetric thermal loading. A numerical model was used together with experimentally measured contact temperature to determine the temperature fields throughout the bearing outer ring. Next, diametric displacement solutions were variationally derived for two mathematical approximations using Hamilton's principle and assuming thin ring behavior. Alternatively, diametric deflections were calculated using a finite element model (FEM) constructed for the bearing outer ring. Then the solutions yielded by the finite element and two analytic techniques were compared to diametric expansion data found experimentally. This analysis yielded vertical expansions in the bearing outer ring's diameter that would be problematic for some bearings during the rework procedure; several recommendations were given to alleviate the problem.

Cell Controller Software Modelling for PCBA Rework Cell

Rework is an integral part of printed circuit board assembly (PCBA) manufacturing. However, the state‐of‐the‐art for PCBA rework still relies on operator activity and is therefore semi‐automatic. As a result, the quality of rework depends very much on the skill of the operator. When developing an automatic PCBA rework cell, the cell controller is an essential part which organises and controls the overall rework operation. This paper describes the software modelling of the cell controller for the PCBA rework cell which has been implemented for reworking through‐hole and surface mounted components. The software model is based on hybrid representations and rule‐based control.