Chapter 7

Real-Time Key Production Performances Analysis Method

Abstract

With the rapid growth of industrial wireless network and auto-ID technologies (e.g., radio frequency identification, Bluetooth and Wi-Fi), many manufacturing companies adopt these advanced technologies to track and trace the real-time manufacturing activities. However, amounts of distributed manufacturing data are obtained by the sensors, most of which are often meaningless and cannot be used by the upper level managers directly. To address this question, this chapter proposes an overall architecture of real-time key production performance analysis method (PPAM). First, the Internet of things devices are extended to manufacturing field to dynamically sense manufacturing data. Then, the multilevel event model and hierarchy timed color Petri net are used to integrate the discrete raw manufacturing data into critical events. At last, the decision tree technologies are applied to extract the production anomalies and find the causes of anomalies.

Keywords

Internet of things (IoT)
manufacturing system
key production performance analysis
hierarchy timed color Petri net (HTCPN)
decision tree

7.1. Introduction

With the rapid growth of smart sensing technologies, it is possible to fulfill the smart manufacturing with the ability of dynamically sensing, optimal scheduling, and real-time control [1]. The innovative era of Internet of things (IoT) is generated as a consequence of the widespread use of sensor technologies, such as RFID, Wi-Fi, GSM, and so on. It denotes uniquely distinguishable things and their virtual depictions under an Internet-alike framework [24]. By applying the IoT devices to traditional manufacturing field, real-time and multisource data (RMD) from manufacturing activities can become more available and pervasive, as discussed in Chapter 3.
Amounts of distributed manufacturing data are obtained by the sensors, most of which are often meaningless and cannot be used by the upper level managers directly. However, the production anomalies often disturb the normal manufacturing activities. The key production performance analysis (KPPA) is the base to find the anomalies. If the production performance (PP) cannot be on time, the anomaly cannot be found and managed in time, which will lead to the aggravation of process disturbance. Therefore, it is important for the enterprises managers to improve their production management pattern with advanced technologies and models to fulfill the real-time KPPA, so that the managers can make optimal decisions based on real-time production status and the anomaly can be detected and eliminated dynamically.
In general, Petri nets (PNs) are recognized to be dominant in process modeling of discrete event system (DES), both graphically and mathematically [5,6]. Decision tree (DT) is a supervised knowledge acquisition technique, which can extract the rules from either expert knowledge or historical data, and it is a widely used data-driven approach in decision support and rule obtainment [7,8]. Hence, the PNs and DTs are used as our KPPA tools.
By combining IoT technologies, PNs, and DTs, this work develops an all-in-one real-time key production performance analysis method (PPAM). The aim of this chapter is to answer the following two great challenges: (1) how to build up an events-driven real-time key PPAM to process the huge real-time data captured by distributed auto-ID devices to meaningful and value-added PP information? (2) How to efficiently analyze the PP, so that the real-time anomaly can be extracted timely and the causes of the anomaly can be diagnosed?
The rest of this chapter is arranged as follows. Section 7.2 reviews the related works. Section 7.3 describes the overall architecture of real-time KPPAM. Section 7.4 gives the event hierarchy of multilevel event, while the extraction of critical event (CrE) is presented in Section 7.5. Section 7.6 gives the real-time production anomaly analysis method.

7.2. Related works

Three categories of literature are relevant to this research. They are real-time production monitoring technique, real-time production key performance indicators (KPIs) analysis, and real-time production anomaly analysis.

7.2.1. Real-Time Production Monitoring Technique

In the area of real-time production monitoring technique, Guo et al. proposed an RFID-based smart decision support system architecture for production monitoring and scheduling in a distributed manufacturing environment. The RFID, cloud technology, and intelligent techniques are used in the architecture [9]. Chai et al. presented a cooperative manufacturing execution systems; it uses real-time information to realize lean production [10]. By applying the concept of cloud computing into manufacturing field, Wang and Xu provided an interoperable production mode [11]. Wang et al. developed a framework, that is, Wise-ShopFloor (web-based-integrated sensor-driven e-ShopFloor), for real-time monitoring and remote control of networked CNC machines [12]. Chen et al. proposed an RFID-based enterprise application integration framework for real-time management of dynamic manufacturing processes [13]. Chongwatpol and Sharda proposed a creative information visibility-based scheduling (VBS) rule that utilized information generated from the real-time traceability systems for tracking work in processes (WIPs), parts and components, and raw materials to adjust production schedules [14]. Arkan and Van proposed an RFID-based real-time location system (RTLS) solution for obtaining multiitem WIP visibility within a company [15]. Bevilacqua et al. presented a case study for implementation of an RFID system in a furniture industry involved in the fashion sector; the case company is an Italian enterprise which is a leader in the furniture industry [16].

7.2.2. Real-Time Production KPIs Analysis

In the production KPIs analysis aspect, Georgiadis and Michaloudis merged discrete event simulation and continuous dynamics in a unified hybrid simulation environment. By coordinating the simulations run in real time, the results can be associated with information from the shop-floor frontline [17]. Zang et al. applied an event-processing method for management systems using RFID, where the framework, information structures, optimization manners, and algorithms are discussed in detail [18]. Considering the difference businesses in different companies, Huang et al. presented an agent-based workflow management method [19] and Zhang et al. proposed a smart objects management system for RFID-enabled real-time reconfigurable manufacturing [20]. Kumaraguru et al. proposed an approach to integrate real-time analytics with continuous performance management, which can form the base for further research on fulfilling likely interoperability issues and essential standardization efforts to support improvement of a system [21]. Blaha et al. designed a paradigm that enables real-time monitoring using cognitive models and its implementation was demonstrated with a fatigue-sensitive task [22]. Li proposed an aggregation method by overlapping decomposition approach to approximate the production rate for systems with rework loops; the systems were decomposed into four serial production lines, with machines modified to accommodate the interactions with other machines and buffers [23]. Colledani and Tolio designed a new approximate analytical method to estimate the quality and productivity performance measures of asynchronous production lines, thus the associations between the quality control and system production logistics performance can be captured [24]. Lao and Liu integrated data envelopment analysis (DEA) and geographic information systems (GIS) to evaluate the performance of bus lines within a public transit system, considering both the operations and operational environment [25]. Lin et al. proposed a three-phase method to measure the performance of a highly value-added footwear manufacturing system considering reworking actions, in which the system consists of multiple production lines [26]. Using RFID-enabled shop-floor production data, Zhong et al. proposed a data mining approach (DT-based model) to estimate realistic standard operation time and unknown dispatching rules [27].
The modeling of manufacturing activities plays an important role in real-time PPA. Lv et al. developed a novel RFID-based CPN analysis strategy, where the behaviors of the dynamic production status can be described through colored tokens [28]. To model the dynamic behavior of manufacturing systems, Wu and Zhou offered an intelligent token PN (ITPN) for modeling and control of reconfigurable production systems, where colored tokens are extended as macrotokens so that they can represent job instances with real-time awareness about system status just like smart cards in real life [29]. Zhang et al. used the hierarchy timed color Petri net (HTCPN) method to construct the real-time production events, where the events are displayed with a multilevel event model [30]. Başak and Albayrak presented a PN-based decision system modeling method for real-time scheduling and control of flexible automotive manufacturing systems [31]. Wang et al. proposed a new colored PN model for real-time scheduling of multiprocessor system on chip platform [32]. Similarly, a model that described the reconfiguring process of a manufacturing system was developed by adopting colored timed object-oriented PNs [33]. Ha and Suh designed PWF-nets based on timed colored PNs and proposed a method of organizing PWF-nets that are composed of workflow patterns, so that the difficulty in workflow management because of the uncertain and dynamic characteristics can be tackled [34].

7.2.3. Real-Time Production Anomaly Analysis

To analysis production anomalies, two main steps need to be taken, that is, the anomaly extraction and anomaly cause diagnosis. In the area of anomaly extraction, Evans et al. presented a distinct experience-based decision support system, which uses factual information of historical decision to compute the confidence factors [35]. Zarei et al. presented an intelligent method based on artificial neural networks (ANNs) to identify bearing defects of induction motors [36]. Cabral presented a PN approach for online diagnosis of DESs modeled by finite state automata; the method is based on the construction of a Petri net diagnoser (PND) which is constructed in polynomial time and requires less memory than other methods proposed in the literature [37]. Cabasino et al. proposed a method for online diagnosis of DESs based on labeled PNs [38]. He et al. proposed a DT learning-based model for bivariate process mean shift monitoring and fault identification [39]. Maier et al. presented new model-based approaches for testing and diagnosis of automation systems; the models are not created manually but learned automatically by monitoring the plant behavior [40]. Similarly, Faltinski et al. presented a new model-based approach for the prediction of energy consumption in production plants in order to detect anomalies. Hybrid timed automaton models of the supervised production plant are generated and executed in parallel to the system so that the anomalies can be detected automatically [41]. Yin et al. considered the real-time implementation of fault-tolerant control systems with performance optimization [42].
In the anomaly cause diagnosis aspect, Chioua et al. designed a top-down approach for root cause analysis using KPIs; the differences between bottom-up and top-down methods for root cause analysis are studied in the paper [43]. Wang et al. presented a graphic modeling approach, that is, fault diagnosis method based on fuzzy reasoning spiking neural P systems (FDSNP), for power transmission networks [44]. Groenewald and Aldrich proposed a root cause analysis method for processing fault situations on an industrial concentrator circuit by use of causality maps and extreme learning machines; the maps are combined with two approaches based on the use of extreme learning machines [45]. A DBN-based framework for root cause reasoning was proposed to deal with abnormal situation by Hu et al., and fault propagation behavior of process system is studied [46]. Alaeddini and Dogan designed a root cause analysis in statistical process control based on Bayesian networks (BNs); the cause and effect relationship among chart patterns, process information, and possible root causes/assignable causes are considered in the BNs [47]. An improved PLS (IPLS) approach is presented to cope with the problems for fault diagnosis related to KPI of the underlying process encountered by the standard approach [48]. Li et al. designed a new causality analysis index based on dynamic time warping to determine the causal direction between pairs of faulty variables [49].

7.2.4. Research Gap

Up to now, comprehensive research on the real-time production PAM has been done. However, less research effort is paid to the following issues.
1. Amounts of primitive data are captured after the multiple sensors are attached to the traditional manufacturing resources. However, most of the data are meaningless. There is a wide gap between the primitive data and the key PP information. It is necessary to build up an event-driven real-time KPPA model and procedure to process the huge real-time data captured by distributed auto-ID devices to meaningful and value-added manufacturing information.
2. Production anomalies are inevitable in real-time processes and the anomalies analyses are essential to ensure the normal manufacturing activities. In general, the anomalies are often found and diagnosed by the experts, thus the process for anomalies detection are always subjective. How to dynamically provide the upper level applications with the quantitative and qualitative information of anomalies persuasively and objectively is an important issue.

7.3. Overall architecture of real-time production performance analysis model

In order to meet the wide information gap between the physical manufacturing systems and enterprise information systems (EISs), this chapter proposes a real-time KPPAM. The IoT technologies, PNs, and DTs are combined to develop an efficient real-time KPPA architecture. The overall architecture of the proposed model is presented in Fig. 7.1. The KPPAM consists of three main modules, namely, configuration of smart sensors, CrE-based information extracting process, and real-time key production anomaly analysis. They are explained next.
image
Figure 7.1 Overall architecture of real-time production performance analysis model.

7.3.1. Configuration of Smart Sensors

The goal of this module is to construct a smart manufacturing environment based on IoT technologies, thus the information bridge between physical manufacturing systems and upper-level information systems can be established. The IoT technologies, such as RFID, wireless, etc., are applied to the traditional manufacturing things based on the information requirements. Besides, the optimal algorithms are used to decide the configuration pattern, so that a smart manufacturing environment can be established in an optimal manner. At last, the amounts of manufacturing data can be timely obtained by upper-level applications. More details can be found in Chapter 3.

7.3.2. Critical Event–Based Information Extracting Process

This module aims to model the dynamic behavior of the manufacturing system and process the large number of raw manufacturing data captured to CrEs of KPPA. As shown in the middle of Fig. 7.1, multilevel event model are used to analyze real-time PP. Four levels of events are established in this model, namely primitive events (PEs), basic events (BEs), complex events (CEs), and CrEs. The extracting processes are fulfilled by using HTCPN technologies, which will obtain the up-level events by continuously reading and integrating the primitive data. More details will be presented in Sections 7.4 and 7.5.

7.3.3. Real-Time Key Production Anomaly Analysis

Evaluating the real-time key PP condition is an important step in improving production efficiency. After the CrEs are obtained, the PPs are going to be evaluated to find the anomalies. First, the quantitative information of PP are obtained from the lower-level modules, and the information of the related factors are also called. Second, each kind of key PP are assessed to find the anomalies, respectively. The classic decision tree classifier, namely, C4.5, is used for the construction of anomaly extraction rules due to its ability to analyze continuous attributes. At last, the corresponding anomaly cause analysis rules are called to acquire the reasons as soon as an anomaly is extracted. Since most of the captured information of manufacturing resources has fuzzy attributes, the Fuzzy Interactive Dichotomizer 3 (Fuzzy-ID3) algorithm is used to obtain anomalies cause diagnosis rules. More details are given in Section 7.6.

7.4. The event hierarchy of critical event

The real-time production activities are complicated and interconnected, thereby the complexity of modeling and simulation is increased. The precise event model is the foundation of the KPPAM. As shown in Fig. 7.2, a four-level event hierarchy is discussed in this chapter. The detailed information of event at each level is shown as follows.
image
Figure 7.2 The event hierarchy of multilevel event.
PEs are raw events captured by the IoT devices. Due to the reading characteristic of high-speed and automatic reading of the IoT devices, the PEs are often obtained in a large volume. BEs are resource level events, which are formed by the aggregation of qualified raw data. Readers are referred to Chapter 3 for more details about PE and BE.
CEs are cell level events, for example, the process of a whole production line from material released to production offline. In general, the BEs denote the time and space status, and are connected with each other, so that they can be used to acquire the status of CE.
Definition 7.1: CEs can be represented as CE=(CE.ID,Attri,Context,T)image where, CE.ID denotes the unique ID; Attri denotes the attributes, such as the event elements; Context describes the context information, such as material.ID, process.ID, the relationships among subevents, etc.; T is the time when the event occurs.
CrEs are highest level events, whose state changes have a large effect on the production management. Various enterprise information systems are concerned about different sides of PP, therefore, the CrEs have different meanings for them. For example, the change of total production cost is the CrE for the financial managers, while the real-time progress is the cared events for project managers.
Definition 7.2: CrEs can be represented as CrE=(CrE.ID,Attri,Context,T)image where, CrE.ID is the unique ID, Attri denotes the attributes of the event, Context describes the context information, T denotes occur time.

7.5. HTCPN-based critical event analysis

In order to acquire the CrEs, the HTCPN is used to model the constraint relationships and sequential relationships of the set of operations according to the multilevel events. Instead of modeling the static process, the HTCPN aims to model dynamic and hierarchical information of the manufacturing resources.

7.5.1. Basic Concepts of HTCPN

HTCPN is a graphical modeling language with a well-defined semantics, which has been proved to be a suitable tool to model dynamic manufacturing system. HTCPN, as a normal extension of the classic PN, have three main advantages for production modeling: (1) HTCPN can decrease the dimension of traditional PN in a great extent; (2) HTCPN can model deterministic firing durations, which helps to obtain exact performance estimates; and (3) HTCPN can use a unified net to model similar components/subsystems, and the nets can be involved repeatedly when modeling a complex system.
Definition 7.3: An HTCPN is an 8-tuple N = 〈P, T, C, I, O, G, D, M
where, P = {Pt, Pm} is the set of places, Pt and Pm are traditional and macroplaces, respectively. The places are used to represent resources status of the system; T = {Ti, Tt, Ts, Tm} is the set of transitions, Ti, Tt, Ts, and Tm are immediate, timed, random, and macrotransitions, respectively. The macrotransitions are replaceable transitions that can be substituted by detailed sub-HTCPN systems. The transitions are used to represent the activity; C represents the color mapping from PT to W, an element of C(s) is named as a color of s and C(s) is the color set of s, s is the attribute of P or T. The colored tokens are used to represent particular type of product; the tokens can carry colored attributes, for example, time, quantity, and so on; I(O) denotes the forward (backward) incidence matrix of P × T, where I(P, T) is a mapping from C(P) × C(T) to N = {0, 1, 2,…} and O(P, T) is a mapping from C(T) × C(P) to N = {0, 1, 2,…}. I/O functions are used to represent the relationship between transitions and places; G denotes the guard function, which is used to describe the trigger condition for each transition T; D represents the time duration of timed transition “Tt” or random transition “Ts.” Once a transition in Tt or Ts is enabled, it cannot fire until D units of time are passed; M denotes a marking representing the number of tokens in P. M0 represents the initial marking.

7.5.2. HTCPN Model Construction

To model the multilevel event, mainly five steps are considered to build an HTCPN.
Step 1: Summarize the outline of the production process in shop floor, and then construct the PN model for the CrE, where all the elements and constraints are considered into the PN.
Step 2: Further construct the sub-PNs for the upper-level HTCPN. Since the upper-level events are integrated by the lower-level events, the macrotransitions in the upper-level events can be replaced by substitutions which can be described in detail by sub-PNs.
Step 3: Repeat Step 2 until each bottom element is described by a PE captured by the sensor, which means that no further extension can be executed.
Step 4: Construct the contacts among the PNs at different levels, so that the relationships among the sub-PNs are corresponding with the entire multilevel model.
Step 5: Establish the connection between the HTCPN and the manufacturing resources. As a result, the HTCPN can model the dynamic behavior of the real-time manufacturing system.

7.5.3. Connection Between HTCPN and Manufacturing Resources

As shown in Fig. 7.3, the connection between the established HTCPN and manufacturing resources is fulfilled by a middleware. On one hand, the manufacturing resources are monitored by the multiple sensors, and the real-time information are captured and uploaded to the middleware on time. On the other hand, the marking of the HTCPN alters based on the dynamic information acquired from the middleware. Thus, the tokens in the HTCPNs can be connected with the manufacturing resources. Once the status of a manufacturing resource alters, the color of the token will be altered immediately.
image
Figure 7.3 Connection between the HTCPN and manufacturing resources.
Fig. 7.4 shows a case for the PN-based production PAM. In the existing marking, four kinds of colored tokens are presented in the PN: two materials M01 (dark gray) in Place P0, one material M02 (light gray) in Place P1, and one Part M0 (black) in Place P2. Each token carries the related manufacturing information by the color. For example, the black token (M0) carries the status information with five components (MID, WID, PQ, GT, PT): MID is the material ID, WID is the workstation ID, PQ is the present quality, GT is the getting time, and PT is the present time. If the manufacturing process works normally, the status of the token will alter following the logic of PN. For example, the aforementioned two dark gray tokens and one light gray token will be integrated to obtain a black token, that is to say, the materials are successfully manufactured. Nevertheless, if something goes erroneous in the process, the output token will alter to another color to display the state variation.
image
Figure 7.4 A case for PN-based production performance model.

7.5.4. Production Performance Extraction

After the HTCPN model is established and the tokens are linked with the manufacturing resources, the model can change its markings according to the real-time condition. Thus, the performance of the PN can reflect the real-time PP. In order to obtain the PP easily, three actions are used to analyze the manufacturing processes.
1. Observe intermediate marking for the real-time status of inventory and WIP. For that the tokens are connected with the resources in shop-floor frontline, the dynamic status can be reflected by the marking of the PNs.
2. Set additional places to record the firing status of the transitions, for example, the trigger frequency and time. Given that the transitions denote the process activity and the firing status records the process data (throughput, process quality, manufacturing time, etc.), the PP related to the process data can be obtained by setting extra places.
3. Analyze the performance of PNs to measure the PP related to overall production, for example, production cycle time, average time taken for jobs to wait in the queue, queue length, and so on.
From previously mentioned steps, the PP can be acquired after the simulation, and then the simulation report can be obtained, which will be uploaded to the upper-level applications to provide the performance information.

7.6. Real-time production anomaly diagnosis

DT is one of the most popular machine learning techniques [7,50]. It can be used to establish the relationships between a large volume of input candidate attributes and an output attribute. This section discusses a DT-based anomaly extraction and cause diagnosis method for classification in a new manufacturing environment by learning from the historical cases.
Three main steps are essential in the classification. First, when a newly observed case comes, the related manufacturing information (PP and resource condition) of the historical cases is called, and the tree builder is triggered to construct the DTs for the production anomaly extraction and cause diagnosis. Then, the PP is assessed to find the anomaly according to the new rules from the DTs. At last, the anomaly cases will be further diagnosed to discover the causes of anomalies so that the managers can tackle the anomalies as soon as possible. The key elements in the DT-based production anomaly analysis are described as follows.

7.6.1. New Cases

In order to describe a new PP analysis problem simply and directly, the newly obtained information is represented as a new case (C).

C={Pt,R}

image(7.1)
where Pt = {Pt1, …, Pti, …, Ptn} is a set of attributes for PP, Pti(1 ≤ i ≤ n) is the ith kind of attribute, for example, the quantitative value. R = {R1, …, Rj, …, Rm}is a set of attributes for manufacturing resources. Rj(1 ≤ j ≤ m) is the attribute of the jth kind of resource; they can be either crisp or fuzzy values.

7.6.2. Historical Cases

A new production anomaly analysis event is evaluated based on anomaly analysis rules. It is significant to feedback the exception analysis, so that experiences are learned by knowledge mined from historical cases. Thereby, the possibility of the success of classification for new anomalies can be increased.
The historical anomaly case can be denoted as

H={Pt,R,D}

image(7.2)
where, D is the serious degree of production anomaly, four levels of degrees are considered, that is, red, yellow, blue, and green.

7.6.3. Decision Variables

To evaluate production anomaly, multiple decision variables are involved. Although performance attributes are always with crisp values, anomaly attributes cover both crisp and fuzzy values owing to the ambiguity or uncertainty during information capturing stage. Variables with crisp values are the attributes that are calculated according to a traditional set, that is, the membership of any value for the attributes is either 1 or 0. Variable with a fuzzy value defines their value with the membership that varied from 0 to 1, which are always determined by the membership function.
Here, the triangular membership function is used to convert the numerical data into fuzzy values. For example, if feature A is valued as numeral x, the values of feature A for all items uU can be denoted as X = {x(u), uU}. Then, X can be grouped to k semantic clusters Ti, i ∈ {1, …, k}. Semantic clusters Ti has a triangular membership function as:

uT1(x)(x)=1,xm1(m2x)/(m2m1),m1<x<m20,xm2

image(7.3)

uTk(x)(x)=1,xmk(xmk1)0,xmk1/(mkmk1),mk1<x<mk

image(7.4)

uTi(x)(x)=0,xmi+1(mi+1x)/(mi+1mi),mi<x<mi+1,1<i<k(xmi+1)/(mimi+1),mi+1<x<mi0,xmi+1

image(7.5)
where, mi, i ∈ {1, …, k} denotes the ith center of semantic clusters.

7.6.4. Tree Builder

Mainly three steps of rule induction are needed in DT learning. Step 1: create a large DT from historical cases according to feature selection approaches; Step 2: prune the branches and nodes that have little statistical influence on the tree; and Step 3: improve the understandability of obtained tree. Since the DT technologies have been widely discussed, we give the feature selection approaches briefly.
Fuzzy-ID3 is an extension of the classical tree-building ID3 algorithm and it has the ability to analyze both crisp and fuzzy variables. Fuzzy-ID3 algorithm is similar to ID3; the difference is that while ID3 selects the test attribute based on the information gain computed by using the probability of ordinary data, Fuzzy-ID3 does that by using the likelihood of membership values for the data set.
Assume a set of data E, and each data has r kinds of attributes and one classified class S = {S1, …, Sn} and fuzzy sets F = {Fi1, Fi2, …, Fim} for each attribute Ai, m is the number of clusters for Ai. Let Esnimage be a fuzzy/crisp set in E which has Sn kinds of class and |E| be the total number of membership or crisp values of the set of data E. Then, the information gain G(A,E) for attribute A by a fuzzy/crisp set of data E is described as:

G(A,E)=I(D)Entropy(A,E)

image(7.6)
where

I(D)=i=1n(pklog2pk)

image(7.7)

Entropy(A,E)=j=1m(pijI(Efij))

image(7.8)

pk=|Esn||E|

image(7.9)

pij=|EFij|j=1m|EFij|

image(7.10)
For a case where identical information gains are calculated, one is either selected randomly or chosen based on its importance within the project, and the DT is generated step by step until all the nodes are chosen.
C4.5 can only handle the crisp set and it applies the “information gain ratio” to obtain splits at the intermediate nodes in the tree:

Gainratio=Gain(A,E)Split(E)

image(7.11)
where,

Split(E)=i=1s|Ei||E|×log2p|Ei||E|

image(7.12)
If a is an attribute that carries continuous value, the attribute need to be discretized into two intervals afore the split.

7.6.5. Anomaly Extraction and Causes Diagnosis

After a real-time PP case is acquired, the rules correlated to the information can be used to assess the PP condition. If one anomaly event is detected, the anomaly label (e.g., Label L1) will be affixed to it, thus the following anomaly cause diagnosis process can easily identify the anomaly.
To detect causes for a new anomaly case, this chapter uses the reverse maximum matching (RMM) approach. After a new anomaly event is found, the information correlated to the anomaly, that is, all the real-time manufacturing resources data and fuzzy rules, are involved from the database. Then, the rules which have the same anomaly degree with the new anomaly are retained. Finally, based on the membership and certainty of historical rules, the causes are obtained. The main processes for the anomaly diagnosis are presented as follows:
1. Compute matching membership between the real-time PP case and each decision rule, and the result is deemed as the fitting membership between the case and the rule.
2. If only one rule have the highest fitting membership, this rule is chosen as the cause.
3. If several rules share the same highest fitting membership, the rule with the highest certainty is chosen.
Finally, the production anomaly analysis result is uploaded to the evaluation managers for acceptability assessment. If the anomaly analysis case is acknowledged, the anomaly can be dealt according to the causes, and the new case can be added into the database. Through the update of the anomaly cases and new knowledge supplemented, modifications on the database are necessary to ensure the knowledge is up to date and reliable. As a result, good base for future optimal decision making is laid.

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