Argon Chen

Optimal levels of process parameters for products with multiple characteristics

The purpose of off-line quality control is to design robust products using robust manufacturing processes before the actual manufacturing of the product. Most of the research work has focused on determining the optimal level settings of process parameters for products with a single quality characteristic. In this paper, we employ the loss function approach to determine the optimal level settings of the process parameters of the production processes for products with multiple characteristics.

Age-based double EWMA controller and its application to CMP processes

In the originally proposed run-by-run control scheme, the EWMA statistic is used as an estimate of the process deviation from its target. However, the controller based on the EWMA statistic is not sufficient for controlling a wearing out process. The PCC controller has been thus proposed to enhance the run-by-run controller capability. In this paper, we first reexamine the fundamentals of the PCC formulations and propose an adjustment that is advantageous in controlling processes subject to both random shifts and drifts. The adjusted PCC controller is then further refined to take into account the process age. This age-based double EWMA scheme is then applied to the CMP process, which is known in the semiconductor industry to be rather unstable.

Real-time health prognosis and dynamic preventive maintenance policy for equipment under aging Markovian deterioration

An often seen practice of preventive maintenance (PM) is to construct a machines reliability model based on its historical failure records. The reliability model is then used to determine the PM schedule by minimizing the machines long-run operation cost or average machine downtime. Machines in many hi-tech manufacturing sectors are using sophisticated sensor technologies to provide sufficient immediate online data for real-time observation of equipment condition. Not only is the historical data but also the real time condition now available for scheduling a more effective PM policy. This research is to determine an effective PM policy based on real-time observations of equipment condition. We first use the multivariate process capability index to integrate the equipments multiple parameters into an overall equipment health index. This health index serves as the basis for real-time health prognosis under an aging Markovian deterioration model. A dynamic PM schedule is then determined based on the health prognosis.

An economic design of [xbar] control chart using quadratic loss function

Abstract The quadratic loss function is used in Taguchis on-line cost model to estimate the quality cost. However, Taguchis on-line quality control approach is different from the widely used statistical process control techniques where control charts are the primary tools for quality control. Duncans economic design of x control chart is the first attempt to design the control charts in terms of process cost. In this paper, we present a new economic design based on the loss function approach as advocated by Taguchi. We also obtain the optimal parameters of the control chart that minimize the total quality cost.

Design of EWMA and CUSUM control charts subject to random shift sizes and quality impacts

Statistical process control charts are important tools for detecting process shifts. To ensure accurate, responsive fault detection, control chart design is critical. In the literature, control charts are typically designed by minimizing the control charts responding time, i.e., average run length (ARL), to an anticipated shift size under a tolerable false alarm rate. However, process shifts, originating from various variation sources, often come with different sizes and result in different degrees of quality impacts. In this paper, we propose a new performance measure for EWMA and CUSUM control chart design to take into consideration the variable shift sizes and corresponding quality impacts. Unlike economic designs of control charts that suffer from a complex cost structure and intensive numerical computation, the proposed design methodology does not involve any cost estimation and the design procedure is as simple as looking up tables. Given the Gaussian random shifts and quadratic quality loss function, we show that the proposed design has a significant reduction in the quality impact as compared to conventional ARL-based designs. Guidelines and useful worksheets for practical implementation of the proposed designs are then suggested to practitioners with different knowledge levels of the process excursions.

Recipe-Independent Indicator for Tool Health Diagnosis and Predictive Maintenance

Advanced sensor and information technologies have made real-time tool data readily accessible to tool and process engineers. A significant number of tool parameters (status variable identifications) are collected during wafer processing, and a large amount of tool data is acquired and available for fault detection and classification (FDC). Many IC makers have substantially improved the process capabilities by implementing FDC. With the real-time tool data, one can also evaluate the overall tool condition so that tool maintenance can be more effectively scheduled and the post-maintenance tool condition can be more easily qualified. However, due to the frequent change of recipes and the diversity of operations, the overall tool health is very difficult to evaluate. In this paper, we propose a recipe-independent health indicator based on the generalized moving variance. It is shown that the indicator faithfully reveals the tool condition regardless of recipe/operation changes. With the tool health indicator, possible tool faults can be identified and proper maintenance measures can be scheduled accordingly. The proposed indicator will be demonstrated and validated through the case studies of a plasma-enhanced chemical vapor deposition and a physical vapor deposition tool from a local fab.

A cost-effective methodology for a run-by-run EWMA controller

In this paper, we present a cost-effective methodology for a run-by-run EWMA controller. This controller is an integrated approach that combines the advantages of statistical process control and feedback control. It adjusts the equipment settings only when the control chart detects an abnormal trend. Using simulations, we take into consideration the control sensitivity, robustness, and adjustment number required to determine an optimal weight for a minimum cost. As the simulation results demonstrate, the cost-effective run-by-run controller is able to keep drifting process outputs close to the target with only few runs of adjustment.

Design and Performance Analysis of the Exponentially Weighted Moving Average Mean Estimate for Processes Subject to Random Step Changes

The exponentially weighted moving average (EWMA) is a well-known and popular statistic used for smoothing and forecasting time series and as a process mean estimator, due to its simplicity and ability to capture nonstationarity. The EWMA statistic has been shown to be an optimal mean estimator for a certain disturbance process and an effective estimator for various other processes. In this article we focus on a practical disturbance process—relatively small random step changes that are difficult to distinguish from white noise and usually overlooked by practitioners. We propose an optimal EWMA parameter for step-change disturbance processes, as well as methodologies to identify and estimate the process models. The EWMA estimators performance is then evaluated analytically. We demonstrate that a well-designed EWMA control scheme can effectively reduce the process variation even for processes subject to infrequent, small step changes. A semiconductor process example illustrates the design and analysis.

Demand planning approaches to aggregating and forecasting interrelated demands for safety stock and backup capacity planning

Results of demand planning serve as the basis of every planning activity in a demand–supply network and ultimately determine the effectiveness of manufacturing and logistic planning, such as capacity and safety stock planning, in the network. The uncertainty of demand signals that are propagated and magnified over the network becomes the crucial cause of ineffective operation plans. With the globalization of demand–supply networks and the desire for a more integrated operation plan, demand planning is now one of the greatest challenges facing manufacturers. To manage the demand variability, appropriate demand aggregation and statistical forecasting approaches are known to be effective. This paper will use the bivariate VAR(1) time-series model as a study vehicle to investigate the effects of aggregating two interrelated demands. It is shown that the aggregated time series of two VAR(1) times series is equivalent to the sum of two AR(1) time series. Through theoretical development, the paper further explores the properties of the aggregated time series and provides guidelines for practitioners to determine proper aggregation and forecasting approaches. An important finding of this research is that demand aggregation is far more effective than statistical forecasting in operations planning for any two demands with low positive correlation or negative correlation.

An alternative mean estimator for processes monitored by SPC charts

Statistical Process Control (SPC) chart is a graphical tool that helps to identify a possible process shift. Though the SPC chart is, in theory, a monitoring tool that reveals only the result of a statistical hypothesis testing, in practice the charts signaling is often used for making process adjustment. In this paper we develop a robust estimator of the process mean for processes monitored by SPC charts. This mean estimate can serve as an important reference for investigating assignable causes and taking appropriate corrective actions. When the control chart is implemented as a control device, the mean estimate can also provide a more accurate assessment of the amount of adjustment to be made to the process. We also demonstrate in this paper that when the process shift is relatively small, the proposed mean estimate outperforms the mean estimate usually used for the CUSUM scheme.