A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical pro...A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.展开更多
In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy di...In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.展开更多
Accelerated life tests play a vital role in reliability analysis,especially as advanced technologies lead to the production of highly reliable products to meet market demands and competition.Among these tests,progress...Accelerated life tests play a vital role in reliability analysis,especially as advanced technologies lead to the production of highly reliable products to meet market demands and competition.Among these tests,progressive-stress accelerated life tests(PSALT)allow for continuous changes in applied stress.Additionally,the generalized progressive hybrid censoring(GPHC)scheme has attracted significant attention in reliability and survival analysis,particularly for handling censored data in accelerated testing.It has been applied to various failure models,including competing risks and step-stress models.However,despite its growing relevance,a notable gap remains in the literature regarding the application of GPHC in PSALT models.This paper addresses that gap by studying PSALT under a GPHC scheme with binomial removal.Specifically,it considers lifetimes following the quasi-Xgamma distribution.Model parameters are estimated using both maximum likelihood and Bayesian methods under gamma priors.Interval estimation is provided through approximate confidence intervals,bootstrap methods,and Bayesian credible intervals.Bayesian estimators are derived under squared error and entropy loss functions,using informative priors in simulation and non-informative priors in real data applications.A simulation study is conducted to evaluate various censoring schemes,with coverage probabilities and interval widths assessed via Monte Carlo simulations.Additionally,Bayesian predictive estimates and intervals are presented.The proposed methodology is illustrated through the analysis of two real-world accelerated life test datasets.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
In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete informat...In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.展开更多
In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this pap...In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.展开更多
This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is ...This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible.展开更多
In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore...In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.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
In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.
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
The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and lea...The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and least-squares estimation （LSE） while it was hard to build confidence intervals （CI）. The concept of generalized confidence interval （GCI） was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also Ran out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.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 stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength...The stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength model is demanding, although lacking. We propose a nonparametric method for the inference of the stress-strength model when the observations are subject to right censoring. The asymptotic properties are also established. The practical utility of the proposed method is assessed through both simulated and real data sets.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
Wavelet has rapid development in the current mathematics new areas. It also has a double meaning of theory and application. In signal and image compression, signal analysis, engineering technology has a wide range of ...Wavelet has rapid development in the current mathematics new areas. It also has a double meaning of theory and application. In signal and image compression, signal analysis, engineering technology has a wide range of applications. In this paper, we use wavelet method, for estimating the density function for censoring data. We evaluate the mean integrated squared error, convergence ratio of given estimator. Also, we obtain empirical distribution of given estimator and verify the conclusion by two simulation examples.展开更多
Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the depend...Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.展开更多
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 two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved li...The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.展开更多
文摘A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.
基金funded by Researchers Supporting Project number(RSPD2025R969),King Saud University,Riyadh,Saudi Arabia.
文摘In this present work,we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution.These estimates have been obtained using gamma priors based on various loss functions such as squared error,entropy,weighted balance,and minimum expected loss functions.An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators.The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error.Additionally,the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.
基金supported and funded by the Deanship of Scientifc Research at ImamMohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘Accelerated life tests play a vital role in reliability analysis,especially as advanced technologies lead to the production of highly reliable products to meet market demands and competition.Among these tests,progressive-stress accelerated life tests(PSALT)allow for continuous changes in applied stress.Additionally,the generalized progressive hybrid censoring(GPHC)scheme has attracted significant attention in reliability and survival analysis,particularly for handling censored data in accelerated testing.It has been applied to various failure models,including competing risks and step-stress models.However,despite its growing relevance,a notable gap remains in the literature regarding the application of GPHC in PSALT models.This paper addresses that gap by studying PSALT under a GPHC scheme with binomial removal.Specifically,it considers lifetimes following the quasi-Xgamma distribution.Model parameters are estimated using both maximum likelihood and Bayesian methods under gamma priors.Interval estimation is provided through approximate confidence intervals,bootstrap methods,and Bayesian credible intervals.Bayesian estimators are derived under squared error and entropy loss functions,using informative priors in simulation and non-informative priors in real data applications.A simulation study is conducted to evaluate various censoring schemes,with coverage probabilities and interval widths assessed via Monte Carlo simulations.Additionally,Bayesian predictive estimates and intervals are presented.The proposed methodology is illustrated through the analysis of two real-world accelerated life test datasets.
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.
文摘In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.
基金Supported by the NSF of China(69971016) Supported by the Shanghai Higher Learning Science Supported by the Technology Development Foundation(00JC14507)
文摘In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.
基金This work is partially supported by National Natural Science Foundation of China (10071090 and 10271013).
文摘This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible.
基金Supported by the NSF of China(69971016)Supported by the Shanghai Higher Learning Science and Technology Development Foundation(04DB24)
文摘In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.
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.
文摘In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.
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Project(71371182) supported by the National Natural Science Foundation of China
文摘The multiply type-I censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation （MLE） and least-squares estimation （LSE） while it was hard to build confidence intervals （CI）. The concept of generalized confidence interval （GCI） was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also Ran out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.
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(11301545,11401341,11326087)the Fundamental Research Fund for the Central Universities(31541311216)+2 种基金Scientific Research Fund of Fujian Education Department(JA13301)Qingyang Regional Technology Cooperation Planning Project(KH201304)Gansu Education Science "twelfth five-year" Planning Project(GS[2013]GHB1097)
文摘The stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength model is demanding, although lacking. We propose a nonparametric method for the inference of the stress-strength model when the observations are subject to right censoring. The asymptotic properties are also established. The practical utility of the proposed method is assessed through both simulated and real data sets.
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Wavelet has rapid development in the current mathematics new areas. It also has a double meaning of theory and application. In signal and image compression, signal analysis, engineering technology has a wide range of applications. In this paper, we use wavelet method, for estimating the density function for censoring data. We evaluate the mean integrated squared error, convergence ratio of given estimator. Also, we obtain empirical distribution of given estimator and verify the conclusion by two simulation examples.
基金supported by the National Natural Science Foundation of China(71571144 71401134)the Program of International Cooperation and Exchanges in Science and Technology Funded by Shaanxi Province(2016KW-033)
文摘Middle censoring is an important censoring scheme,in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull(MOBW) distribution.The maximum likelihood estimations(MLEs), midpoint approximation(MPA) estimations and approximate confidence intervals(ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter.The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals(CIs). Finally,two numerical examples are used to show the performance of the proposed methods.
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 two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.
