Anomalies in Bayesian launch range safety analysis

Philipson, Lloyd L.

doi:10.1016/0951-8320(95)00066-b

Cited by 9 publications

(3 citation statements)

References 1 publication

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“…Azaiez and Bier, 6 showed that the conditions to attain perfect aggregation in general independent systems are still notably exacting and thus, a way to quantify the error magnitude is desired when the perfect aggregation is absent. Philipson,7,8 attempted to find the source of the Bayesian aggregation error and drew an extreme conclusion that such error was due to a fundamental logical problem in Bayesian procedure. Such claim has motivated other studies 9,10 to also find the source of the Bayesian aggregation error and prove that this error is a natural consequence when the information at the component level is ignored.…”

Section: Introductionmentioning

confidence: 99%

Copula‐based Bayesian reliability assessment for series systems

Octavina,

Lin,

Yeh

2024

Quality & Reliability Eng

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Bayesian reliability assessment plays an integral role in determining the success of product development and deployment into the market, especially when limited information is available to estimate the reliability of products. Nevertheless, the Bayesian reliability approach has untapped research potential when it is used to evaluate systems consisting of dependent components, that is, a situation that reflects real‐world conditions. This study addresses the research gap by applying a copula to encode the dependency structure between the failure rates of the components, particularly for the simple series systems. Unfortunately, this study found that Bayesian aggregation error still occurs when information is used at different levels. By employing Monte Carlo simulation and classification tree learning, this study also investigates the key factors affecting such error over a wide range of possible scenarios and derives useful guidelines for reliability practitioners so that they can choose a more suitable analysis under certain circumstances.

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Section: Introductionmentioning

confidence: 99%

Copula‐based Bayesian reliability assessment for series systems

Octavina,

Lin,

Yeh

2024

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…While most of the early research focused on finding the conditions under which perfect aggregation can be obtained, especially in cases where failures of components are independent to each other [8,12], recent studies tried to identify the sources of the aggregation error [13][14][15] (in similar independent cases). Philipson [16,17] used a different term "Bayesian anomaly" for the similar phenomenon (i.e., aggregation error) discussed in other papers, but took a more extreme view to argue that the aggregation error is a fundamental problem in a Bayesian reliability analysis and even suggested a basic restructuring of the Bayes procedure [18]. However, other researchers [13][14][15] disagreed with such argument and suggested that the aggregation error should not be construed as the evidence of inadequacy of Bayesian methods.…”

Section: Introductionmentioning

confidence: 99%

Copula-Based Bayesian Reliability Analysis of a Product of a Probability and a Frequency Model for Parallel Systems When Components Are Dependent

2021

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While the dependence assumption among the components is naturally important in evaluating the reliability of a system, studies investigating the issues of aggregation errors in Bayesian reliability analyses have been focused mainly on systems with independent components. This study developed a copula-based Bayesian reliability model to formulate dependency between components of a parallel system and to estimate the failure rate of the system. In particular, we integrated Monte Carlo simulation and classification tree learning to identify key factors that affect the magnitude of errors in the estimation of posterior means of system reliability (for different Bayesian analysis approaches—aggregate analysis, disaggregate analysis, and simplified disaggregate analysis) to provide important guidelines for choosing the most appropriate approach for analyzing a model of products of a probability and a frequency for parallel systems with dependent components.

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“…Failed to recognize or address such dependency embedded in data sets will lead to conflicting results 33,34 . The term “Bayesian anomaly” is first proposed by Philipson 35,36 as a special case of the general aggregation errors 37,38 . This concept stems from the reliability community and is then extended to describe the discrepancy between estimated values of using system‐level information and that of using component‐level information in different scenarios 28–31 .…”

Section: Introductionmentioning

confidence: 99%

On investigation of the Bayesian anomaly in multiple imprecise dependent information aggregation for system reliability evaluation

et al. 2021

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The increasing complexity of the modern engineering system has made the multisource information fusion a necessary yet challenging task. In the context of reliability engineering, the information fusion process is either ineffective or less efficient as the aggregation error increases with respect to the collection of multiple dependent pieces of evidence. To address this challenge, this paper proposes a comprehensive Bayesian approach for system reliability evaluation that considers multiple, dependent sources of information. We show that the so‐called “Bayesian anomaly,” a type of aggregation error, is caused by misuse of the dependent information and could be eliminated if all available information is properly addressed. A topological technique is employed as a tool for information fusion in the likelihood construction. A likelihood‐based approach is then developed to formulate the overall likelihood as well as the reliability model. These two techniques are embedded into a comprehensive Bayesian framework to allow for an efficient evaluation of the system reliability. Our approach has also been extended to include imprecise information, such as interval and/or censored data, which is more frequently encountered in practical engineering. We demonstrate the proposed method through several numerical cases and one real‐life application example. This study provides a better understanding of the role of dependent information in system reliability evaluation. In addition, it presents an efficient pathway to extract the inherent dependency information embedded in imperfect data sets.

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Anomalies in Bayesian launch range safety analysis

Cited by 9 publications

References 1 publication

Copula‐based Bayesian reliability assessment for series systems

Copula‐based Bayesian reliability assessment for series systems

Copula-Based Bayesian Reliability Analysis of a Product of a Probability and a Frequency Model for Parallel Systems When Components Are Dependent

On investigation of the Bayesian anomaly in multiple imprecise dependent information aggregation for system reliability evaluation

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