Mohamed Limam

On fuzzy and probabilistic control charts

In this article, different procedures of constructing control charts for linguistic data, based on fuzzy and probability theory, are discussed. Three sets of membership functions, with different degrees of fuzziness, are proposed for fuzzy approaches. A comparison between fuzzy and probability approaches, based on the Average Run Length and samples under control, is conducted for real data. Contrary to the conclusions of Raz and Wang (1990b) the choice of degree of fuzziness affected the sensitivity of control charts.

Variable window adaptive Kernel Principal Component Analysis for nonlinear nonstationary process monitoring

On-line control of nonlinear nonstationary processes using multivariate statistical methods has recently prompt a lot of interest due to its industrial practical importance. Indeed basic process control methods do not allow monitoring of such processes. For this purpose this study proposes a variable window real-time monitoring system based on a fast block adaptive Kernel Principal Component Analysis scheme. While previous adaptive KPCA models allow only handling of one observation at a time, in this study we propose a way to fast update or downdate the KPCA model when a block of data is provided and not only one observation. Using a variable window size procedure to determine the model size and adaptive chart parameters, this model is applied to monitor two simulated benchmark processes. A comparison of performances of the adopted control strategy with various Principal Component Analysis (PCA) control models shows that the derived strategy is robust and yields better detection abilities of disturbances.

On SPC for Short Run Autocorrelated Data

ABSTRACT The existence of a large amount of historical data set and the assumption that process observations are independent and identically distributed are two necessary conditions to effectively and efficiently implement traditional control charts. In many manufacturing environments there is neither enough observations nor the data are i.i.d. In this article we show that the use of Q statistics in conjunction with residuals control charts is an appropriate Statistical Process Control (SPC) tool for short run autocorrelated data. A performance analysis is conducted to compare he proposed method to traditional residuals control charts. Results indicate that residual control charts provide much better shift detection properties than charts based on Q statistics. However, as the under control data set increases, the superiority of residual charts decreases.

Kernel k-means clustering based local support vector domain description fault detection of multimodal processes

The multimodal and nonlinear structure of a system makes process modeling and control quite complex. To monitor processes that have these characteristics, this paper presents a procedure based on kernel techniques for unsupervised learning that are able to separate different nonlinear process modes and to effectively detect faults. These techniques are named Kernel k-means (KK-means) clustering and support vector domain description (SVDD). In order to assess this monitoring strategy two different simulation studies as well as a real case study of an Etch Metal process are performed. Results show that the proposed control chart provides efficient fault detection performance with reduced false alarm rates.

Multivariate Fuzzy Multinomial Control Charts

Abstract Two approaches for constructing control charts to monitor multivariate attribute processes when data set is presented in linguistic form are suggested. Two monitoring statistics T2f and W2 are developed based on fuzzy and probability theories. The first is similar to the Hotelling’s T2 statistic and is based on representative values of fuzzy sets. The distribution of W2 statistic, being a linear combination of dependent chi-square variables, is derived using Satterthwaite’s approximation. Resulting multivariate control charts are compared based on the average run length (ARL). A numerical example is given to illustrate the application of the proposed multivariate control charts and the interpretation of out-of-control signals.

An assessment of the kernel-distance-based multivariate control chart through an industrial application

Traditional multivariate quality control charts assume that quality characteristics follow a multivariate normal distribution. However, in many industrial applications the process distribution is not known, implying the need to construct a flexible control chart appropriate for real applications. A promising approach is to use support vector machines in statistical process control. This paper focuses on the application of the ‘kernel-distance-based multivariate control chart’, also known as the ‘k-chart’, to a real industrial process, and its assessment by comparing it to Hotellings T2 control chart, based on the number of out-of-control observations and on the Average Run Length. The industrial application showed that the k-chart is sensitive to small shifts in mean vector and outperforms the T2 control chart in terms of Average Run Length. Copyright

On Mining Summaries by Objective Measures of Interestingness

Knowledge discovery in databases is used to discover useful and understandable knowledge from large databases. A process of knowledge discovery consists of two steps, the data mining step and the evaluation step. In this paper, evaluating and ranking the interestingness of summaries generated from databases, which is a part of the second step, is studied using diversity measures. Sixteen previously analyzed diversity measures of interestingness are used along with three not previously considered ones, brought from different well-known areas. The latter three measures are evaluated theoretically according to five principles that a measure must satisfy to be qualified acceptable for ranking summaries. A theoretical correlation study between the eight measures that satisfy all five principles is presented based on mathematical proofs. An empirical evaluation is conducted using three real databases. Then, a classification of the eight measures is deduced. The resulting classification is used to reduce the number of measures to only two, which are the best over all criteria, and that produce non-similar results. This helps the user interpret the most important discovered knowledge in his decision making process.

A kernel distance-based representative subset selection method

This paper proposes a new representative subset selection method called kernel distance-based sample set partitioning based on joint x–y distances, referred to as KSPXY. The proposed method is a modified version of the original sample set partitioning based on joint x–y distances (SPXY) algorithm, where the kernel distance is used as an alternative to the Euclidean distance. The proposed KSPXY algorithm is used with partial least-squares (PLS) to predict three chemical quality characteristics of diesel fuel. We compare the PLS-KSPXY modelling strategy with two modelling strategies involving the use of SPXY and Kennard–Stone (KS) algorithms with PLS. Based on the root mean-squared error of prediction, results show that the proposed KSPXY algorithm performs better than SPXY and KS algorithms in improving the predictive ability of the PLS model. The difference between PLS–KSPXY and the other two modelling strategies is statistically significant. The paper provides also the MATLAB code for the proposed KSPXY algorithm, developed by the authors.

The Change Point Model: SPC Method for Short Run Autocorrelated Data

Abstract Traditional control charts are designed for processes were outputs are independent and identically distributed (i.i.d), and large amount of historical data set are available before the start of a production run. In many manufacturing environments there is neither enough observations nor the data are i.i.d. In this paper we propose the unknown parameters change point formulation in conjunction with residuals of various time series models as a statistical process control alternative for short run autocorrelated data. Based on the average run length and standard deviation of the run length as criteria of control chart’s performance, the proposed alternative is compared to other short run SPC techniques. Simulation results show that the change point model formulation provides better shift detection properties than residual charts based on the Q statistics.

Fuzzy multinomial control charts

Two approaches for constructing control charts to monitor multivariate attribute processes when data is presented in linguistic form are suggested. Two monitoring statistics T and W2 are developed based on fuzzy and probability theories. The first is similar to the Hottelings T2 statistic and is based on representative values of fuzzy sets. The W2 statistic, being a linear combination of dependent chi-square variables, its distribution is derived by Satterthwaites approximation. Resulting multivariate control charts are compared based on the average run length (ARL). A numerical example is given to illustrate the application of the proposed multivariate control charts and the interpretation of out-of-control signals.