**6.4 Detection of wafer defects**

258 Fuzzy Inference System – Theory and Applications

*6. If Time is REG, NSO (IR) is UNA and CNSO (IR) is UNA and NSO (VIS) is not OPT then* 

*7. If Time is REG, NSO (UV) is UNA and NSO (VIS) is not UNA then the OUTPUT is UNA.* 

*8. If Time is REG, NSO (IR) is UNA and CNSO (IR) is UNA and RSN (IR) is UNA and NSO (UV) is UNA and NSO (VIS) is UNA and NSO (Te) is UNA then the OUTPUT is UNA.* 

*9. If Time is REG and RSN (IR) is UNA and NSO (Te) is UNA and CNSO (Te) is UNA and* 

*10. If Time is REG and CNSO (IR) is UNA and CNSO (UV) is UNA and RSN (UV) is UNA and CNSO (VIS) is UNA and RNS (VIS) is UNA and CNSO (Te) is UNA then the OUTPUT is* 

The second fuzzy system is used to display messages which explain the occurred defect or the anomaly operation in the considered weld. The considered events for this aim are the common ones such as current increase, current decrease, voltage variation, gases assistance decrease, contamination of with materials having different thermal properties and occurrence of hole in the metal. The second FIS is similar to the first one working with analogous membership functions and rules and provides six outputs, one for each considered defect. It is evident that a single defect could be associated to one or more causes.

*RSN (Te) is UNA then the OUTPUT is UNA. (weigth =0.18).* 

*the OUTPUT is UNA. (weigth =0.18).* 

*(weigth =0.18).* 

*(weigth =0.18).* 

*UNA. (weigth =0.18).* 

Fig. 6. Diagram of the proposed approach

An interesting industrial application which exploits the advantages of the fuzzy theory is due to (Tong et al., 2003). The authors propose a process control chart which integrate both fuzzy theory and engineering experience in order to monitor the defects on a wafer which have been clustered.

The wafer manufacturing process contains many step, such as alignment, etch and deposition. It is a very complex process; the occurrence of defects on the wafer surface is unavoidable and decreases the wafer yield.

Typically Integrated Circuits (IC) manufacturers use c-charts to monitor wafer defects. This technique assumes that wafer defects are randomly and independently distributed so that the number of defects has a Poisson distribution. A limit of this approach is that the real defect clustering infringes this constraint creating a non acceptable occurrences of false alarms. A modified c-chart, introduced in order to solve this problem, is presented by Albin & Friedman (Albin & Friedman, 1991) and it is based on a Neyman Type-A distribution. Unfortunately also this approach presents a considerable limit, as it can monitor only the variation in the number of defects but it is not able to detect variation located within the wafer. The authors demonstrate that applying fuzzy theory in combination with engineering experience it is possible to build a process control chart which is able to monitor the clustered defect and defect clustering simultaneously. The proposed algorithm is illustrated in Fig.7.

The KLA 2110 wafer inspection system (Castucci et al., 1991) is adopted to obtain the wafer map. This system provides in-line wafer inspection information such as number of defects, size of defects, placement of defects and, finally, type of defects. The number of defects are determined and the cluster index is calculated. Some cluster indices are provide to calculate

Fuzzy Inference Systems Applied to Image Classification in the Industrial Field 261

output of the fuzzy system. In the proposed examples the number of defected can be

Also, for each fuzzy set a triangular membership function is constructed accordingly.

The corresponding rules created to monitor the process can be written as follow:

of defects is low clustering is significant and also under control.

*R1: IF Defect is very high and C1 is term 1, then value is term 10 R2: IF Defect is very high and C1 is term 2, then value is term 10* 

*Ri: IF Defect is medium and C1 is term 10, then value is term 2* 

*R70: IF Defect is very low and C1 is term 10, then value is term 1* 

rules which determine when the process is out of control.

**6.5 Detection of defective products in the paper industry** 

equipped with a fast-rotating circular blade.

Clustering phenomena is classified in ten classes and the output can be classified in ten levels as well. Finally, according to the process control a set of rules based on experts knowledge has been defined. It is important to consider that, when many defects are present, without clustering, the process is considered out of control, while when the number

Subsequently a fuzzy system according to the rules and a fuzzy control chart can be designed also building eventual control limits. Once the defect data are stored, they are transformed into output of the fuzzy inference rules and a control chart which monitor both number of defects and clustering is constructed. The last important step is determine the

The main advantages of the proposed approach include the possibility to incorporate within the fuzzy system the knowledge of experts and the experience of engineering. Moreover the proposed chart is easy and very helpful in judging real process conditions and, finally, it is simpler and more efficient respect to Poisson based c-chart and the Neyman-based c-chart.

A further application of a combination of vision systems and fuzzy inference is found in

One of the main phases of the manufacturing of paper rolls for domestic consists in cutting a long semi-finished roll into rolls of standard length by means of an automatic machinery

(Colla et al., 2009) and is related to a quality control task within the paper industry.

classified in seven classes defined as follows:

1. very low 2. low

6. high 7. very high

*.*  . .

. . .

3. medium low 4. medium 5. medium high

the extent of the clustering of the defects; an efficient cluster index is due to Jun et al. (Jun et al., 1999). This particular *Cluster Index* (*CI)* does not require any a-priori assumption concerning the defects distribution. CI is calculated in the following way: let us suppose that *d* represents the number of defects occurred on a wafer, and *Xi* and *Yi* are the coordinates of the generic defect *i (1≤i≤n)* in a two dimensional plane.

Fig. 7. Procedure of proposed approach

Sorting *Xi* and *Yi* in ascending order, we can define *X(i)* and Y*(i)* as the coordinates of the *ith* defect. Moreover the two follow intervals *Ai* and *Bi* are evaluated:

$$\mathbf{A}\_{i} = \mathbf{X}\_{i} \cdots \mathbf{X}\_{i-1} \tag{6}$$

$$\mathbf{B} = \mathbf{Y}\_i \mathbf{\cdot} \quad \mathbf{Y}\_{i:1} \tag{7}$$

Note that *X(0)* and *Y(0)* are considered null.

Finally CI can be defined as in equation (8)

$$\text{CI} = \min\{\mu\_A 2 / \mathfrak{s}\_A 2 \mid \mu\_B 2 / \mathfrak{s}\_B 2 \mid \tag{8}$$

where *µA* and *µB* are the mean value of *Ai* and *Bi* respectively, while *ϭA* and *ϭB* are their standard deviation. *CI=1* when the defect distribution is uniform, moreover if *CI>1* then the defects are clustered.

Once *CI* is available, the membership functions corresponding to number of defects, *CI* and output of the system are evaluated. Number of defects and clustering are important characteristics which mainly determine the wafer yield. In this approach this two variables as input of the FIS, which is Mandani type, and the output of the process represents the output of the fuzzy system. In the proposed examples the number of defected can be classified in seven classes defined as follows:


260 Fuzzy Inference System – Theory and Applications

the extent of the clustering of the defects; an efficient cluster index is due to Jun et al. (Jun et al., 1999). This particular *Cluster Index* (*CI)* does not require any a-priori assumption concerning the defects distribution. CI is calculated in the following way: let us suppose that *d* represents the number of defects occurred on a wafer, and *Xi* and *Yi* are the coordinates of

Sorting *Xi* and *Yi* in ascending order, we can define *X(i)* and Y*(i)* as the coordinates of the *ith*

A*i=Xi - Xi-1* (6)

B*i=Yi - Yi-1* (7)

where *µA* and *µB* are the mean value of *Ai* and *Bi* respectively, while *ϭA* and *ϭB* are their standard deviation. *CI=1* when the defect distribution is uniform, moreover if *CI>1* then the

Once *CI* is available, the membership functions corresponding to number of defects, *CI* and output of the system are evaluated. Number of defects and clustering are important characteristics which mainly determine the wafer yield. In this approach this two variables as input of the FIS, which is Mandani type, and the output of the process represents the

*CI = min{ µA2/ϭA2 , µB2/ϭB2 }* (8)

defect. Moreover the two follow intervals *Ai* and *Bi* are evaluated:

the generic defect *i (1≤i≤n)* in a two dimensional plane.

Fig. 7. Procedure of proposed approach

Note that *X(0)* and *Y(0)* are considered null. Finally CI can be defined as in equation (8)

defects are clustered.


*.*  .

. .

7. very high

Also, for each fuzzy set a triangular membership function is constructed accordingly.

Clustering phenomena is classified in ten classes and the output can be classified in ten levels as well. Finally, according to the process control a set of rules based on experts knowledge has been defined. It is important to consider that, when many defects are present, without clustering, the process is considered out of control, while when the number of defects is low clustering is significant and also under control.

The corresponding rules created to monitor the process can be written as follow:

*R1: IF Defect is very high and C1 is term 1, then value is term 10 R2: IF Defect is very high and C1 is term 2, then value is term 10* 

. *Ri: IF Defect is medium and C1 is term 10, then value is term 2* 

. *R70: IF Defect is very low and C1 is term 10, then value is term 1* 

Subsequently a fuzzy system according to the rules and a fuzzy control chart can be designed also building eventual control limits. Once the defect data are stored, they are transformed into output of the fuzzy inference rules and a control chart which monitor both number of defects and clustering is constructed. The last important step is determine the rules which determine when the process is out of control.

The main advantages of the proposed approach include the possibility to incorporate within the fuzzy system the knowledge of experts and the experience of engineering. Moreover the proposed chart is easy and very helpful in judging real process conditions and, finally, it is simpler and more efficient respect to Poisson based c-chart and the Neyman-based c-chart.

#### **6.5 Detection of defective products in the paper industry**

A further application of a combination of vision systems and fuzzy inference is found in (Colla et al., 2009) and is related to a quality control task within the paper industry.

One of the main phases of the manufacturing of paper rolls for domestic consists in cutting a long semi-finished roll into rolls of standard length by means of an automatic machinery equipped with a fast-rotating circular blade.

Fuzzy Inference Systems Applied to Image Classification in the Industrial Field 263

scenario, each time a new roll is cut, a belt or a robot should place it with its circular section

The vision system exploits one single static analogical B/W camera which acquires the images and digitalizes them. The decision system directly operates on the digitalized grey scale image and, as a result, provides the decision concerning the destination (market or

The main goal of the developed system is to evaluate the quality of single products on the basis of the defects that are eventually present on the internal part of the paper section, neglecting the irregularity of the contour, as this latter defect can be due also to other phases

The quality control system here described implements three subsequent processing stages,

of the manufacture and does not compromise the marketability of the product.

Fig. 9. Flow diagram of the quality control system for the assessment of paper rolls.

defect, a threshold operator which produces a binary image is used.

The first one performs some *image processing* operations which elaborate the grey scale image and aim to put into evidence those areas of the roll section that are affected by surface defects. At this stage, a combination of filters is used to highlight the grey level discontinuities on the images. These filters take into account the grey intensity of each specific point and of its neighbours for calculating the so-called *gradient* associated to each pixel, which is higher in correspondence of strong and abrupt variations of the image. This feature can indicate the presence of defects. In order to select only those points where the grey level change is particularly high and, by consequence, more probably belonging to a

in front of the camera that is part of the vision system.

which are summarized in the flow chart depicted in Fig.9.

recycling) of the inspected product.

These iterated cuts damage the blade of the machinery devoted to this operation due to the resistance of the paper roll. The performance of the damaged blade decreases the quality of the cut and can lead to surface defects on the roll section and on the contour of the roll itself, as shown in Fig. 8.

Fig. 8. Defects on the roll surface.

Unfortunately, independently on the quality of the paper itself, the presence of these defects compromises the marketability of the final product, thus a quality control step is needed in order to perform the selection of the final product. Usually this latter control is manually performed by a human operator which assesses the quality of each product, one by one, taking into account the quantity, intensity and kind of defects that are present on the roll sections. The human operator decides not only if each single roll has to be discarded or put into market but also when to stop the machinery for the maintenance of the cutting blade.

Within this context it would be desirable to automate the process of quality control for different purposes: on one hand in order to avoid an alienating task for the human operator, on the other hand in order to speed-up the control and to increase the repeatability and standardise the performance of the control operations, as, obviously, the results of the quality check are heavily affected by the experience and skills of the human operators. For these reasons a fuzzy inference-based vision system has been developed for the quality control on the previously described process.

This automatic system is placed immediately after the cutting machinery, in order to examine the rolls as soon as they are produced, while in the laboratory experimental set up, the paper roll is manually placed in front of the camera. In the real industrial operating

These iterated cuts damage the blade of the machinery devoted to this operation due to the resistance of the paper roll. The performance of the damaged blade decreases the quality of the cut and can lead to surface defects on the roll section and on the contour of the roll itself,

Unfortunately, independently on the quality of the paper itself, the presence of these defects compromises the marketability of the final product, thus a quality control step is needed in order to perform the selection of the final product. Usually this latter control is manually performed by a human operator which assesses the quality of each product, one by one, taking into account the quantity, intensity and kind of defects that are present on the roll sections. The human operator decides not only if each single roll has to be discarded or put into market but also when to stop the machinery for the maintenance of

Within this context it would be desirable to automate the process of quality control for different purposes: on one hand in order to avoid an alienating task for the human operator, on the other hand in order to speed-up the control and to increase the repeatability and standardise the performance of the control operations, as, obviously, the results of the quality check are heavily affected by the experience and skills of the human operators. For these reasons a fuzzy inference-based vision system has been developed for the quality

This automatic system is placed immediately after the cutting machinery, in order to examine the rolls as soon as they are produced, while in the laboratory experimental set up, the paper roll is manually placed in front of the camera. In the real industrial operating

as shown in Fig. 8.

Fig. 8. Defects on the roll surface.

control on the previously described process.

the cutting blade.

scenario, each time a new roll is cut, a belt or a robot should place it with its circular section in front of the camera that is part of the vision system.

The vision system exploits one single static analogical B/W camera which acquires the images and digitalizes them. The decision system directly operates on the digitalized grey scale image and, as a result, provides the decision concerning the destination (market or recycling) of the inspected product.

The main goal of the developed system is to evaluate the quality of single products on the basis of the defects that are eventually present on the internal part of the paper section, neglecting the irregularity of the contour, as this latter defect can be due also to other phases of the manufacture and does not compromise the marketability of the product.

The quality control system here described implements three subsequent processing stages, which are summarized in the flow chart depicted in Fig.9.

Fig. 9. Flow diagram of the quality control system for the assessment of paper rolls.

The first one performs some *image processing* operations which elaborate the grey scale image and aim to put into evidence those areas of the roll section that are affected by surface defects. At this stage, a combination of filters is used to highlight the grey level discontinuities on the images. These filters take into account the grey intensity of each specific point and of its neighbours for calculating the so-called *gradient* associated to each pixel, which is higher in correspondence of strong and abrupt variations of the image. This feature can indicate the presence of defects. In order to select only those points where the grey level change is particularly high and, by consequence, more probably belonging to a defect, a threshold operator which produces a binary image is used.

Fuzzy Inference Systems Applied to Image Classification in the Industrial Field 265

1. *defect extension* which is measured in terms of the number of pixels belonging to a cluster. Three fuzzy sets correspond to this fuzzy variable and refer to the number of

2. *linearity* is calculated as the mean square distance of pixels of the clusters from the bestfitting straight-line. Also for this variable three fuzzy sets are created: *low*, *medium* and

The output of the designed FIS is represented by a single variable, the so-called *defectiveness*, which reflects the decision about the final roll destination. This variable corresponds to three

The adopted membership functions are Gaussian and their domain depends on the universe where the corresponding fuzzy variable is defined (for instance, 0-200 points for the variable

Seven fuzzy rules derived from the knowledge of expert human operators constitute the adopted inference system. The defectiveness index is evaluated for all the clusters eventually present on a single roll: if a paper roll contains at least one cluster whose

**Defect Extension Linearity Operator Defectiveness** 

**Low** Low and Uncertain **Low** Medium and Defective **Low** High and Defective **Medium** Low and Defective **Medium** Medium and Uncertain **Medium** High and Defective **High** - and Defective

Several tests have been performed for evaluating the proposed quality control system. The value of the defectiveness discrimination threshold must meet two opposite requirements: on one hand the choice of high values of such threshold leads to a high number of *missed detections* (MD) of faulty rolls, on the other hand low values of the threshold rise several socalled *false alarms* (FA) which correspond to pauses on the process for the maintenance of the machinery. Both these situations must be avoided although, according to technical personnel, to avoid missed defect detections is more important, as the presence of faulty

The results obtained by the proposed vision system are extremely good as, with the selected threshold, an extremely low number of defective products are missed and a satisfactory

defectiveness index is higher than a fixed threshold, it is discarded.

rolls can affect the commercial competitiveness of the product.

pixels in the cluster: *low*, *medium* and *high*.

fuzzy sets: *not defective*, *uncertain* and *defective*.

The adopted rules are expressed in Table 3.

Table 3. Adopted Rules

*high*.

*extension*.

This latter operation, together with the faulty zones, puts into evidence the contour of the paper roll which has to be eliminated from the resulting image for the successive processing steps. For this reason the pixels corresponding to the borders of the roll are detected through a specific *edge finding* algorithm based on the Canny method (Canny, 1986) which achieves good results and is not sensitive to the noise present in the examined image.

The second step of the computation analyses the binary image through an ad-hoc developed clustering algorithm which groups the single potentially defective points into macro-defects which represent the potential final defects of the product. The clustering is necessary in order to perform a selection among all the highlighted points and in order to put into evidence some key feature of the potential defects. The result of the clustering is a set of clusters, each one representing a potential defect and characterized by the points it includes. A first selection among these candidate defects is performed by discarding those clusters formed by less than a predefined threshold of points. The remaining ones are passed to the third control stage for the final assessment.

Fig. 10. The result of the image processing and clustering stage: single potentially defective points and clusters are highlighted.

This final decision is taken by means of a FIS (Mandani type) which implements the same rationale adopted by the human operators currently performing this task. In general human operators take into account two main characteristics of the identified critical regions: their extensions and the linearity of their shapes, thus the developed FIS is based on the following two input variables:


The output of the designed FIS is represented by a single variable, the so-called *defectiveness*, which reflects the decision about the final roll destination. This variable corresponds to three fuzzy sets: *not defective*, *uncertain* and *defective*.

The adopted membership functions are Gaussian and their domain depends on the universe where the corresponding fuzzy variable is defined (for instance, 0-200 points for the variable *extension*.

Seven fuzzy rules derived from the knowledge of expert human operators constitute the adopted inference system. The defectiveness index is evaluated for all the clusters eventually present on a single roll: if a paper roll contains at least one cluster whose defectiveness index is higher than a fixed threshold, it is discarded.


The adopted rules are expressed in Table 3.

#### Table 3. Adopted Rules

264 Fuzzy Inference System – Theory and Applications

This latter operation, together with the faulty zones, puts into evidence the contour of the paper roll which has to be eliminated from the resulting image for the successive processing steps. For this reason the pixels corresponding to the borders of the roll are detected through a specific *edge finding* algorithm based on the Canny method (Canny, 1986) which achieves

The second step of the computation analyses the binary image through an ad-hoc developed clustering algorithm which groups the single potentially defective points into macro-defects which represent the potential final defects of the product. The clustering is necessary in order to perform a selection among all the highlighted points and in order to put into evidence some key feature of the potential defects. The result of the clustering is a set of clusters, each one representing a potential defect and characterized by the points it includes. A first selection among these candidate defects is performed by discarding those clusters formed by less than a predefined threshold of points. The remaining ones are passed to the

Fig. 10. The result of the image processing and clustering stage: single potentially defective

This final decision is taken by means of a FIS (Mandani type) which implements the same rationale adopted by the human operators currently performing this task. In general human operators take into account two main characteristics of the identified critical regions: their extensions and the linearity of their shapes, thus the developed FIS is based on the following

good results and is not sensitive to the noise present in the examined image.

third control stage for the final assessment.

points and clusters are highlighted.

two input variables:

Several tests have been performed for evaluating the proposed quality control system. The value of the defectiveness discrimination threshold must meet two opposite requirements: on one hand the choice of high values of such threshold leads to a high number of *missed detections* (MD) of faulty rolls, on the other hand low values of the threshold rise several socalled *false alarms* (FA) which correspond to pauses on the process for the maintenance of the machinery. Both these situations must be avoided although, according to technical personnel, to avoid missed defect detections is more important, as the presence of faulty rolls can affect the commercial competitiveness of the product.

The results obtained by the proposed vision system are extremely good as, with the selected threshold, an extremely low number of defective products are missed and a satisfactory

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#### **7. Conclusions**

In the last years Vision Systems in the industrial field have been widely adopted providing innovative solutions in the direction of industrial application. Vision systems improve the productivity and the quality monitoring becoming a competitive tool to industries which employ this technology.

In this chapter a brief description of vision system is provided and then the principles of industrial quality control have been treated. Several examples of use of fuzzy system in different industrial applications have been described. The results demonstrate how applicable the FISs are in industrial field: their flexibility and the simplicity make this approach an optimal solution to describe complex processes.

#### **8. References**


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**12** 

*1China 2UK* 

**and Expert System** 

**Edge Detection Based on Fuzzy Logic** 

The process of detecting outlines of an object and boundaries between objects and the background in the image is known as edge detection. It is an important tool used in many

Linear time-invariant (LTI) filter is the most common method to the edge detection. On the condition of rst-order filter, an edge is considered as an abrupt variation in gray level between two neighbor pixels. Then the aim is to find out the points in the image which the first-order derivative of the gray level is of high magnitude. The root mean square value

Second order operators are used sometimes. LoG (Laplacian-of-Gaussian) [3] filter is the most commonly used. There are three drawbacks with this operator. Firstly, it produces the greater computational complexity. Secondly, it generates a continuous line to represent all edges in the input image, and is also not adequate to describe more general structures.

Fuzzy logic represents a powerful approach to decision making. Since the concept of fuzzy logic was formulated in 1965 by Zadeh, many researches have been carried out its applications in the various areas of digital image processing: such as image assessment, edge detection, image segmentation, etc [4]. Bezdek et al, trained a neural net to give the same fuzzy output as a normalized Sobel operator [5]. The advantage of the new method over the traditional edge detector is very apparent. In the system described in [6, 7], all inputs to the fuzzy inference systems (FIS) system are obtained by applying to the original image a high-pass filter, a first-order edge detector filter (Sobel operator) and a low-pass (mean) filter. The adopted fuzzy rules and the fuzzy membership functions are specified

Fuzzy image processing is not a unique theory. It is a collection of different fuzzy approaches to image processing. Generally speaking, edge detection with fuzzy logic is

**2. General description composition of the fuzzy inference system** 

applications: such as image processing, computer vision and pattern recognition [1].

(RMS) is often used as the threshold value to the input image [2].

according to the kind of filtering to be executed.

**1. Introduction** 

Shuliang Sun1, Chenglian Liu1,2, Sisheng Chen1 *1Department of Mathematics and Computer Science, Fuqing Branch of Fujian Normal University, Fuqing 2Department of Mathematics , Royal Holloway, University of London,Egham, Surrey, TW20* 

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