Fuzzy Process Control And Development Of Some Models For Fuzzy Control Charts

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2006Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2006Bu çalışmada, bulanık kümeler teorisi kullanılarak belirsizlik içeren dilsel verilerin kontrol diyagramlarına yeni yaklaşımlar geliştirilmiştir. Belirsizlik içeren dilsel veriler, bulanık sayılarla ifade edilmiştir. Dilsel veriler için bulanık kontrol diyagramları α-kesim yaklaşımı kullanılarak geliştirilmiş ve bu suretle muayene sıklığı tanımlanmıştır. Bulanık kontrol diyagramlarının oluşturulmasında, bulanık verilerin taşıdığı bilgilerin kaybolmasını önlemek amacıyla “Direkt Bulanık Yaklaşım” geliştirilmiştir. Bulanık verilerin kontrol diyagramındaki normal olmayan davranış testleri için bulanık bir yaklaşım geliştirilmiştir. Önerilen yaklaşımların pratik kullanımlarının yansıtılması açısından gerçek verilere dayalı nümerik örnekler sunulmuştur.In this study, process control charts under linguistic, vague, and uncertain data are developed in the light of the Fuzzy Set Theory. Linguistic or uncertain data are represented by the use of fuzzy numbers. Fuzzy control charts for the linguistic data are proposed and integrated with the α-cut approach of fuzzy sets in order to set the degree of tightness of the inspection. A new approach called direct fuzzy approach to fuzzy control charts is modeled in order to prevent the loss of information of the fuzzy data during the construction of control charts. Finally, fuzzy unnatural pattern analyses are developed to monitor the abnormal patterns of the fuzzy data on the control charts. Numerical examples using the data of a real case are also given to highlight the practical usage of the proposed approaches.DoktoraPh

A Fuzzy Control Chart Approach for Attributes and Variables

The purpose of this study is to present a new approach for fuzzy control charts. The procedure is based on the fundamentals of Shewhart control charts and the fuzzy theory. The proposed approach is developed in such a way that the approach can be applied in a wide variety of processes. The main characteristics of the proposed approach are: The type of the fuzzy control charts are not restricted for variables or attributes, and the approach can be easily modified for different processes and types of fuzzy numbers with the evaluation or judgment of decision maker(s). With the aim of presenting the approach procedure in details, the approach is designed for fuzzy c quality control chart and an example of the chart is explained. Moreover, the performance of the fuzzy c chart is investigated and compared with the Shewhart c chart. The results of simulations show that the proposed approach ha

Control chart patterns recognition using run rules and fuzzy classifiers considering limited data

Statistical process control chart is a common tool used for monitoring and detecting process variations. The process data streams, when graphically plotted on control chart reveal useful patterns. These patterns can be associated with possible assignable causes if properly recognized. These patterns detections are useful for process diagnostic. Different types of control chart pattern recognition methods are reported in literature. Most of the existing data-driven methods require a large amount for training data before putting into practice. Short production run and short product life cycle processes are usually constrained with limited data availability. Thus there is a need to investigate and develop an effective control chart pattern recogniser (CCPR) methods for process monitoring with limited data. Two methods were investigated in this study to recognize fully developed control chart patterns for process with limited data on X-bar chart. The first method was combination of selected run rules, as run rules do not require training data. Classifiers based on fuzzy set theory were the second method. The performance of these methods was evaluated based on percent correct recognition. The methods proposed in this study significantly reduced the requirements of training data. Different combination of Nelson’s run rules; R2,R5,R6 for shift and trend, R3,R5,R6 for cyclic, R4,R5,R8 for systematic and R7 for stratification patterns were found effective for recognizing. Differentiating between the shift and trend patterns remains challenging task for the run rules. Heuristic based Mamdani fuzzy classifier with fuzzy set simplification operations using statistical features gave more than ninety percent correct patterns recognition results. Adaptive neuro fuzzy inference system (ANFIS) fuzzy classifier with fuzzy c-mean using statistical features gave more prominent results. The findings suggest that the proposed methods can be used in short production run and the process with limited data. The fuzzy classifiers can be further studied for different input representation

An Unsupervised Consensus Control Chart Pattern Recognition Framework

Early identification and detection of abnormal time series patterns is vital for a number of manufacturing. Slide shifts and alterations of time series patterns might be indicative of some anomaly in the production process, such as machinery malfunction. Usually due to the continuous flow of data monitoring of manufacturing processes requires automated Control Chart Pattern Recognition(CCPR) algorithms. The majority of CCPR literature consists of supervised classification algorithms. Less studies consider unsupervised versions of the problem. Despite the profound advantage of unsupervised methodology for less manual data labeling their use is limited due to the fact that their performance is not robust enough for practical purposes. In this study we propose the use of a consensus clustering framework. Computational results show robust behavior compared to individual clustering algorithms

Development of fuzzy process control charts: Direct fuzzy approach

Klasik kontrol diyagramları, W.A. Shewhart tarafından 1920’lerde geliştirilmiş olmasına rağmen yeni uygulama alanları ile günümüzde hala gelişimini sürdürmektedir. Verilerin tam ve kesin olduğu durumlarda klasik kontrol diyagramlarının kullanılması uygundur; ancak subjektifliğin önemli bir rol oynadığı bazı durumlarda bu kadar kesin verilere sahip olmak neredeyse imkânsızdır. Belirsizlik altındaki durumlarda karar analizleri genellikle olasılık teorisi ve/veya bulanık kümeler teorisi kullanılarak yapılmaktadır. Bunlardan birincisi karar vermenin stokastik yapısını diğeri ise insanın düşüncesinin subjektifliğini temsil eder. Bulanık kümeler teorisi, ne rassal ne de stokastik olan insanın zihinsel yapısından kaynaklanan belirsizliğin modellenmesinde mükemmeldir. Belirsiz, kesin olmayan veya dilsel anlatımlar içeren durumlarda bulanık kümeler teorisinin kullanılması kaçınılmazdır. Bu çalışmada, bulanık kümeler teorisi kullanılarak belirsizlik içeren dilsel verilerle kontrol diyagramlarına yeni yaklaşımlar geliştirilmiştir. Belirsizlik içeren dilsel veriler, bulanık sayılarla ifade edilmiştir. Dilsel veriler için bulanık kontrol diyagramları α-kesim yaklaşımı kullanılarak geliştirilmiş ve bu suretle muayene sıklığı tanımlanmıştır. Veri ve kontrol limitlerinin temsili değerler ile klasik biçime (nümerik değerlere) dönüştürülmesi sonucu taşıdığı bilgiler yitirilmektedir. Bulanık kontrol diyagramlarının oluşturulmasında, bulanık verilerin taşıdığı bilgilerin kaybolmasını önlemek amacıyla “Direkt Bulanık Yaklaşım” geliştirilmiştir. Bu yaklaşımda veriler bulanık sayılarla ifade edilmiş ve temsili değerler kullanılmadan kontrol limitleri de bulanık sayılar olarak hesaplanmıştır. Kontrol altında, kontrol dışında kararlarına ek olarak kısmen kontrol altında, kısmen kontrol dışında gibi ara kararlar geliştirilmiştir.  Anahtar Kelimeler: Bulanık proses kontrol diyagramları, bulanık kümeler, dilsel veriler, normal olmayan davranış analizi, belirsizlik. Control charts have been widely used for monitoring process stability and capability. Control charts are based on data representing one or several quality-related characteristics of the product or service. If these characteristics are measurable on numerical scales, then variable control charts are used. If the quality-related characteristics cannot be easily represented in numerical form, then attribute control charts are useful. Even though the first classical control chart was proposed during the 1920's by W.A. Shewhart, today they are still subject to new application areas that deserve further attention. Classical process control charts are suitable when the data are exactly known and precise; but in some cases, it is nearly impossible to have such strict data if human subjectivity plays an important role. It is not surprising that uncertainty exists in the human world. To survive in our world, we are engaged in making decisions, managing and analyzing information, as well as predicting future events. All of these activities utilize information that is available and help us try to cope with information that is not. A rational approach toward decision-making should take human subjectivity into account, rather than employing only objective probability measures. A research work incorporating uncertainty into decision analysis is basically done through the probability theory and/or the fuzzy set theory. The former represents the stochastic nature of decision analysis while the latter captures the subjectivity of human behavior. The fuzzy set theory is a perfect means for modeling uncertainty (or imprecision) arising from mental phenomena which is neither random nor stochastic. Many problems in scientific investigation generate nonprecise data incorporating nonstatistical uncertainty. A nonprecise observation of a quantitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number or a fuzzy interval. A methodology for constructing control charts is proposed when the quality characteristics are vague, uncertain, incomplete or linguistically defined. The binary classification into conforming and nonconforming used in the p-chart might not be appropriate in many situations where product quality does not change abruptly from satisfactory to worthless, and there might be a number of intermediate levels. Without fully utilizing such intermediate information, the use of the p-chart usually results in poorer performance than that of the x-chart. This is evidenced by weaker detectability of process shifts and other abnormal conditions such as unnatural patterns. To supplement the binary classification, several intermediate levels may be expressed by using linguistic terms. For example, the quality of a product can be classified into the following terms: 'perfect', 'good', 'medium', 'poor', or 'bad' depending on its deviation from specifications. Then, the continuous functions selected appropriately can be used to describe the quality characteristic associated with each linguistic term. In this study, the control charts for number of nonconformities are handled. The type of available data is the imprecise number of nonconformities such as "between 5 and 8" or "approximately 6". The statistical model is based on the classical Shewhart control charts. In the literature, there exist few papers on fuzzy control charts, which use defuzziffication methods such as fuzzy mod, fuzzy midrange, fuzzy median, and fuzzy average in the early steps of their algorithms. The use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis. Linguistic data in those works are transformed into numeric values before control limits are calculated. Thus both control limits as well as sample values become numeric. This transformation may cause biased results due to the loss of information included by the samples. For example, two fuzzy samples with the equal fuzzy mod may explain very different characteristics. A new approach called direct fuzzy approach to fuzzy control charts is modeled in order to prevent the loss of information of the fuzzy data during the construction of control charts. In this approach, linguistic or uncertain data are represented by means of triangular and/or trapezoidal fuzzy numbers. Using fuzzy arithmetics, control limits based on the fuzzy data are also determined as fuzzy numbers. The decision about the process control is based on the area measurement method. The proposed approach directly compares the linguistic data in fuzzy space without making any transformation. The percentage area of the fuzzy sample behind the fuzzy control limits is used in the decision and intermediate decision levels are defined. Keywords: Fuzzy control charts, fuzzy sets, linguistic data, unnatural pattern analysis, uncertainty.

Management of Uncertainty by Statistical Process Control and a Genetic Tuned Fuzzy System

In food industry, bioprocesses like fermentation often are a crucial part of the manufacturing process and decisive for the final product quality. In general, they are characterized by highly nonlinear dynamics and uncertainties that make it difficult to control these processes by the use of traditional control techniques. In this context, fuzzy logic controllers offer quite a straightforward way to control processes that are affected by nonlinear behavior and uncertain process knowledge. However, in order to maintain process safety and product quality it is necessary to specify the controller performance and to tune the controller parameters. In this work, an approach is presented to establish an intelligent control system for oxidoreductive yeast propagation as a representative process biased by the aforementioned uncertainties. The presented approach is based on statistical process control and fuzzy logic feedback control. As the cognitive uncertainty among different experts about the limits that define the control performance as still acceptable may differ a lot, a data-driven design method is performed. Based upon a historic data pool statistical process corridors are derived for the controller inputs control error and change in control error. This approach follows the hypothesis that if the control performance criteria stay within predefined statistical boundaries, the final process state meets the required quality definition. In order to keep the process on its optimal growth trajectory (model based reference trajectory) a fuzzy logic controller is used that alternates the process temperature. Additionally, in order to stay within the process corridors, a genetic algorithm was applied to tune the input and output fuzzy sets of a preliminarily parameterized fuzzy controller. The presented experimental results show that the genetic tuned fuzzy controller is able to keep the process within its allowed limits. The average absolute error to the reference growth trajectory is 5.2 × 106 cells/mL. The controller proves its robustness to keep the process on the desired growth profile

Data mining in manufacturing: a review based on the kind of knowledge

In modern manufacturing environments, vast amounts of data are collected in database management systems and data warehouses from all involved areas, including product and process design, assembly, materials planning, quality control, scheduling, maintenance, fault detection etc. Data mining has emerged as an important tool for knowledge acquisition from the manufacturing databases. This paper reviews the literature dealing with knowledge discovery and data mining applications in the broad domain of manufacturing with a special emphasis on the type of functions to be performed on the data. The major data mining functions to be performed include characterization and description, association, classification, prediction, clustering and evolution analysis. The papers reviewed have therefore been categorized in these five categories. It has been shown that there is a rapid growth in the application of data mining in the context of manufacturing processes and enterprises in the last 3 years. This review reveals the progressive applications and existing gaps identified in the context of data mining in manufacturing. A novel text mining approach has also been used on the abstracts and keywords of 150 papers to identify the research gaps and find the linkages between knowledge area, knowledge type and the applied data mining tools and techniques