Modeling and analysis of disease and risk factors through learning Bayesian networks from observational data

This paper focuses on identification of the relationships between a disease and its potential risk factors using Bayesian networks in an epidemiologic study, with the emphasis on integrating medical domain knowledge and statistical data analysis. An integrated approach is developed to identify the risk factors associated with patients' occupational histories and is demonstrated using real‐world data. This approach includes several steps. First, raw data are preprocessed into a format that is acceptable to the learning algorithms of Bayesian networks. Some important considerations are discussed to address the uniqueness of the data and the challenges of the learning. Second, a Bayesian network is learned from the preprocessed data set by integrating medical domain knowledge and generic learning algorithms. Third, the relationships revealed by the Bayesian network are used for risk factor analysis, including identification of a group of people who share certain common characteristics and have a relatively high probability of developing the disease, and prediction of a person's risk of developing the disease given information on his/her occupational history. Copyright © 2007 John Wiley & Sons, Ltd.     

Bayesian networks for multilevel system reliability

Bayesian networks have recently found many applications in systems reliability; however, the focus has been on binary outcomes. In this paper we extend their use to multilevel discrete data and discuss how to make joint inference about all of the nodes in the network. These methods are applicable when system structures are too complex to be represented by fault trees. The methods are illustrated through four examples that are structured to clarify the scope of the problem.     

Bayesian monitoring to detect a shift in process mean

A Bayesian analogue of the Shewhart X‐bar chart is defined and compared with cumulative sum charts. The comparison identifies types of production process where the Bayesian chart has better expected performance than the cumulative sum chart. Implementing the Bayesian chart requires more detailed knowledge of the process structure than is required by the best‐known types of charts, but acquiring this information can yield tangible benefits. Copyright © 2007 John Wiley & Sons, Ltd.     

Bayesian Diagnostic Network： A Powerful Model for Representation and Reasoning of Engineering Diagnostic Knowledge

Engineering diagnosis is essential to the operation of industrial equipment. The key to successful diagnosis is correct knowledge representation and reasoning. The Bayesian network is a powerful tool for it. This paper utilizes the Bayesian network to represent and reason diagnostic knowledge, named Bayesian diagnostic network. It provides a three-layer topologic structure based on operating conditions, possible faults and corresponding symptoms. The paper also discusses an approximate stochastic sampling algorithm. Then a practical Bayesian network for gas turbine diagnosis is constructed on a platform developed under a Visual C environment. It shows that theBayesian net work is a powerful model for representation and reasoning of diagnostic knowledge. The three-layer structure and the approximate algorithm are effective also.     

A conjugate Bayesian approach to control chart for multi-batch and low volume production

Control chart could effectively reflect whether a manufacturing process is currently under control or not. The calculation of control limits of the control chart has been focusing on traditional frequency approach, which requires a large sample size for an accurate estimation. A conjugate Bayesian approach is introduced to correct the calculation error of control limits with traditional frequency approach in multi-batch and low volume production. Bartlett’s test, analysis of variance test and standardisation treatment are used to construct a proper prior distribution in order to calculate the Bayes estimators of process distribution parameters for the control limits. The case study indicates that this conjugate Bayesian approach presents better performance than the traditional frequency approach when the sample size is small.     

Bayesian np control charts with adaptive sample size for finite production runs

The design of a control chart requires the specification of three decision variables, namely the sample size, n, the sampling interval, h, and the action limit under which the process must be stopped for potential repair. In this paper, the Bayesian attribute control chart, namely the np chart for short run production, using a variable sample size is discussed. In a simulated experiment, optimal solutions of the static np chart, the basic Bayesian np chart, and the Bayesian scheme with adaptive sample size are presented. Results of the empirical study show that varying the sample size leads to more cost savings compared with the other two approaches. In order to detect how the input parameters affect decision variables, a regression analysis is conducted. It is obtained that the benefits of using the basic Bayesian np chart and the Bayesian chart with adaptive sample size instead of the static scheme are affected by the length of the production run. Copyright © 2008 John Wiley & Sons, Ltd.     

Markov chain Monte Carlo in Bayesian models for testing gamma and lognormal S-type process qualities

The process capability index C_pu is widely used to measure S-type process quality. Many researchers have presented adaptive techniques for assessing the true C_pu assuming normality. However, the quality characteristic is often abnormal, and the derived techniques based on the normality assumption could mislead the manager into making uninformed decisions. Therefore, this study provides an alternative method for assessing C_pu of non-normal processes. The Markov chain Monte Carlo, an emerging popular statistical tool, is integrated into Bayesian models to seek the empirical posterior distributions of specific gamma and lognormal parameters. Afterwards, the lower credible interval bound of C_pu can be derived for testing the non-normal process quality. Simulations show that the proposed method is adaptive and has good performance in terms of coverage probability.     

Safety analysis in process facilities: Comparison of fault tree and Bayesian network approaches

Safety analysis in gas process facilities is necessary to prevent unwanted events that may cause catastrophic accidents. Accident scenario analysis with probability updating is the key to dynamic safety analysis. Although conventional failure assessment techniques such as fault tree (FT) have been used effectively for this purpose, they suffer severe limitations of static structure and uncertainty handling, which are of great significance in process safety analysis. Bayesian network (BN) is an alternative technique with ample potential for application in safety analysis. BNs have a strong similarity to FTs in many respects; however, the distinct advantages making them more suitable than FTs are their ability in explicitly representing the dependencies of events, updating probabilities, and coping with uncertainties. The objective of this paper is to demonstrate the application of BNs in safety analysis of process systems. The first part of the paper shows those modeling aspects that are common between FT and BN, giving preference to BN due to its ability to update probabilities. The second part is devoted to various modeling features of BN, helping to incorporate multi-state variables, dependent failures, functional uncertainty, and expert opinion which are frequently encountered in safety analysis, but cannot be considered by FT. The paper concludes that BN is a superior technique in safety analysis because of its flexible structure, allowing it to fit a wide variety of accident scenarios.     

Lifecycle risk assessment of a technological system using dynamic Bayesian networks

Investigations of technological systems accidents reveal that technical, human, organizational, as well as environmental factors influence the occurrence of accidents. Despite these facts, most traditional risk assessment techniques focus on technical aspects of systems and have some limitations of incorporating efficient links between risk models and human and organizational factors. This paper presents a method for risk analysis of technological systems. Application of the presented framework makes it possible to analyze the influence of technical, human, organizational, and environmental risk factors on system safety. It encompasses system lifecycle from design to operational phase to give a comprehensive picture of system risks. The developed framework comprises the following main steps: (1) development of a conceptual risk analysis framework, (2) identifying risk influencing factors in different levels of technical, human, organizational, and environmental factors providing the possibility of analyzing interactions in a multi‐level system, (3) modeling system risk using dynamic Bayesian network (DBN), (4) assignment of probabilities and risk quantification in node probability tables (NPTs) based on industry records and experts extracted knowledge, (5) implementation of the model for wind turbines risk analysis combining use of V‐model, risk factors, and DBN in order to analyze the risk, and (6) analyzing different scenarios and the interactions in different levels. Finally, the various steps of the framework, the research objective fulfillment, and case study results are presented and discussed.     

Monitoring of Proportional‐Integral Controlled Processes using a Bayesian Time Series Analysis Method

Recently, there has been interest in applying statistical process monitoring methods to processes controlled with feedback controllers in order to eliminate assignable causes and achieve reduced overall variability. In this paper, we propose a Bayesian change‐point method to monitor processes regulated with proportional‐integral controllers. The approach is based on fitting an exponential rise model to the control input actions in response to a step shift and employs a change‐point method to detect the change. Simulation studies show that the proposed method has better run‐length performance in detecting step shifts in controlled processes than Shewhart chart on individuals and special‐cause chart on residuals of time series model. Copyright © 2013 John Wiley & Sons, Ltd.     

Novel Bayesian CUSUM and EWMA control charts via various loss functions for monitoring processes

In this work, both the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been reconfigured to monitor processes using a Bayesian approach. Our construction of these charts are informed by posterior and posterior predictive distributions found using three loss functions: the squared error, precautionary, and linex. We use these control charts on count data, performing a simulation study to assess chart performance. Our simulations consist of sensitivity analysis of the out-of-control shift size and choice of hyper-parameters of the given distributions. Practical use of theses charts are evaluated on real data.     

Modeling of latent structure of indomethacin solid dispersion tablet using Bayesian networks

Background: When designing pharmaceutical products, the relationships between causal factors and pharmaceutical responses are intricate. A Bayesian network (BN) was used to clarify the latent structure underlying the causal factors and pharmaceutical responses of a tablet containing solid dispersion (SD) of indomethacin (IMC).

Method: IMC, a poorly water-soluble drug, was tested with polyvinylpyrrolidone as the carrier polymer. Tablets containing a SD or a physical mixture of IMC, different quantities of magnesium stearate, microcrystalline cellulose, and low-substituted hydroxypropyl cellulose, and subjected to different compression force were selected as the causal factors. The pharmaceutical responses were the dissolution properties and tensile strength before and after the accelerated test and a similarity factor, which was used as an index of the storage stability.

Result: BN models were constructed based on three measurement criteria for the appropriateness of the graph structure. Of these, the BN model based on Akaike’s information criterion was similar to the results for the analysis of variance. To quantitatively estimate the causal relationships underlying the latent structure in this system, conditional probability distributions were inferred from the BN model. The responses were accurately predicted using the BN model, as reflected in the high correlation coefficients in a leave-one-out cross-validation procedure.

Conclusion: The BN technique provides a better understanding of the latent structure underlying causal factors and responses.     

Bayesian networks for maritime traffic accident prevention: Benefits and challenges

Bayesian networks are quantitative modeling tools whose applications to the maritime traffic safety context are becoming more popular. This paper discusses the utilization of Bayesian networks in maritime safety modeling. Based on literature and the author's own experiences, the paper studies what Bayesian networks can offer to maritime accident prevention and safety modeling and discusses a few challenges in their application to this context. It is argued that the capability of representing rather complex, not necessarily causal but uncertain relationships makes Bayesian networks an attractive modeling tool for the maritime safety and accidents. Furthermore, as the maritime accident and safety data is still rather scarce and has some quality problems, the possibility to combine data with expert knowledge and the easy way of updating the model after acquiring more evidence further enhance their feasibility. However, eliciting the probabilities from the maritime experts might be challenging and the model validation can be tricky. It is concluded that with the utilization of several data sources, Bayesian updating, dynamic modeling, and hidden nodes for latent variables, Bayesian networks are rather well-suited tools for the maritime safety management and decision-making.     

A Bayesian procedure for process capability assessment

The usual practice of judging process capability by evaluating point estimates of some process capability indices has a flaw that there is no assessment on the error distributions of these estimates. However, the distributions of these estimates are usually so complicated that it is very difficult to obtain good interval estimates. In this paper we adopt a Bayesian approach to obtain an interval estimation, particularly for the index C_pm. The posterior probability p that the process under investigation is capable is derived; then the credible interval, a Bayesian analogue of the classical confidence interval, can be obtained. We claim that the process is capable if all the points in the credible interval are greater than the pre‐specified capability level ω, say 1.33. To make this Bayesian procedure very easy for practitioners to implement on manufacturing floors, we tabulate the minimum values of Ĉ_pm/ω, for which the posterior probability p reaches the desirable level, say 95%. For the special cases where the process mean equals the target value for C_pm and equals the midpoint of the two specification limits for C_pk, the procedure is even simpler; only chi‐square tables are needed. Copyright © 1999 John Wiley & Sons, Ltd.     

An adaptive EWMA control chart for monitoring the process mean in Bayesian theory under different loss functions

The Shewhart control chart is used for detecting the large shift and an exponentially weighted moving average (EWMA) control chart is used for detecting the small/moderate shift in the process mean. A scheme that combines both the Shewhart control chart and the EWMA control chart in a smooth way is called the adaptive EWMA (AEWMA) control chart. In this paper, we proposed a new AEWMA control chart for monitoring the process mean in Bayesian theory under different loss functions (LFs). We used informative (conjugate prior) under two different LFs: (1) squared error loss function and (2) linex loss function for posterior and posterior predictive distributions. We used the average run length and standard deviation of run length to measure the performance of the AEWMA control chart in the Bayesian theory. A comparative study is conducted for comparing the proposed AEWMA control chart in Bayesian theory with the existing Bayesian EWMA control chart. We conducted a Monte Carlo simulation study to evaluate the proposed AEWMA control chart. For the implementation purposes, we presented a real-data example.     

Bayesian inference for parameters estimation using experimental data

A finite element (FE) model is developed for a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy) which accounts for uncertainties in geometry, material properties, and boundary conditions as well as limited knowledge on the behavior of connections and other components. Ambient vibration tests (AVTs) are carried out to identify the main dynamic parameters which are used for model updating in the Bayesian framework. Sensitivity analysis is performed to identify the main mechanical parameters affecting natural frequencies and mode shapes to be used as updating parameters. Finally, the posterior probability distributions of the selected updating parameters is estimated and used to assess the accuracy of the FE-based model. The importance of using a proper informative reference data set in the updating framework is assessed using different observations together with the importance of reliable surrogate models able to reduce the computational costs related to the whole framework.     

A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets

We consider change‐point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet‐based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise‐contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning‐free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.     

Deriving control parameter settings from process models to control capsule fillers integrated into continuous manufacturing

The aim of this work was to investigate the mean fill weight control of a continuous capsule-filling process, whether it is possible to derive controller settings from an appendant process model. To that end, a system composed out of fully automated capsule filler and an online gravimetric scale was used to control the filled weight. This setup allows to examine challenges associated with continuous manufacturing processes, such as variations in the amount of active pharmaceutical ingredient (API) in the mixture due to fluctuations of the feeders or due to altered excipient batch qualities. Two types of controllers were investigated: a feedback control and a combination of feedback and feedforward control. Although both of those are common in the industry, determining the optimal parameter settings remains an issue. In this study, we developed a method to derive the control parameters based on process models in order to obtain optimal control for each filled product. Determined via rapid automated process development (RAPD), this method is an effective and fast way of determining control parameters. The method allowed us to optimize the weight control for three pharmaceutical excipients. By conducting experiments, we verified the feasibility of the proposed method and studied the dynamics of the controlled system. Our work provides important basic data on how capsule filler can be implemented into continuous manufacturing systems.     

A generic method for estimating system reliability using Bayesian networks

This study presents a holistic method for constructing a Bayesian network (BN) model for estimating system reliability. BN is a probabilistic approach that is used to model and predict the behavior of a system based on observed stochastic events. The BN model is a directed acyclic graph (DAG) where the nodes represent system components and arcs represent relationships among them. Although recent studies on using BN for estimating system reliability have been proposed, they are based on the assumption that a pre-built BN has been designed to represent the system. In these studies, the task of building the BN is typically left to a group of specialists who are BN and domain experts. The BN experts should learn about the domain before building the BN, which is generally very time consuming and may lead to incorrect deductions. As there are no existing studies to eliminate the need for a human expert in the process of system reliability estimation, this paper introduces a method that uses historical data about the system to be modeled as a BN and provides efficient techniques for automated construction of the BN model, and hence estimation of the system reliability. In this respect K2, a data mining algorithm, is used for finding associations between system components, and thus building the BN model. This algorithm uses a heuristic to provide efficient and accurate results while searching for associations. Moreover, no human intervention is necessary during the process of BN construction and reliability estimation. The paper provides a step-by-step illustration of the method and evaluation of the approach with literature case examples.