Using Bayesian networks for root cause analysis in statistical process control
Introduction
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, 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.
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.
Section snippets
Root cause analysis literature
There are a number of RCA methods in SPC, meanwhile there are other successful methods in other engineering fields mainly based on artificial intelligence techniques that are considered in this research. In this regard, Section 2.1 reviews the methods developed in SPC context. Next, Section 2.2 studies the methods from other engineering fields.
Proposed Bayesian network
This section discusses the design process of the proposed Bayesian network. For this purpose, Section 3.1 provides an introduction to Bayesian network as a general framework for next sections. Section 3.2 discusses the detail structure of the proposed network. Finally Section 3.3 explains the data structure of the proposed method.
Verification and validation
To verify the performance of the proposed method two independent sets of simulation studies have been conducted. In the first series of simulations, the proposed method is compared with K-Nearest Neighbor (KNN) and Multi-Layer Perceptron (MLP). In the next series of simulations, the proposed method is evaluated under various conditions to gain detail information about its performance.
For each set of simulation studies, various sets of input–output data are generated using statistical
Conclusions
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
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