Deviance residual-based control charts for monitoring the beta-distributed processes

Beta-distributed process outputs are common in manufacturing industry because they range from 0 to 1 based on inputs like yield. Under the normality assumption, Shewarts control charts and Hotelling's control charts based on the deviance residual have been applied to monitor the process mean of the beta-distributed process outputs. The normality assumption can be violated according to the shape of the beta distribution. Therefore, without the normality assumption, we propose antirank control charts, exponentially weighted moving average (EWMA) control charts and cumulative sum (CUSUM) control charts. The proposed control charts outperform the existing control charts in the experimental results. The previous research has been focused on monitoring the process mean only. For the first time, in order to monitor the process variance of the beta-distributed process outputs, we propose the multivariate exponentially weighted mean squared deviation (MEWMS) chart, the first norm distance of the MEWMS deviation from its expected value (MEWMSL₁) chart, the chart based on MEWMS deviation with the approximated distribution of trace (MEWMS_AT), the multivariate trace sum squared deviation (MTSSD) chart and the multivariate matrix sum squared deviation (MMSSD) chart based on the deviance residual. The proposed control charts are compared and recommended in terms of the experimental results. This research can be a guideline for practitioners who monitor the deviance residual.     

Wavelet-based SPC procedure for complicated functional data

Functional data characterize the quality or reliability performance of many manufacturing processes. As can be seen in the literature, such data are informative in process monitoring and control for nanomachining, for ultra-thin semiconductor fabrication, and for antenna, steel-stamping, or chemical manufacturing processes. Many functional data in manufacturing applications show complicated transient patterns such as peaks representing important process characteristics. Wavelet transforms are popular in the computing and engineering fields for handling these types of complicated functional data. This article develops a wavelet-based statistical process control (SPC) procedure for detecting ‘out-of-control’ events that signal process abnormalities. Simulation-based evaluations of average run length indicate that our new procedure performs better than extensions from well-known methods in the literature. More importantly, unlike recent SPC research on linear profile data for monitoring global changes of data patterns, our methods focus on local changes in data segments. In contrast to most of the SPC procedures developed for detecting a known type of process change, our idea of updating the selected parameters adaptively can handle many types of process changes whether known or unknown. Finally, due to the data-reduction efficiency of wavelet thresholding, our procedure can deal effectively with large data sets.     

An approach of fuzzy logic evaluation and control in SPC

Quality control plays an important part in most industrial systems. Its role in providing relevant and timely data to management for decision‐making purposes is vital. A method that uses statistical techniques to monitor and control product quality is called statistical process control (SPC), where control charts are test tools frequently used for monitoring the manufacturing process. Engineers or managers can evaluate an abnormal process by using SPC zone rules in control charts. In the conventional use of the zone rules the user is only able to determine whether or not the process is out of control. What action should be taken to adjust the process is uncertain and is evaluated based on knowledge of the system and past experiences. This paper explores the integration of fuzzy logic and control charts to create and design a fuzzy–SPC evaluation and control (FSEC) method based on the application of fuzzy logic to the SPC zone rules. A simulation program implementing FSEC was written in Borland C++ 5.0 and simulation results were obtained and analysed. The abnormal processes simulated were automatically adjusted for each of the zone rules tested and showed an improved performance after the control action, thus confirming the merit of the technique as a special method with the specific numerical control action based on a quality evaluation criterion. Copyright © 2000 John Wiley & Sons, Ltd.     

A moving average S control chart for monitoring process variability

An efficient alternative to the S control chart for detecting shifts of small magnitude in the process variability using a moving average based on the sample standard deviation s statistic is proposed. Control limit factors are derived for the chart for different values of sample size and span w. The performance of the moving average S chart is compared to the S chart in terms of average run length. The result shows that the performance of moving average S chart for varying values of w outweigh those of the S chart for small and moderate shifts in process variability.     

A due-date based production control policy using WIP balance for implementation in semiconductor fabrications

Production control policies are critical in the re-entrant processes of semiconductor fabrication. Manufacturing control policies such as input dispatching rules, CONWIP, and optimization-based rules have been implemented according to the managerial objectives of the wafer fabrication line. When few semiconductor wafer fabrication facilities were available, and the semiconductor industry was a seller's market, fabrications were operated to achieve both a high rate of production and high utilization of equipment. With the availability of more fabrications and the gradual shift to a buyer's market, customer satisfaction became a major measure of performance in semiconductor manufacturing. In this paper, due-date based production control policies for semiconductor fabrications are suggested, and their performances evaluated. Target balance (TB) optimization models using production target, due-dates, and WIP (work-in-process) are presented. The evaluation result shows that the TB models perform better than the ones cited in the literature.     

In-house development of scheduling decision support systems: case study for scheduling semiconductor device test operations

Most manufacturing processes can benefit from an automated scheduling system. However, the design of a fast, computerised scheduling system that achieves high-quality results and requires minimal resources is a difficult undertaking. Efficient scheduling of a semiconductor device test facility requires an information system that provides good schedules quickly. Semiconductor device testing is the last stage of the long semiconductor manufacturing process, and therefore is subjected to customer service pressures. The cost of an off-the-shelf computerised scheduling system may be prohibitive for many companies. In addition, many companies are taken aback by other characteristics of off-the-shelf scheduling systems, such as code confidentiality, maintenance costs, and failure rates. We draw upon the literature and our field case to discuss some of the trade-offs between in-house development and off-the-shelf acquisition of software. We describe the in-house design and implementation of a scheduling decision support system for one device test facility. Using the design and implementation process of this system as a case study, we discuss how one facility uses in-house design of systems in a strategic way, as a competitive capability.     

Learning by Doing: A Series of Hands-on Projects for SPC

A series of simple hands-on class projects are used to illustrate statistical process control (SPC) tools such as run charts, histograms, probability plots, X and MR control charts, Xbar and R control charts, Xbar and s control charts, process capability analysis, and measurement systems analysis.     

A modified CUSUM control chart for monitoring industrial processes

Control charts are the most popular tool of statistical process control for monitoring variety of processes. The detection ability of these control charts can be improved by introducing various transformations. In this study, we have enhanced the performance of CUSUM charts by introducing a link relative variable transformation technique. Link relative variable converts the original process variable in a form which is relative to its mean. So, the link relative represents the relative positioning of the observations. Average run length (ARL ) is used to compare our technique with the previous studies. The comparison shows the overall good detection performance of our scheme for a span of shifts in the mean. A real‐world example from the electrical engineering process is also included to demonstrate the application of proposed control chart.     

The balance chart: A new SPC Concept

This paper outlines a new technique of statistical process control which goes a considerable way to resolving several existing problems. The technique described may be of particular value to automated control, small batch control and control of gauged processes. A new charting technique is described and compared with traditional control charts. The operation of the balance chart is outlined for attribute and variable processes and in precontrol mode. A graphical system for determining estimated Cp, Cpk and process mean values from limited process data is also included.     

Testing control chart subgroups for rationality

One of the key issues in statistical process control (SPC) is the forming ‘rational subgroups’. Rational subgroups are defined as

• 1 Subgroups displaying only random within-variation.
• 2 Subgroups having small within-variation to compare with variation between subgroups.

In a previous paper¹ we developed an approach of choosing the proper subgroup size for control charts for statistical process control. The approach is particularly appropriate for batch industries where some batch-to-batch variation is to be expected and should be accommodated. In this paper we will deal with the question of whether or not subgroups are rational. A randomness test can be used to verify rationality. The measure selected is the ratio of several different variance estimators. An example is provided to demonstrate the application of the measure.     

A control scheme for monitoring the frequency and magnitude of an event

While many control charts have been developed for monitoring the time interval (t) between the occurrences of an event, many other charts are employed to examine the magnitude (x) of the event. These two types of control charts have usually been investigated and applied separately with limited syntheses in conventional statistical process control (SPC) methods. This article presents an SPC method for simultaneously monitoring the time interval t and magnitude x. It, essentially, combines a t chart and an x chart, and is therefore referred to as a t&x chart. The new chart is more effective than an individual t chart or individual x chart for detecting the out-of-control status of the event, in particular for detecting downward shifts (sparse occurrence and/or small magnitude). More profound is that, compared with an individual t or x chart, the detection effectiveness of the t&x chart is more invariable against different types of shifts, i.e. t shift, x shift and joint shift in t and x. The t&x chart has demonstrated its potential not only for manufacturing systems, but also for non-manufacturing sectors such as supply chain management, office administration and health care industry.     

A GLR control chart for monitoring a multinomial process

The problem of detecting changes in the parameter p in a Bernoulli process with two possible categories for each observation has been extensively investigated in the SPC literature, but there is much less work on detecting changes in the vector parameter p in a multinomial process where there are more than two categories. A few papers have considered the case in which the direction of the change in p is known, but there is almost no work for the important case in which the direction of the change is unknown and individual observations are obtained. This paper proposes a multinomial generalized likelihood ratio (MGLR) control chart based on a likelihood ratio statistic for monitoring p when individual observations are obtained and the direction and size of the change in p are unknown. A set of 2‐sided Bernoulli cumulative sum (CUSUM) charts is proposed as a reasonable competitor of the MGLR chart. It is shown that the MGLR chart has better overall performance than the set of 2‐sided Bernoulli CUSUM charts over a wide range of unknown shifts. Equations are presented for obtaining the control limit of the MGLR chart when there are three or four components in p .     

A hybrid learning-based model for on-line monitoring and diagnosis of out-of-control signals in multivariate manufacturing processes

In multivariate statistical process control, most multivariate quality control charts are shown to be effective in detecting out-of-control signals based upon overall statistics. But these charts do not relieve the need for pinpointing the source(s) of the out-of-control signals. In addition, these charts cannot provide more detailed process information, such as quantitative abnormal assessment values and visualisation of process changes, which would be very useful for quality practitioners to locate the assignable causes that give rise to the out-of-control situation. In this study, a hybrid learning-based model has been investigated for monitoring and diagnosing out-of-control signals in a bivariate process. In this model, a minimum quantisation error (MQE) chart based on the self-organization map (SOM) neural network (NN) was developed for monitoring process changes (i.e., mean shifts), and a selective NN ensemble approach (DPSOEN) was developed for diagnosing signals that are judged as out-of-control signals by MQE charts. The simulation results demonstrate that the proposed model outperforms the conventional multivariate control scheme in terms of average run length (ARL), and can accurately classify the source(s) of out-of-control signals. An extensive experiment is also carried out to examine the effects of six statistical features on the performance of DPSOEN.     

Multivariate SPC for recipe preservation of batch processes

The performances of the Hotelling's T² control chart and the squared prediction error control chart based on the multi‐way principal component analysis are evaluated for monitoring within batch process variation for the purpose of recipe preservation. A nonlinear model for simulated batch process data is provided. The model allows for cross correlation of error terms at a given time period and serial correlation of error terms across time periods. The performance characterizations of the two monitoring schemes are provided for a variety of levels of cross correlation and serial correlation. The impact of the time period at which process shifts occur is also investigated for the monitoring schemes. The T² control chart is recommended for the cases considered. Copyright © 2009 John Wiley & Sons, Ltd.     

A new adaptive EWMA control chart for monitoring the process dispersion

The exponentially weighted moving average (EWMA), cumulative sum (CUSUM), and adaptive EWMA (AEWMA) control charts have had wide popularity because of their excellent speed in tracking infrequent process shifts, which are expected to lie within certain ranges. In this paper, we propose a new AEWMA dispersion chart that may achieve better performance over a range of dispersion shifts. The idea is to first consider an unbiased estimator of the dispersion shift using the EWMA statistic, and then based on the magnitude of this shift, select an appropriate value of the smoothing parameter to design an EWMA chart, named the AEWMA chart. The run length characteristics of the AEWMA chart are computed with the help of extensive Monte Carlo simulations. The AEWMA chart is compared with some of the existing powerful competitor control charts. It turns out that the AEWMA chart performs substantially and uniformly better than the EWMA‐S², CUSUM‐S², existing AEWMA, and HHW‐EWMA charts when detecting different kinds of shifts in the process dispersion. Moreover, an example is also used to explain the working and implementation of the proposed AEWMA chart.     

The density control chart: a general approach for constructing a single chart for simultaneously monitoring multiple parameters

The majority of the existing literature on simultaneous control charts, i.e. control charting mechanisms that monitor multiple population parameters such as mean and variance on a single chart, assume that the process is normally distributed. In order to adjust and maintain the overall type-I error probability, these existing charts rely largely on the property that the sample mean and sample variance are independent under the normality assumption. Furthermore, the existing charting procedures cannot be readily extended to non-normal processes. In this article, we propose and study a general charting mechanism which can be used to construct simultaneous control charts for normal and non-normal processes. The proposed control chart, which we call the density control chart, is essentially based on the premise that if a sample of observations is from an in-control process, then another sample of observations is no less likely to be also from the in-control process if the likelihood of the latter is no less than the likelihood of the former. The density control chart is developed for normal and non-normal processes where the distribution of the plotting statistic of the density control chart can be explicitly derived. Real examples are given and discussed in these cases. We also discuss how the density control chart can be constructed in cases when the distribution of the plotting statistic cannot be determined. A discussion of potential future research is also given.