scholarly journals Parameter Estimation of a Multistate Model for an Aging Piece of Equipment under Condition-Based Maintenance

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Qihong Duan ◽  
Xiang Chen ◽  
Dengfu Zhao ◽  
Zheng Zhao
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Model Calculation ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Condition Based Maintenance ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Simulation Studies ◽  
Multistate Model

We study a multistate model for an aging piece of equipment under condition-based maintenance and apply an expectation maximization algorithm to obtain maximum likelihood estimates of the model parameters. Because of the monitoring discontinuity, we cannot observe any state's duration. The observation consists of the equipment's state at an inspection or right after a repair. Based on a proper construction of stochastic processes involved in the model, calculation of some probabilities and expectations becomes tractable. Using these probabilities and expectations, we can apply an expectation maximization algorithm to estimate the parameters in the model. We carry out simulation studies to test the accuracy and the efficiency of the algorithm.

Parameter Estimation for α-GMM Based on Maximum Likelihood Criterion

2009 ◽  
Vol 21 (6) ◽  
pp. 1776-1795 ◽  
Author(s):  
Dalei Wu
Keyword(s):  
Parameter Estimation ◽  
Computational Complexity ◽  
Maximum Likelihood ◽  
Expectation Maximization ◽  
Speaker Recognition ◽  
Expectation Maximization Algorithm ◽  
Training Data ◽  
Model Parameters ◽  
Maximum Likelihood Criterion ◽  
Method Model

α-integration and α-GMM have been recently proposed for integrated stochastic modeling. However, there has not been an approach to date for estimating model parameters for α-GMM in a statistical way, based on a set of training data. In this letter, parameter updating formulas are mathematically derived based on maximum likelihood criterion using an adapted expectation-maximization algorithm. With this method, model parameters for α-GMM are reestimated in an iterative way. The updating formulas were found to be simple and systematically compatible with the GMM equations. This advantage renders the α-GMM a superset of the GMM but with similar computational complexity. This method has been effectively applied to realistic speaker recognition applications.

scholarly journals Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3032
Author(s):  
Man-Ho Ling ◽  
Narayanaswamy Balakrishnan ◽  
Chenxi Yu ◽  
Hon Yiu So
Keyword(s):  
Maximum Likelihood ◽  
Failure Modes ◽  
Expectation Maximization Algorithm ◽  
Simulated Data ◽  
Operating Conditions ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Lifetime Distributions ◽  
Gamma Frailty

A device that performs its intended function only once is referred to as a one-shot device. Actual lifetimes of such kind of devices under test cannot be observed, and they are either left-censored or right-censored. In addition, one-shot devices often consist of multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. In this paper, we develop an efficient expectation–maximization algorithm for determining the maximum likelihood estimates of model parameters, on the basis of one-shot device test data with multiple failure modes under a constant-stress accelerated life-test, with the dependent components having exponential lifetime distributions under gamma frailty that facilitates an easily understandable interpretation. The maximum likelihood estimate and confidence intervals for the mean lifetime of k-out-of-M structured one-shot device under normal operating conditions are also discussed. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations. Three examples including Class-H failure modes data, mice data from ED01 experiment, and simulated data with four failure modes are used to illustrate the proposed inferential methods.

scholarly journals A comparison of optimization solvers for log binomial regression including conic programming

2021 ◽  
Author(s):  
Florian Schwendinger ◽  
Bettina Grün ◽  
Kurt Hornik
Keyword(s):  
Maximum Likelihood ◽  
Augmented Lagrangian Method ◽  
Expectation Maximization Algorithm ◽  
Epidemiological Studies ◽  
Maximum Likelihood Estimates ◽  
Regression Coefficients ◽  
Simulation Studies ◽  
Relative Risks ◽  
Binomial Regression ◽  
Optimization Solvers

AbstractRelative risks are estimated to assess associations and effects due to their ease of interpretability, e.g., in epidemiological studies. Fitting log-binomial regression models allows to use the estimated regression coefficients to directly infer the relative risks. The estimation of these models, however, is complicated because of the constraints which have to be imposed on the parameter space. In this paper we systematically compare different optimization algorithms to obtain the maximum likelihood estimates for the regression coefficients in log-binomial regression. We first establish under which conditions the maximum likelihood estimates are guaranteed to be finite and unique, which allows to identify and exclude problematic cases. In simulation studies using artificial data we compare the performance of different optimizers including solvers based on the augmented Lagrangian method, interior-point methods including a conic optimizer, majorize-minimize algorithms, iteratively reweighted least squares and expectation-maximization algorithm variants. We demonstrate that conic optimizers emerge as the preferred choice due to their reliability, lack of requirement to tune hyperparameters and speed.

A new survival model with surviving fraction: An application to colorectal cancer data

2018 ◽  
Vol 28 (9) ◽  
pp. 2665-2680
Author(s):  
Gladys DC Barriga ◽  
Vicente G Cancho ◽  
Daniel V Garibay ◽  
Gauss M Cordeiro ◽  
Edwin MM Ortega
Keyword(s):  
Colorectal Cancer ◽  
Maximum Likelihood ◽  
Expectation Maximization Algorithm ◽  
Survival Model ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Ratio Test ◽  
Data Set ◽  
Cancer Data ◽  
Proposed Model

We propose a new survival model for lifetime data in the presence of surviving fraction and obtain some of its properties. Its genesis is based on extensions of the promotion time cure model, where an extra parameter controls the heterogeneity or dependence of an unobserved number of lifetimes. We construct a regression model to evaluate the effects of covariates in the cured fraction. We discuss inference aspects for the proposed model in a classical approach, where some maximum likelihood tools are explored. Further, an expectation maximization algorithm is developed to calculate the maximum likelihood estimates of the model parameters. We also perform an empirical study of the likelihood ratio test in order to compare the promotion time cure and the proposed models. We illustrate the usefulness of the new model by means of a colorectal cancer data set.

scholarly journals Uniqueness of Maximum Likelihood Estimators for a Backup System in a Condition-Based Maintenance

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Qihong Duan ◽  
Ying Wei ◽  
Xiang Chen
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Maximum Likelihood Estimators ◽  
Condition Based Maintenance ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Process Data ◽  
Parameter Estimation Problem ◽  
Backup System ◽  
The Em Algorithm

A parameter estimation problem for a backup system in a condition-based maintenance is considered. We model a backup system by a hidden, three-state continuous time Markov process. Data are obtained through condition monitoring at discrete time points. Maximum likelihood estimates of the model parameters are obtained using the EM algorithm. We establish conditions under which there is no more than one limitation in the parameter space for any sequence derived by the EM algorithm.

scholarly journals A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

2019 ◽  
pp. 731-744 ◽  
Author(s):  
Zubair Ahmad Ahmad ◽  
Eisa Mahmoudi Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Financial Risk ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Set ◽  
Loss Model ◽  
New Class ◽  
Proposed Model ◽  
Loss Distributions ◽  
Loss Data

Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

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