Computational Intelligence and Neuroscience

Volume 2016, Article ID 8289508, 8 pages

http://dx.doi.org/10.1155/2016/8289508

## Intelligent Process Abnormal Patterns Recognition and Diagnosis Based on Fuzzy Logic

^{1}School of Business, Huaihua University, Huaihua, Hunan 418000, China^{2}School of Mechanical and Power Engineering, North University of China, Taiyuan, Shanxi 030051, China

Received 20 July 2016; Revised 25 October 2016; Accepted 2 November 2016

Academic Editor: Elio Masciari

Copyright © 2016 Shi-wang Hou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Locating the assignable causes by use of the abnormal patterns of control chart is a widely used technology for manufacturing quality control. If there are uncertainties about the occurrence degree of abnormal patterns, the diagnosis process is impossible to be carried out. Considering four common abnormal control chart patterns, this paper proposed a characteristic numbers based recognition method point by point to quantify the occurrence degree of abnormal patterns under uncertain conditions and a fuzzy inference system based on fuzzy logic to calculate the contribution degree of assignable causes with fuzzy abnormal patterns. Application case results show that the proposed approach can give a ranked causes list under fuzzy control chart abnormal patterns and support the abnormity eliminating.

#### 1. Introduction

Control charts are widely used in abnormity monitoring and control in manufacturing and other processes. It applies statistical signal to detect process variation, locates the assignable causes, improves the process performance, and maintains the process in satisfied quality level. For example, [1] used Shewhart control charts supplemented with runs rules to detect shifts in process variance. In [2], two stability metrics were proposed to identify underlying variation as common or special cause in biopharmaceutical processes. Reference [3] developed control charts by use of batch statistical process monitoring to perceive the process trajectory. The process variations can be divided into two categories: random and abnormal. Generally, the former is inherent in the process and is hard to eliminate; the latter indicates that there are some special sources of exceptions, which can be detected and eliminated or limited in certain range. Furthermore, the latter can be represented in control chart as a form of abnormal pattern. So it is a quick and easy way to recognize and diagnose the process by use of the abnormal signals of control chart.

However, there are uncertainties, ambiguities, and vagueness associated with the process abnormal patterns recognition and diagnosis. By considering the cause-selecting problem as a pattern classification problem, artificial neural network could deal with this problem partly in [4–7], but its internal operation mechanism cannot be obtained distinctly. If the uncertainty could be quantified to indicate the extent to which each nonrandom pattern happens and the degree to which each associated cause exists, it will facilitate the decision making. So, many researchers have introduced fuzzy logic into this field. Kahraman et al. used triangular membership functions to define various unnatural patterns in [8]. A fuzzy test was defined for each unnatural pattern using the membership value of the th sample to confirm the presence of the unnatural pattern. But only simple triangular fuzzy membership functions were used to define all the patterns. Zalila et al. proposed a fuzzy supervision method for SPC which could alert operators on the process state using visual signals in [9]. These visual signals were generated using a fuzzy rule base which monitored the process center and state of dispersion. Wang and Rowlands developed a fuzzy rule based inference system based on zone rules in control charts in [10]. The input variables were the degree of membership of a point in each zone represented by fuzzy sets, and the output was the process state, mapped by eleven fuzzy If-Then rules. This approach provided improved results in terms of interpretation of data and consistency, as the numeric output from the fuzzy system indicated whether or not action should be taken, if the process was out of control. Another excellent application of fuzzy logic to control chart for individuals was developed by Tannock in [11]. In this approach, two fuzzy sets, namely, centered fuzzy set and random fuzzy set, were used. Three typical unnatural patterns: shift, Trend, and cyclical patterns were examined using these two fuzzy sets. The membership function of the centered fuzzy set was defined by the Operating Characteristic (OC) Curve of the equivalent Shewhart control chart, which considered the mean and standard deviation of the incoming distribution. The membership of the random set was determined by calculating the correlation coefficient of the series window at sample number with the previous window . The absolute value of correlation coefficient was subtracted from unity to obtain the degree of membership, such that highly correlated data were not considered to be very random.

An investigation into the use of fuzzy logic to modify SPC rules was described in [12], with the aim of reducing the generation of false alarms and also improving the detection and detection-speed of real faults. In [13], the author proposed a neural-fuzzy model for detecting mean shifts and classifying their magnitude in multivariate process. By using a fuzzy classifier, the outputs of NN were classified into various decision intervals. Finally, the shift status was determined through an additional two-point-in-an-interval decision rule. Based on the concepts of fuzzy statistical confidence intervals and the necessity of strict dominance index, a new fuzzy control chart was proposed in [14]. In their approach, control lines of the chart were calculated as critical values of certain fuzzy statistical tests. With given significance level and necessity index, the process status was judged by the interval location relative to the control lines. Reference [15] used a fuzzy inference system to transfer the inspector’s subjective rating of the products quality to a crisp number and proposed a new approach to monitoring the process when vagueness and uncertainty arise. The results showed the proposed approach could detect abnormal shifts in the process especially in small shifts.

However, all these approaches use fuzzy logic only in analyzing the control chart patterns to determine the process state. Diagnosing the assignable cause from the signals from the patterns has not been explored in these approaches.

Reference [16–18] proposed some approach to solve production problems by use of RFID-enabled technology. By attaching RFID facilities with production resources, the manufacturing process was converted into smart objects that can sense and interact. This technology can obtain the state information of nonfuzzy physical quantities. But it is still hard to realize the automatic measuring of uncertain quality attribute.

To handle the abovementioned uncertain problems, this paper proposed a fuzzy logic based inference system (FIS). The system included an input submodule, six fuzzy inference submodules, and one aggregation submodule. Each inference submodule took the characteristic numbers of control charts’ abnormity pattern as input. After fuzzifying the input through respective membership function, the results were input into the corresponding inference submodules. Each submodule output its inference result by centroid defuzzifying method. In aggregation submodule, All the evidence supporting each cause from all the inference submodules were aggregated using fuzzy connective operators, and the causes were ranked according to the final aggregating results based on given fuzzy threshold.

The rest of the article is organized as follows. Section 2 defines four basic abnormal patterns and establishes an empirical relationship model between abnormal patterns and assignable causes. Fuzzy inference system framework and design procedure are presented in Section 3. The performance of the proposed system is studied in Section 4 on the basis of an application case study. Section 5 ends with a summary and conclusions.

#### 2. Problem Description

For a controlled process, points plotted on control chart present a random pattern following normal distribution. The random state of control chart will be broken when the process is out of control, and some abnormal patterns will be shown on the control chart. These unnatural patterns can be detected by a set of rules based on the principle of small probability events. And also the causes for the current abnormity can be located based on the empirical mapping relationship between the abnormal patterns and assignable causes.

##### 2.1. Control Chart Abnormal Patterns Definition

This paper considered four common abnormal patterns defined by the following rules:(1)Out of Control Limit (OCL): one or more points go beyond three sigma control limit.(2)Freak: two of three consecutive points go beyond one sigma limit on the same side of the center line.(3)Run: seven or more consecutive points are on the same side of centerline.(4)Trend: seven or more points continuously increase or decrease.

##### 2.2. Empirical Mapping Relationship between Abnormal Patterns and Assignable Causes

The empirical mapping relationship between abnormal patterns and assignable causes can be built based on the nature of variation produced by the cause. According to the process abnormity implicated by control chart nonrandom pattern, assignable causes can be divided into three categories as follows (see reference [19–21]).

*(i) Isolated Causes (Denoted as **)*. Isolated causes are those that will cause a single measurement to vary drastically, resulting in one particular point falling outside the control limits producing at OCL pattern on the control chart. These causes have one-time effect. The possible causes that come under this category are as follows:(i)A mistake in measurement, recording, or plotting(ii)Damage in handling(iii)Defect in raw material used for that unit alone(iv)False alarm

*(ii) Causes for Shift (Denoted as **)*. These causes produce a considerable shift in the process mean. These can be identified by the Freak and Run patterns on the control chart. They indicate that some event has taken place that has affected a few samples causing a drift in the mean. Usual causes that could produce this effect are as follows:(i)Tool break(ii)Change in raw material or supplier(iii)Change in inspection methods or standards(iv)Adjustments made in machine settings(v)Introduction of new workers or inspectors

*(iii) Gradual Causes (Denoted as **)*. These causes tend to change the process mean gradually over time and produce increasing or decreasing trends on the control chart and are identified by the Trend pattern. Trend patterns are produced by causes such as the following:(i)Gradual introduction of new raw material(ii)Loosening fixtures(iii)Operator fatigue(iv)Machine tool wear

So, the chart abnormal pattern-cause relationship can be modeled as shown in Figure 1.