Fugee Tsung

MONITORING GENERAL LINEAR PROFILES USING MULTIVARIATE EXPONENTIALLY WEIGHTED MOVING AVERAGE SCHEMES

We propose a statistical process control scheme that can be implemented in industrial practice, in which the quality of a process can be characterized by a general linear profile. We start by reviewing the general linear profile model and the existing monitoring methods. Based on this, we propose a novel multivariate exponentially weighted moving average monitoring scheme for such a profile. We introduce two other enhancement features, the variable sampling interval and the parametric diagnostic approach, to further improve the performance of the proposed scheme. Throughout the article, we use a deep reactive ion etching example from semiconductor manufacturing, which has a profile that fits a quadratic polynomial regression model well, to illustrate the implementation of the proposed approach.

Pushing Quality Improvement Along Supply Chains

In this paper, we consider a buyer who designs a product and owns the brand, yet outsources the production to a supplier. Both the buyer and the supplier incur quality-related costs, e.g., costs of customer goodwill and future market share loss by the buyer and warranty-related costs shared by both the buyer and the supplier whenever a nonconforming item is sold to a customer. Therefore, both parties have an incentive to invest in quality-improvement efforts. This paper explores the roles of different parties in a supply chain in quality improvement. We show that the buyers involvement can have a significant impact on the profits of both parties and of the supply chain as a whole, and he cannot cede the responsibility of quality improvement to the supplier in many cases. We also investigate how quality-improvement decisions interact with operational decisions such as the buyers order quantity and the suppliers production lot size.

Monitoring Profiles Based on Nonparametric Regression Methods

The use statistical process control (SPC) in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries. The SPC problem with a nonlinear profile is particularly challenging. This article proposes a novel scheme to monitor changes in both the regression relationship and the variation of the profile online. It integrates the multivariate exponentially weighted moving average procedure with the generalized likelihood ratio test based on nonparametric regression. The proposed scheme not only provides an effective SPC solution to handle nonlinear profiles, which are common in industrial practice, but it also resolves the latent problem in popular parametric monitoring methods of being unable to detect certain types of changes due to a misspecified, out-of-control model. Our simulation results demonstrate the effectiveness and efficiency of the proposed monitoring scheme. In addition, a systematic diagnostic approach is provided to locate the change point of the process and identify the type of change in the profile. Finally, a deep reactive ion-etching example from semiconductor manufacturing is used to illustrate the implementation of the proposed monitoring and diagnostic approach.

Likelihood Ratio-Based Distribution-Free EWMA Control Charts

Nonparametric or distribution-free charts are useful in statistical process control when there is a lack of or limited knowledge about the underlying process distribution. Most existing approaches in the literature are for monitoring location parameters. They may not be effective with a change of distribution over time in many applications. This paper develops a new distribution-free control chart based on the integration of a powerful nonparametric goodness-of-fit test and the exponentially weighted moving-average (EWMA) control scheme. Benefiting from certain desirable properties of the test and the proposed charting statistic, our proposed control chart is computationally fast, convenient to use, and efficient in detecting potential shifts in location, scale, and shape. Thus, it offers robust protection against variation in various underlying distributions. Numerical studies and a real-data example show that the proposed approaches are quite effective in industrial applications, particularly in start-up and short-run situations.

A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison

To detect and estimate nonconstant, time-varying mean shifts, statistical process control (SPC) tools, such as the cumulative score (Cuscore) and generalized likelihood ratio test (GLRT) charts, have recently been proposed. However, their efficiency is based on previous and exact knowledge of a reference pattern. In this article a reference-free Cuscore (RFCuscore) chart is proposed that can trace and detect dynamic mean changes quickly without knowing the reference pattern. In addition, a unified framework that contains most of the control charts is presented and applied for a theoretical comparison of the RFCuscore, Cuscore, GLRT, and CUSUM charts in detecting dynamic mean changes. Moreover, numerical simulations and a real example are used to illustrate and verify the results. Both theoretical analysis and numerical results show that the RFCuscore chart performs not only robustly, but also quickly in detecting both small and large dynamic mean changes.

A Multivariate Sign EWMA Control Chart

Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate SPC methodology for monitoring location parameters. It is based on adapting a powerful multivariate sign test to online sequential monitoring. The weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA). It is affine-invariant and has a strictly distribution-free property over a broad class of population models. That is, the in-control (IC) run length distribution can attain (or is always very close to) the nominal one when using the same control limit designed for a multivariate normal distribution. Moreover, when the process distribution comes from the elliptical direction class, the IC average run length can be calculated via a one-dimensional Markov chain model. This control chart possesses some other favorable features: it is fast to compute with a similar computational effort to the MEWMA chart; it is easy to implement because only the multivariate median and the associated transformation matrix need to be specified (estimated) from the historical data before monitoring; it is also very efficient in detecting process shifts, particularly small or moderate shifts when the process distribution is heavy tailed or skewed. Two real-data examples from manufacturing show that it performs quite well in applications. This article has supplementary material online.

The Autoregressive T2 Chart for Monitoring Univariate Autocorrelated Processes

In this paper we investigate the autoregressive T2 control chart for statistical process control of autocorrelated processes. The method involves the monitoring, using Hotellings T2 statistic, of a vector formed from a moving window of observations of the univariate autocorrelated process. It is shown that the T2 statistic can be decomposed into the sum of the squares of the residual errors for various order autoregressive time series models fit to the process data. Guidelines for designing the autoregressive T2 chart are presented, and its performance is compared to that of residual-based CUSUM and Shewhart individual control charts. The autoregressive T2 chart has a number of characteristics, including some level of robustness with respect to modeling errors, that make it an attractive alternative to residual-based control charts for autocorrelated processes.

Joint monitoring of PID-controlled processes

Statistical process control (SPC) monitoring of the special causes of a process, along with engineering feedback control such as proportional-integral-derivative (PID) control, is a major tool for on-line quality improvement. In this paper, a strategy t..

Dual CUSUM control schemes for detecting a range of mean shifts

Conventional quality control procedures, such as the CUmulative SUM (CUSUM) and exponentially weighted moving average charts are usually designed based on a mean shift with a given size. In practice, the exact value of the shift size is often unknown and can only be reasonably assumed to vary within a certain range. Such a range of shifts deteriorates the performance of existing control charts. In this paper, a quality control scheme, a Dual CUSUM (DCUSUM), is applied that combines two CUSUM charts to detect the range of shifts. The out-of-control signal is triggered if either one of the CUSUM statistics goes out of the DCUSUM control limits. In particular, a design procedure for the DCUSUM charts is developed and an analytical formula for the Average Run Length (ARL) calculation is obtained via the Markov chain method. The proposed DCUSUM charts are compared with the conventional CUSUM and combined Shewhart-CUSUM charts. Based on a proposed criterion, the integrated relative ARL, the proposed schemes show better performance in detecting a range of mean shifts.

A mean-shift pattern study on integration of SPC and APC for process monitoring

To detect a long-term mean shift of an autocorrelated process, traditional Process Control (SPC) techniques can be applied to monitor a process with Automatic Process Control (APC) or Engineering Process Control (EPC). In this paper, we investigate the relationships between the run-length performance, the mean-shift pattern, and the autocorrelation structure of the original process. For both monitoring the output and monitoring the control action of the APC-controlled process, we study how the mean-shift pattern affects the run-length distribution of the monitoring process. We compare the performance of the two monitoring approaches and make recommendations for various autocorrelated processes. We find that one can indicate the average run-length performance of an automatic-controlled process by examining the mean-shift pattern of the monitoring process.