استفاده از شبکه های بیزی برای تجزیه و تحلیل علت ریشه ای در کنترل فرآیند آماری

Despite their fame and capability in detecting out-of-control conditions, control charts are not effective tools for fault diagnosis. There are other techniques in the literature mainly based on process information and control charts patterns to help control charts for root cause analysis. However these methods are limited in practice due to their dependency on the expertise of practitioners. In this study, we develop a network for capturing the cause and effect relationship among chart patterns, process information and possible root causes/assignable causes. This network is then trained under the framework of Bayesian networks and a suggested data structure using process information and chart patterns. The proposed method provides a real time identification of single and multiple assignable causes of failures as well as false alarms while improving itself performance by learning from mistakes. It also has an acceptable performance on missing data. This is demonstrated by comparing the performance of the proposed method with methods like neural nets and K-Nearest Neighbor under extensive simulation studies.

Root cause analysis (RCA) is targeting at identifying the causes of problems in processes for directing counteractive actions (Rooney & Heuvel, 2004). Control charts typically do not have this feature; however non-random patterns on the chart can be used as a source for RCA (Doty, 1996, Montgomery, 2005 and Smith, 2004). However, large number of possible relations among patterns and causes makes the process of cause/s identification difficult. Certain information from the process (at the time of change) can be used in accompany with chart patterns to simplify this process. As a simple example, if we know from pattern analysis that either machine condition or the quality of input-material has caused an out-of-control situation, when the process data shows that the operating machine has not been serviced for a while but the material has recently been tested showing no problem, there is a high chance that the bad condition of the operating machine has caused the problem. The relationship structure among chart patterns, process information, and assignable causes can are represented in Fig. 1. The chart patterns considered here which are among the most frequent patterns in control charts are discussed in Section 3.3.1. Meanwhile, the specific pieces of information from the process that are included in the network have been discussed in Section 3.3.2. Full-size image (19 K) Fig. 1. Relationship among chart patterns, process information and possible root causes. Figure options Bayesian networks are powerful tools for knowledge representation and inference under the uncertainty. The graphical nature of Bayesian networks allows seeing relationships among different variables and features. Using conditional independencies in the structure, they are able to perform probabilistic inference. They can not only learn from their mistakes but also they work with incomplete data. Such characteristics make Bayesian network a suitable candidate for modeling relationship structure in Fig. 1. For this purpose, the rest of the paper is organized as follows: Section 2 reviews different techniques of RCA in the literature. Section 3 presents an introduction to Bayesian network, followed by detailed design of model and proposed data structure. Section 4 compares the proposed Bayesian network method with K-Nearest Neighbor (KNN) and Multi-Layer Perceptron (MLP), and discusses its performance under various conditions. Finally, Section 5 presents the conclusions and areas for future research.

In this study we developed a hybrid intelligent approach based Bayesian networks for fault detection and diagnosis in control charts. The proposed Bayesian network use control chart patterns in accompany with as set of specific information from the process at the time of change as inputs and provides a ranked list of most important root causes with related probability of occurrence as the output. Through two sets of extensive simulation studies we verified the proposed method under different conditions. In the first series we compared the performance of the proposed method with neural nets and nearest neighbor classifiers. Next, we calculate detail statistics on its performance under different out-of-control situations under variable sizes of datasets and different rate of missing data. The proposed method is easy to construct and implement. Meanwhile it can be constructed based on either direct or indirect approach. It learns from its mistakes and robust to noise and missing data.