scholarly journals Estimation of Failure Probability and Its Applications in Lifetime Data Analysis

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Ming Han
Keyword(s):  
Bayesian Estimation ◽  
Failure Probability ◽  
Estimation Method ◽  
Computing Methods ◽  
Lifetime Data ◽  
Hierarchical Bayesian ◽  
Lifetime Data Analysis ◽  
Hierarchical Bayesian Methods ◽  
Hierarchical Bayesian Method ◽  
Definition Of

Since Lindley and Smith introduced the idea of hierarchical prior distribution, some results have been obtained on hierarchical Bayesian method to deal with lifetime data. But all those results obtained by means of hierarchical Bayesian methods involve complicated integration compute. Though some computing methods such as Markov Chain Monte Carlo (MCMC) are available, doing integration is still very inconvenient for practical problems. This paper introduces a new method, named E-Bayesian estimation method, to estimate failure probability. In the case of one hyperparameter, the definition of E-Bayesian estimation of the failure probability is provided; moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation and the property of E-Bayesian estimation of the failure probability are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.

E-Bayesian Estimation Method and its Applications in Reliability Engineering

2011 ◽  
Vol 199-200 ◽  
pp. 308-312
Author(s):  
Ming Han
Keyword(s):  
Bayesian Estimation ◽  
Failure Probability ◽  
Evaluation Method ◽  
Science And Technology ◽  
Estimation Method ◽  
New Method ◽  
Hierarchical Bayesian ◽  
Reliability Engineering ◽  
Hierarchical Bayesian Estimation ◽  
Definition Of

Evaluation method of reliability of industrial products needs to be improved effectively with the advance of science and technology. This paper introduces a new method, named E-Bayesian estimation method, to estimate failure probability in reliability engineering. The definition of E-Bayesian estimation of the failure probability is provided, moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation of the failure probability were provided, and properties of the E-Bayesian estimation, i.e. relations between E-Bayesian estimation and hierarchical Bayesian estimation, are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.

Estimation of Failure Probability for Bearing and its Applications in the Case of Zero-Failure Data

2014 ◽  
Vol 915-916 ◽  
pp. 318-322 ◽  
Author(s):  
Ming Han
Keyword(s):  
Bayesian Estimation ◽  
Failure Probability ◽  
Estimation Method ◽  
Engineering Application ◽  
New Method ◽  
Hierarchical Bayesian ◽  
Failure Data ◽  
Hierarchical Bayesian Estimation ◽  
Definition Of

This paper introduces a new method, named E-Bayesian estimation method, to estimate failure probability. In the case of zero-failure data, the definition of E-Bayesian estimation of failure probability is provided; moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation and the property of E-Bayesian estimation of the failure probability are also provided. For the estimate failure probability, in the following sections we will see simple the E-Bayesian estimation method is method than hierarchical Bayesian estimation method. Finally, the calculated results of bearing show that the proposed method is feasible and convenient in engineering application.

Estimation of Failure Probability and its Applications in Reliability Data Analysis

2010 ◽  
Vol 118-120 ◽  
pp. 601-605
Author(s):  
Han Ming
Keyword(s):  
Parameter Estimation ◽  
Data Analysis ◽  
Bayesian Estimation ◽  
Failure Probability ◽  
Evaluation Method ◽  
Estimation Method ◽  
New Method ◽  
Reliability Parameter ◽  
Hierarchical Bayesian Estimation ◽  
Definition Of

Evaluation method of reliability parameter estimation needs to be improved effectively with the advance of science and technology. This paper develops a new method of parameter estimation, which is named E-Bayesian estimation method. In the case one hyper-parameter, the definition of E-Bayesian estimation of the failure probability is provided, moreover, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation, and the property of E-Bayesian estimation of the failure probability are also provided. Finally, calculation on practical problems shows that the provided method is feasible and easy to perform.

Estimation of Failure Rate and its Applications in the Case of Zero-Failure Data

2014 ◽  
Vol 945-949 ◽  
pp. 1046-1049
Author(s):  
Ming Han
Keyword(s):  
Bayesian Estimation ◽  
Failure Rate ◽  
Estimation Method ◽  
New Method ◽  
Hierarchical Bayesian ◽  
Failure Data ◽  
Hierarchical Bayesian Estimation ◽  
Definition Of

This paper introduces a new method, named E-Bayesian estimation method, to estimate failure rate in zero-failure data. The definition of E-Bayesian estimation of the failure rate is given, based on the definition, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation of the failure rate were provided, and properties of the E-Bayesian estimation, i. e. relations between E-Bayesian estimation and hierarchical Bayesian estimation, was discussed. Calculations were performed on practical problems, showing that the proposed new method is feasible and easy to operate.

Estimation of Failure Rate and its Applications

2013 ◽  
Vol 756-759 ◽  
pp. 3149-3152
Author(s):  
Ming Han
Keyword(s):  
Parameter Estimation ◽  
Bayesian Estimation ◽  
Failure Rate ◽  
Estimation Method ◽  
Hierarchical Bayesian ◽  
Parameter Estimation Method ◽  
Hierarchical Bayesian Estimation

This paper introduces a new parameter estimation method, E-Bayesian estimation method, to estimate failure rate. The definition, properties, E-Bayesian estimation and hierarchical Bayesian estimation of failure rate are given. A example is also discussed. Through the example the efficiency and easiness of operation of this method are commended.

scholarly journals Characterization of uncertainties in atmospheric trace gas inversions using hierarchical Bayesian methods

2014 ◽  
Vol 14 (8) ◽  
pp. 3855-3864 ◽  
Author(s):  
A. L. Ganesan ◽  
M. Rigby ◽  
A. Zammit-Mangion ◽  
A. J. Manning ◽  
R. G. Prinn ◽  
...  
Keyword(s):  
Sulfur Hexafluoride ◽  
A Priori ◽  
Trace Gas ◽  
Hierarchical Bayesian ◽  
Hierarchical Method ◽  
Measurement Uncertainties ◽  
Hierarchical Bayesian Methods ◽  
Hierarchical Bayesian Method ◽  
Atmospheric Trace Gas ◽  
Model Measurement

Abstract. We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDFs) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more complete estimation of emissions and their uncertainties than traditional Bayesian inversions, which rely heavily on expert judgment. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties than traditional methods.

scholarly journals Characterization of uncertainties in atmospheric trace gas inversions using hierarchical Bayesian methods

2013 ◽  
Vol 13 (12) ◽  
pp. 33403-33431
Author(s):  
A. L. Ganesan ◽  
M. Rigby ◽  
A. Zammit-Mangion ◽  
A. J. Manning ◽  
R. G. Prinn ◽  
...  
Keyword(s):  
Sulfur Hexafluoride ◽  
A Priori ◽  
Trace Gas ◽  
Hierarchical Bayesian ◽  
Hierarchical Method ◽  
Measurement Uncertainties ◽  
Hierarchical Bayesian Methods ◽  
Hierarchical Bayesian Method ◽  
Atmospheric Trace Gas ◽  
Model Measurement

Abstract. We present a hierarchical Bayesian method for atmospheric trace gas inversions. This method is used to estimate emissions of trace gases as well as "hyper-parameters" that characterize the probability density functions (PDF) of the a priori emissions and model-measurement covariances. By exploring the space of "uncertainties in uncertainties", we show that the hierarchical method results in a more complete estimation of emissions and their uncertainties than traditional Bayesian inversions, which rely heavily on expert judgement. We present an analysis that shows the effect of including hyper-parameters, which are themselves informed by the data, and show that this method can serve to reduce the effect of errors in assumptions made about the a priori emissions and model-measurement uncertainties. We then apply this method to the estimation of sulfur hexafluoride (SF6) emissions over 2012 for the regions surrounding four Advanced Global Atmospheric Gases Experiment (AGAGE) stations. We find that improper accounting of model representation uncertainties, in particular, can lead to the derivation of emissions and associated uncertainties that are unrealistic and show that those derived using the hierarchical method are likely to be more representative of the true uncertainties in the system. We demonstrate through this SF6 case study that this method is less sensitive to outliers in the data and to subjective assumptions about a priori emissions and model-measurement uncertainties, than traditional methods.

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