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.     

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.     

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.     

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.     

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.     

A simulation study of new multi-objective composite dispatching rules,CONWIP, and push lot release in semiconductor fabrication

This paper evaluates dispatching rules and order release policies in two wafer fabrication facilities (thereafter referred to as ‘fab’) representing ASIC (application specific integrated circuit) and low-mix high-volume production. Order release policies were fixed-interval (push) release, and constant work-in-process (CONWIP) (pull) policy. Following rigorous fab modelling and statistical analysis, new composite dispatching rules were found to be robust for average and variance of flow time, as well as due-date adherence measures, in both production modes.     

New dispatching rules for shop scheduling: A step forward

This paper provides a set of new dispatching rules for the minimization of various performance measures such as mean, maximum and variance of flow time and tardiness in dynamic shops. A static rule which minimizes the number of tardy jobs is also proposed. To evaluate these proposed rules, their relative performance is analysed in open job shops and reported in comparison with the standard benchmark rules such as the SPT (shortest process time) and EDD (earliest due-date), popular rules like ATC (apparent tardiness cost) and MOD (modified operational due-date), and the best performing rules in current literature such as RR, PT + WINQ, PT + WINQ + SL and AT-RPT. Thereafter, a comparative analysis of the relative performance of these rules is carried out in job shops (with no machine revisitation of jobs) and flow shops (with missing operations on jobs) in dynamic environments. Based on the simulation study and analysis of results in different manufacturing environments viz. job shops and flow shops, observations and conclusions are made, highlighting some interesting aspects about the effect of routeing on the individual performance of rules.     

A comparison study of control charts for statistical monitoring of functional data

The quality of products and processes is more and more often becoming related to functional data, which refer to information summarised in the form of profiles. The recent literature has pointed out that traditional control charting methods cannot be directly applied in these cases and new approaches for profile monitoring are required. While many different profile monitoring approaches have been proposed in the scientific literature, few comparison studies are available. This paper aims at filling this gap by comparing three representative profile monitoring approaches in different production scenarios. The performance comparison will allow us to select a specific approach in a given situation. The competitor approaches are chosen to represent different levels of complexity, as well as different types of modelling approaches. In particular, at a lower level of complexity, the ‘location control chart’ (where the upper and lower control limits are ±K standard deviations from the sample mean at each profile location) is considered to be representative of industrial practice. At a higher complexity level, approaches based on combining a parametric model of functional data with multivariate and univariate control charting are considered. Within this second class, we analyse two different approaches. The first is based on regression and the second focuses on using principal component analysis for modelling functional data. A manufacturing reference case study is used throughout the paper, namely profiles measured on machined items subject to geometrical specification (roundness).     

Data transformation for geometrically distributed quality characteristics

Recently there has been an increasing interest in techniques of process monitoring involving geometrically distributed quality characteristics, as many types of attribute data are neither binomial nor Poisson distributed. The geometric distribution is particularly useful for monitoring high‐quality processes based on cumulative counts of conforming items. However, a geometrically distributed quantity can never be adequately approximated by a normal distribution that is typically used for setting 3‐sigma control limits. In this paper, some transformation techniques that are appropriate for geometrically distributed quantities are studied. Since the normal distribution assumption is used in run‐rules and advanced process‐monitoring techniques such as the cumulative sum or exponentially weighted moving average chart, data transformation is needed. In particular, a double square root transformation which can be performed using simple spreadsheet software can be applied to transform geometrically distributed quantities with satisfactory results. Simulated and actual data are used to illustrate the advantages of this procedure. Copyright © 2000 John Wiley & Sons, Ltd.     

多品种小批量生产的SPC应用研究

综述了多品种小批量生产方式的特点以及该生产方式下SPC(统计过程控制)的应用现状,指出常规控制图不适用于多品种小批量生产的问题,提出结合通用控制图、累积和(Cumulative-Sum,CUSUM)控制图和指数加权移动平均(Exponentially Weighted Moving-Averages,EWMA)控制图的解决方法,并总结出该SPC方法用于处理多品种小批量生产中微小偏差的步骤。     

Discriminant locality preserving projection chart for statistical monitoring of manufacturing processes

In this paper, we propose a novel multivariate projection chart called the discriminant locality preserving projection chart. The basic idea of the chart is to seek an optimal linear projection of the original data including both the in-control reference data and the newly observed data for monitoring. The projection strives to not only preserve the locality structure of the original data but also maximise the separation between the in-control reference data and the newly observed data. With this projection, the low-dimensional projected data will then be monitored through a T² type of statistics. Comparing with the existing projection-based control chart, the proposed chart preserves the local data structure and adaptively identifies the best projection direction to detect the out-of-control data, and thus has more discriminating power, particularly for non-linearly related multidimensional data. The design issues of this chart are discussed in details in this paper. The effectiveness of the proposed method is verified by numerical studies and a real case study of forging process monitoring.     

A kalman filtering process control scheme with an application in semiconductor short run manufacturing

A quality control chart for monitoring a short run process during the start-up phase is presented in this article. The chart is based on the Kalman filter recursive equations being applied to a stable process where the process variance is unknown prior to the start of the production run. The run length properties of this control scheme are discussed. It is shown that for the proposed scheme the run length properties are independent of the unknown process variance and that these properties are appropriate for monitoring a stable process during start-up. An economic model for the optimal design of the control scheme is presented and illustrated with a wet etching process used in semiconductor manufacturing.     

Statistical monitoring and control of a low defect process

Advanced technologies today are such that it is possible to keep the occurrence of defects in manufactured products at very low levels. The use of the conventional c-chart for statistical control of defects in such products would encounter serious practical difficulties because the low defect counts would render invalid the theoretical assumptions used in the construction of the chart. Based on reasoning with fundamental probability distributions, this paper offers a simple and reliable solution that is particularly suited to on-line inspection and testing operations such as those found in an automated manufacturing environment.     

Operating charts for continuous sedimentation IV: limitations for control of dynamic behaviour

The nonlinear behaviour of a one-dimensional idealized model of continuous sedimentation has been investigated in this series of papers. The model is a scalar hyperbolic conservation law with a space-discontinuous flux function and a point source. Parameters in the equation are the two input variables (concentration and flux) and the control variable (a volume flow). The most desired type of solution contains a large concentration discontinuity and is referred to as ‘optimal operation’. Operating charts (concentration-flux diagrams) have proved to be a means for classifying the nonlinear behaviour. In this paper, some fundamental results on the dynamic behaviour are presented, which give information on the limitations of the range of the control variable. When this is used together with the previously introduced optimal control strategies for step inputs, the process can be controlled.