A new extended exponential lifetime model called Harris extended-exponential(HEE)distribution for data modelling with increasing and decreasing hazard rate shapes has been considered.In the reliability context,researc...A new extended exponential lifetime model called Harris extended-exponential(HEE)distribution for data modelling with increasing and decreasing hazard rate shapes has been considered.In the reliability context,researchers prefer to use censoring plans to collect data in order to achieve a compromise between total test time and/or test sample size.So,this study considers both maximum likelihood and Bayesian estimates of the Harris extended-exponential distribution parameters and some of its reliability indices using a progressive Type-II censoring strategy.Under the premise of independent gamma priors,the Bayesian estimation is created using the squared-error and general entropy loss functions.Due to the challenging form of the joint posterior distribution,to evaluate the Bayes estimates,samples from the full conditional distributions are generated using Markov Chain Monte Carlo techniques.For each unknown parameter,the highest posterior density credible intervals and asymptotic confidence intervals are also determined.Through a simulated study,the usefulness of the various suggested strategies is assessed.The optimal progressive censoring plans are also shown,and various optimality criteria are investigated.Two actual data sets,taken from engineering and veterinary medicine areas,are analyzed to show how the offered point and interval estimators can be used in practice and to verify that the proposed model furnishes a good fit than other lifetimemodels:alpha power exponential,generalized-exponential,Nadarajah-Haghighi,Weibull,Lomax,gamma and exponential distributions.Numerical evaluations revealed that in the presence of progressively Type-II censored data,the Bayes estimation method against the squared-error(symmetric)loss is advised for getting the point and interval estimates of the HEE distribution.展开更多
An inverse problemin practical scientific investigations is the process of computing unknown parameters from a set of observations where the observations are only recorded indirectly,such as monitoring and controlling...An inverse problemin practical scientific investigations is the process of computing unknown parameters from a set of observations where the observations are only recorded indirectly,such as monitoring and controlling quality in industrial process control.Linear regression can be thought of as linear inverse problems.In other words,the procedure of unknown estimation parameters can be expressed as an inverse problem.However,maximum likelihood provides an unstable solution,and the problembecomes more complicated if unknown parameters are estimated from different samples.Hence,researchers search for better estimates.We study two joint censoring schemes for lifetime products in industrial process monitoring.In practice,this type of data can be collected in fields such as the medical industry and industrial engineering.In this study,statistical inference for the Chen lifetime products is considered and analyzed to estimate underlying parameters.Maximum likelihood and Bayes’rule are both studied for model parameters.The asymptotic distribution of maximumlikelihood estimators and the empirical distributions obtained withMarkov chainMonte Carlo algorithms are utilized to build the interval estimators.Theoretical results using tables and figures are adopted through simulation studies and verified in an analysis of the lifetime data.We briefly describe the performance of developed methods.展开更多
The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerate...The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.展开更多
A novel extended Lindley lifetime model that exhibits unimodal or decreasing density shapes as well as increasing,bathtub or unimodal-then-bathtub failure rates, named the Marshall-Olkin-Lindley (MOL) model is studied...A novel extended Lindley lifetime model that exhibits unimodal or decreasing density shapes as well as increasing,bathtub or unimodal-then-bathtub failure rates, named the Marshall-Olkin-Lindley (MOL) model is studied.In this research, using a progressive Type-II censored, various inferences of the MOL model parameters oflife are introduced. Utilizing the maximum likelihood method as a classical approach, the estimators of themodel parameters and various reliability measures are investigated. Against both symmetric and asymmetric lossfunctions, the Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) technique with theassumption of independent gamma priors. From the Fisher information data and the simulatedMarkovian chains,the approximate asymptotic interval and the highest posterior density interval, respectively, of each unknownparameter are calculated. Via an extensive simulated study, the usefulness of the various suggested strategies isassessedwith respect to some evaluationmetrics such as mean squared errors, mean relative absolute biases, averageconfidence lengths, and coverage percentages. Comparing the Bayesian estimations based on the asymmetric lossfunction to the traditional technique or the symmetric loss function-based Bayesian estimations, the analysisdemonstrates that asymmetric loss function-based Bayesian estimations are preferred. Finally, two data sets,representing vinyl chloride and repairable mechanical equipment items, have been investigated to support theapproaches proposed and show the superiority of the proposed model compared to the other fourteen lifetimemodels.展开更多
This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation ...This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.展开更多
In this paper, based on a new type of censoring scheme called an adaptive type-II progressive censoring scheme introduce by Ng et al. [1], Naval Research Logistics is considered. Based on this type of censoring the ma...In this paper, based on a new type of censoring scheme called an adaptive type-II progressive censoring scheme introduce by Ng et al. [1], Naval Research Logistics is considered. Based on this type of censoring the maximum likelihood estimation (MLE), Bayes estimation, and parametric bootstrap method are used for estimating the unknown parameters. Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Point estimation and confidence intervals based on maximum likelihood and bootstrap method are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators. Numerical examples using real data set are presented to illustrate the methods of inference developed here. Finally, the maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo simulation study.展开更多
The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu...The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.展开更多
Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes,...Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.展开更多
This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units re...This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.展开更多
This paper considers the Bayesian and expected Bayesian(E-Bayesian) estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censori...This paper considers the Bayesian and expected Bayesian(E-Bayesian) estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme(PHCS). The estimations are obtained based on Gamma conjugate prior for the parameter under squared error(SE) and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.展开更多
In this article, we study the problem of predicting future records and order statistics (two-sample prediction) based on progressive type-II censored with random removals, where the number of units removed at each fai...In this article, we study the problem of predicting future records and order statistics (two-sample prediction) based on progressive type-II censored with random removals, where the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval bounds prediction. Bayesian point prediction under symmetric and symmetric loss functions is discussed. The maximum likelihood (ML) prediction intervals using “plug-in” procedure for future records and order statistics are derived. An example is discussed to illustrate the application of the results under this censoring scheme.展开更多
In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate func...In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped.Some mathematical properties of the new distribution are derived including quantiles and moments.The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data.For this purpose,we consider two estimation methods,namely maximum likelihood and maximum product of spacing estimation methods.To compare the efficiency of the proposed estimators,a simulation study is carried out.To show the applicability of the new model as well as the estimation methods,one real data for failure times of software is analyzed.Based on the empirical parts,we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.展开更多
Currently, progressive censoring is intensively investigated by several researchers due to its ability to remove subjects from the experiment before the final termination point, thus saving time and cost. The closed f...Currently, progressive censoring is intensively investigated by several researchers due to its ability to remove subjects from the experiment before the final termination point, thus saving time and cost. The closed form of marginal density of failure times under progressive type II censoring is essential to study the properties of statistical analysis under different censoring schemes. In this paper, we provide a different presentation of the marginal distribution under progressive type-II censoring and we derive closed forms for different special cases. In order to study the similarity/dissimilarity of marginal densities of order statistics for failure times, the overlap measure is used. We discovered that the overlap measure depends only on the effective size m. A numerical example based on a real life data regarding failure times of aircrafts' windshields is provided to quantify the amount of redundant information provided by the order statistics of the failure times under different progressive type-II schemes based on the overlap measure. Moreover, this data set is used as a pilot study to estimate the effective size m needed for future studies.展开更多
The paper deals with the estimation problem for the generalized Pareto distribution based on progressive type-II censoring with random removals. The number of components removed at each failure time is assumed to foll...The paper deals with the estimation problem for the generalized Pareto distribution based on progressive type-II censoring with random removals. The number of components removed at each failure time is assumed to follow a binomial distribution. Maximum likelihood estimators and the asymptotic variance-covariance matrix of the estimates are obtained. Finally, a numerical example is given to illustrate the obtained展开更多
In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum like...In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum likelihood and the least squares method estimators for the unknown parameters of the inverse Weibull distribution are derived. A comparison between these estimators is provided by using extensive simulation and two criteria, namely, absolute bias and mean squared error. It is concluded that the estimators based on the least squares method are superior compared to the maximum likelihood and the approximate maximum likelihood estimators. Real life data example is provided to illustrate our proposed estimators.展开更多
This paper deals with the Bayesian inferences of unknown parameters of the progressively Type II censored Weibull-geometric (WG) distribution. The Bayes estimators cannot be obtained in explicit forms of the unknown p...This paper deals with the Bayesian inferences of unknown parameters of the progressively Type II censored Weibull-geometric (WG) distribution. The Bayes estimators cannot be obtained in explicit forms of the unknown parameters under a squared error loss function. The approximate Bayes estimators will be computed using the idea of Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions. Also the point estimation and confidence intervals based on maximum likelihood and bootstrap technique are also proposed. The approximate Bayes estimators will be obtained under the assumptions of informative and non-informative priors are compared with the maximum likelihood estimators. A numerical example is provided to illustrate the proposed estimation methods here. Maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo Simulation展开更多
Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model ...Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.展开更多
This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). ...This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.展开更多
This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss functi...This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss function. We propose to apply Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples, and they have in turn, been used to compute the Bayes estimates with the help of importance sampling technique. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider two sample Bayes prediction to predicting future order statistics and upper record values from Burr type XII distribution based on progressive first failure censored data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics and upper record values. A real life data set is used to illustrate the results derived.展开更多
基金This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project Number(PNURSP2023R175),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘A new extended exponential lifetime model called Harris extended-exponential(HEE)distribution for data modelling with increasing and decreasing hazard rate shapes has been considered.In the reliability context,researchers prefer to use censoring plans to collect data in order to achieve a compromise between total test time and/or test sample size.So,this study considers both maximum likelihood and Bayesian estimates of the Harris extended-exponential distribution parameters and some of its reliability indices using a progressive Type-II censoring strategy.Under the premise of independent gamma priors,the Bayesian estimation is created using the squared-error and general entropy loss functions.Due to the challenging form of the joint posterior distribution,to evaluate the Bayes estimates,samples from the full conditional distributions are generated using Markov Chain Monte Carlo techniques.For each unknown parameter,the highest posterior density credible intervals and asymptotic confidence intervals are also determined.Through a simulated study,the usefulness of the various suggested strategies is assessed.The optimal progressive censoring plans are also shown,and various optimality criteria are investigated.Two actual data sets,taken from engineering and veterinary medicine areas,are analyzed to show how the offered point and interval estimators can be used in practice and to verify that the proposed model furnishes a good fit than other lifetimemodels:alpha power exponential,generalized-exponential,Nadarajah-Haghighi,Weibull,Lomax,gamma and exponential distributions.Numerical evaluations revealed that in the presence of progressively Type-II censored data,the Bayes estimation method against the squared-error(symmetric)loss is advised for getting the point and interval estimates of the HEE distribution.
基金Let Pub(www.letpub.com)for its linguistic assistance during the preparation of this manuscript.This study was funded by Taif University Researchers Supporting Project number(TURSP-2020/279),Taif University,Taif,Saudi Arabia.
文摘An inverse problemin practical scientific investigations is the process of computing unknown parameters from a set of observations where the observations are only recorded indirectly,such as monitoring and controlling quality in industrial process control.Linear regression can be thought of as linear inverse problems.In other words,the procedure of unknown estimation parameters can be expressed as an inverse problem.However,maximum likelihood provides an unstable solution,and the problembecomes more complicated if unknown parameters are estimated from different samples.Hence,researchers search for better estimates.We study two joint censoring schemes for lifetime products in industrial process monitoring.In practice,this type of data can be collected in fields such as the medical industry and industrial engineering.In this study,statistical inference for the Chen lifetime products is considered and analyzed to estimate underlying parameters.Maximum likelihood and Bayes’rule are both studied for model parameters.The asymptotic distribution of maximumlikelihood estimators and the empirical distributions obtained withMarkov chainMonte Carlo algorithms are utilized to build the interval estimators.Theoretical results using tables and figures are adopted through simulation studies and verified in an analysis of the lifetime data.We briefly describe the performance of developed methods.
文摘The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.
文摘A novel extended Lindley lifetime model that exhibits unimodal or decreasing density shapes as well as increasing,bathtub or unimodal-then-bathtub failure rates, named the Marshall-Olkin-Lindley (MOL) model is studied.In this research, using a progressive Type-II censored, various inferences of the MOL model parameters oflife are introduced. Utilizing the maximum likelihood method as a classical approach, the estimators of themodel parameters and various reliability measures are investigated. Against both symmetric and asymmetric lossfunctions, the Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) technique with theassumption of independent gamma priors. From the Fisher information data and the simulatedMarkovian chains,the approximate asymptotic interval and the highest posterior density interval, respectively, of each unknownparameter are calculated. Via an extensive simulated study, the usefulness of the various suggested strategies isassessedwith respect to some evaluationmetrics such as mean squared errors, mean relative absolute biases, averageconfidence lengths, and coverage percentages. Comparing the Bayesian estimations based on the asymmetric lossfunction to the traditional technique or the symmetric loss function-based Bayesian estimations, the analysisdemonstrates that asymmetric loss function-based Bayesian estimations are preferred. Finally, two data sets,representing vinyl chloride and repairable mechanical equipment items, have been investigated to support theapproaches proposed and show the superiority of the proposed model compared to the other fourteen lifetimemodels.
基金This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(Grant Number IMSIU-RG23142).
文摘This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.
文摘In this paper, based on a new type of censoring scheme called an adaptive type-II progressive censoring scheme introduce by Ng et al. [1], Naval Research Logistics is considered. Based on this type of censoring the maximum likelihood estimation (MLE), Bayes estimation, and parametric bootstrap method are used for estimating the unknown parameters. Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Point estimation and confidence intervals based on maximum likelihood and bootstrap method are also proposed. The approximate Bayes estimators obtained under the assumptions of non-informative priors, are compared with the maximum likelihood estimators. Numerical examples using real data set are presented to illustrate the methods of inference developed here. Finally, the maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo simulation study.
基金supported by the National Natural Science Foundation of China(70471057)
文摘The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.
基金supported by the National Natural Science Foundation of China(11501433)the Fundamental Research Funds for the Central Universities(JB180711)
文摘Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.
基金supported by the National Statistical Science Research Project of China(2019LZ32)
文摘This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.
基金supported by the National Natural Science Foundation of China(7117116471401134+1 种基金71571144)the Natural Science Basic Research Program of Shaanxi Province(2015JM1003)
文摘This paper considers the Bayesian and expected Bayesian(E-Bayesian) estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme(PHCS). The estimations are obtained based on Gamma conjugate prior for the parameter under squared error(SE) and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.
文摘In this article, we study the problem of predicting future records and order statistics (two-sample prediction) based on progressive type-II censored with random removals, where the number of units removed at each failure time has a discrete binomial distribution. We use the Bayes procedure to derive both point and interval bounds prediction. Bayesian point prediction under symmetric and symmetric loss functions is discussed. The maximum likelihood (ML) prediction intervals using “plug-in” procedure for future records and order statistics are derived. An example is discussed to illustrate the application of the results under this censoring scheme.
基金the Deanship Scientific Research(DSR)King Abdulaziz University,Jeddah under Grant No.(G:337-130-1441).
文摘In this paper,we propose a new extension of the traditional Rayleigh distribution called the modified Kies Rayleigh distribution.The new distribution contains one scale and one shape parameter and its hazard rate function can be increasing and bathtub-shaped.Some mathematical properties of the new distribution are derived including quantiles and moments.The parameters of modified Kies Rayleigh distribution are estimated based on progressively Type-II censored data.For this purpose,we consider two estimation methods,namely maximum likelihood and maximum product of spacing estimation methods.To compare the efficiency of the proposed estimators,a simulation study is carried out.To show the applicability of the new model as well as the estimation methods,one real data for failure times of software is analyzed.Based on the empirical parts,we can conclude that the proposed model can be considered as a good model in the field of life testing and reliability analysis compared with other competing models.
文摘Currently, progressive censoring is intensively investigated by several researchers due to its ability to remove subjects from the experiment before the final termination point, thus saving time and cost. The closed form of marginal density of failure times under progressive type II censoring is essential to study the properties of statistical analysis under different censoring schemes. In this paper, we provide a different presentation of the marginal distribution under progressive type-II censoring and we derive closed forms for different special cases. In order to study the similarity/dissimilarity of marginal densities of order statistics for failure times, the overlap measure is used. We discovered that the overlap measure depends only on the effective size m. A numerical example based on a real life data regarding failure times of aircrafts' windshields is provided to quantify the amount of redundant information provided by the order statistics of the failure times under different progressive type-II schemes based on the overlap measure. Moreover, this data set is used as a pilot study to estimate the effective size m needed for future studies.
文摘The paper deals with the estimation problem for the generalized Pareto distribution based on progressive type-II censoring with random removals. The number of components removed at each failure time is assumed to follow a binomial distribution. Maximum likelihood estimators and the asymptotic variance-covariance matrix of the estimates are obtained. Finally, a numerical example is given to illustrate the obtained
文摘In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum likelihood and the least squares method estimators for the unknown parameters of the inverse Weibull distribution are derived. A comparison between these estimators is provided by using extensive simulation and two criteria, namely, absolute bias and mean squared error. It is concluded that the estimators based on the least squares method are superior compared to the maximum likelihood and the approximate maximum likelihood estimators. Real life data example is provided to illustrate our proposed estimators.
文摘This paper deals with the Bayesian inferences of unknown parameters of the progressively Type II censored Weibull-geometric (WG) distribution. The Bayes estimators cannot be obtained in explicit forms of the unknown parameters under a squared error loss function. The approximate Bayes estimators will be computed using the idea of Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions. Also the point estimation and confidence intervals based on maximum likelihood and bootstrap technique are also proposed. The approximate Bayes estimators will be obtained under the assumptions of informative and non-informative priors are compared with the maximum likelihood estimators. A numerical example is provided to illustrate the proposed estimation methods here. Maximum likelihood, bootstrap and the different Bayes estimates are compared via a Monte Carlo Simulation
文摘Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained.This paper deals with estimation of the stress strength reliability model R=P(Y<X)when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter.The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples.Two progressive Type-II hybrid censoring schemes were used,Case I:A sample size of stress is the equal sample size of strength,and same time of hybrid censoring,the product of spacing function under progressive Type-II hybrid censoring schemes.Case II:The sample size of stress is a different sample size of strength,in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T 2 e0;1T.The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed.A comparison study with classical methods as the maximum likelihood estimation method is discussed.Furthermore,to compare the performance of various cases,Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures.Finally,two real datasets are analyzed for illustrative purposes,first data for the breaking strengths of jute fiber,and the second data for the waiting times before the service of the customers of two banks.
文摘This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.
文摘This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss function. We propose to apply Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples, and they have in turn, been used to compute the Bayes estimates with the help of importance sampling technique. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider two sample Bayes prediction to predicting future order statistics and upper record values from Burr type XII distribution based on progressive first failure censored data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics and upper record values. A real life data set is used to illustrate the results derived.