Shing I. Chang

A neural fuzzy control chart for detecting and classifying process mean shifts

We propose a neural fuzzy (NF) control chart for identifying process mean shifts. A supervised multi-layer backpropagation neural network is trained off-line to detect various mean shifts in a production process. In identifying mean shifts in real-time usage, the neural networks outputs are classified into various decision regions using a fuzzy set scheme. The approach offers better performance and additional advantages over conventional control charts. Simulation results show that the proposed NF control charts are superior to conventional X-bar charts and CUSUM charts in terms of the average run lengths (ARL). The proposed system also has the ability to identify the magnitude of a mean shift, in addition to the Shewhart-type control chart heuristic rules. Correct classification percentages are studied. Furthermore, general guidelines are given for the proper use of the proposed NF charts.

A fuzzy approach for multiresponse optimization: an off-line quality engineering problem

Abstract Multiresponse optimization techniques are used to identify settings of process parameters that make the products performance close to target values in the presence of multiple quality characteristics. In this study, a fuzzy multiresponse optimization procedure is proposed to search an appropriate combination of process parameter settings based on multiple quality characteristics or responses. Fuzzy regression models are first used to model the relations between process parameters and responses. The possibility distributions of the prediction responses are then obtained. The problem is reduced to a multiobjective optimization problem with fuzzy objectives. A strategy of optimizing the most possible response values and minimizing the deviations from the most possible values is proposed. We consider not only the most possible value, but also the imprecision of the prediction responses. Through a die casting example, we show how to use our approach to reach an appropriate machine setting which simultaneously optimize both casting quality and die life.

Fuzzy MADM: An outranking method

Abstract Multi-attribute decision making forms an important part of the decision process for both the small (an individual) and the large (an organization) problems. When available information is precise, many methods exist to solve this problem. But the uncertainty and fuzziness inherent in the structure of information make rigorous mathematical models inappropriate for solving this type of problems. This paper incorporates the fuzzy set theory and the basic nature of subjectivity due to the ambiguity to achieve a flexible decision approach suitable for uncertain and fuzzy environment. The proposed method can take both crisp and fuzzy inputs. An outranking intensity is introduced to determine the degree of overall outranking between competing alternatives, which are represented by fuzzy numbers. The comparison of these degrees is made through the concept of overall existence ranking index. A numerical example is given to illustrate the approach.

An integrated neural network approach for simultaneous monitoring of process mean and variance shifts a comparative study

Diagnosis of assignable causes is one of the primary concerns of quality practitioners. Knowledge of the type of process shift, either due to process mean or variance, can greatly aid identification of assignable causes. However, properties of control charts used for monitoring process mean and variance simultaneously are seldom studied in the statistical process control (SPC) literature. In this study, we propose a combined neural network control scheme to compare with other traditional SPC charts, such as X and R , CUSM and EWMA charts, and other neural network and Bayesian classification techniques in terms of average run length (ARL), and percentage of correct classifications. With an extensive literature survey and computer simulations, we find that the proposed neural network control scheme outperforms other SPC charts in the majority of situations for individual observations and a subgroup sample size of five.

A two-stage neural network approach for process variance change detection and classification

Statistical process control charts (SPCC) have become one of the most commonly used tools for monitoring process variability in todays manufacturing environment. Meanwhile, neural networks have been gradually recommended as alternatives to SPCC due to their superior performances, especially in the case of monitoring process mean and unnatural patterns. Little attention has been given to the use of neural networks for monitoring the process variance. This paper describes a neural network approach to monitor process variance changes and to predict change-magnitudes. The performances of the proposed neural network monitoring scheme are compared to those of SPCC for a sample size of five and for individual observations. Simulation results show that the performance of the proposed method is comparable to that of SPCC in terms of average run lengths. In addition, the proposed neural network scheme has the capability to estimate the magnitude of the variance change by combining with a bootstrap resampling schem...

Statistical process control for monitoring non-linear profiles using wavelet filtering and B-Spline approximation

A statistical process control framework is proposed to monitor non-linear profiles. The proposed methodology aims at identifying mean shifts or ‘shape changes’ in a profile. Discrete wavelet transformation (DWT) is applied to separate variation or noise from profile contours. B-splines are adopted to generate critical points to define the shape of a profile. The proposed method is innovative in that users can divide a profile into multiple segments to be monitored simultaneously. The high dimensionality problem that hinders the implementation of multivariate control charts can be solved by this framework. The distance difference statistic for each segment provides diagnostic information when the process of interest is out of control. These proposed statistics form a vector to be fed into any multivariate control chart such as the Hotelling T 2 control chart. A decomposition method can also be applied on the T 2 statistics when an out-of-control profile is detected. A simulation study applied to a forging process is conducted to demonstrate the property of the proposed method. The proposed method is capable of detecting profile shifts and identifying the exact location of problematic segments.

Multivariate EWMA control charts using individual observations for process mean and variance monitoring and diagnosis

Most multivariate control charts in the literature are designed to detect either mean or variation shifts rather than both. A simultaneous use of the Hotelling T 2 and |S| control charts has been proposed but the Hotelling T 2 reacts to mean shifts, dispersion changes, and changes of correlations among responses. The combination of two multivariate control charts into one chart sometimes loses the ability to provide detailed diagnostic information when a process is out-of-control. In this research a new multivariate control chart procedure based on exponentially weighted moving average (EWMA) statistics is proposed to monitor process mean and variance simultaneously to identify proper sources of variations. Two multivariate EWMA control charts using individual observations are proposed to achieve a quick detection of mean or variance shifts or both. Simulation studies show that the proposed charts are capable of identifying appropriate types of shifts in terms of correct detection percentages. A manufacturing example is used to demonstrate how the proposed charts can be properly set-up based on average run length values via simulations. In addition, correct detection rates of the proposed charts are explored.

An algorithm to generate near D-optimal designs for multiple response surface models

An algorithm is proposed to generate near D-optimal designs for multiple response surface models, i.e., a first-order or second-order polynomial model for each response with cuboidal design regions. For a class of designs generated by the proposed algorithm, simulation results indicate that the designs generated are near D-optimal and do not depend on ∑. An example is given to demonstrate how multiresponse D-optimal designs can be used to provide benchmarks to other experimental designs for multiple response problems.

On monitoring of multiple non-linear profiles

Most state-of-the-art profile monitoring methods involve studies of one profile. However, a process may contain several sensors or probes that generate multiple profiles over time. Quality characteristics presented in multiple profiles may be related multiple aspects of product or process quality. Existing charting methods for simultaneous monitoring of each multiple profile may result in high false alarm rates. Or worse, they cannot correctly detect potential relationship changes among profiles. In this study, we propose two approaches to detect process shifts in multiple non-linear profiles. A simulation study was conducted to evaluate the performance of the proposed approaches in terms of average run length under different process shift scenarios. Pros and cons of the proposed methods are discussed. A guideline for choosing the proposed methods is introduced. In addition, a hybrid method combining the salient points of both approaches is explored. Finally, a real-world data-set from a vulcanisation process is used to demonstrate the implementation of the proposed methods.

SHORT-RUN STATISTICAL PROCESS CONTROL: MULTICRITERIA PART FAMILY FORMATION

Owing to customer demands and short product life cycles, manufacturing trends have shifted towards a wide variety of mixed products with small batch sizes. It is difficult to apply traditional control charts efficiently and effectively in such environments, and it is not necessary to plot a control chart for each individual part. In this study, we propose a multicriteria part family formation technique and algorithm for implementing short-run SPC charting. We first carry out simulation to obtain ARLs for various shifts, and then use a maximin approach to help obtain a compromise or satisfactory ratio of standard deviations allowable within part families—type I and type II errors of Shewhart X control charts are considered simultaneously. This research establishes Shewhart X control charts for each part family to examine the quality status of all part types in the same family. We also provide a numerical example for purposes of illustration.