International Journal of Reliability and Applications, Jun 1, 2013
ABSTRACT The availability equivalence factors of a general repairable series-parallel system is d... more ABSTRACT The availability equivalence factors of a general repairable series-parallel system is discussed in this paper based on the availability function of the system. The system components are assumed to be repairable and independent but not identical. The life and repair times of the system components are exponentially distributed with different parameters. Two types of availability equivalent factors of the system are derived. The results derived in this paper generalizes those given in the literature. A case study is introduced to illustrate how the idea of this work can be applied.
International Journal of Statistics and Economics, Jan 20, 2008
Recently, Sarhan and Kundu (2007) introduced a new distribution named generalized linear failure ... more Recently, Sarhan and Kundu (2007) introduced a new distribution named generalized linear failure rate distribution. This paper deals with the problem of estimating the parameters of this distribution in the case where the data is grouped and censored. We use both the maximum likelihood and Bayes techniques. The results obtained are illustrated on a set of real data.
In this paper, we introduce a new generalization of the Weibull distribution. This new distributi... more In this paper, we introduce a new generalization of the Weibull distribution. This new distribution generalizes several distributions, among them are the modified Weibull, the generalized linear failure rate and the exponentiated Weibull distributions. The properties of this distribution are investigated. The maximum likelihood estimates of the four unknown parameters indexed to this new distribution are obtained. A set of real data is used to explain how this new distribution can fit a real data better than some other known distributions.
This paper discusses statistical inference in connection with a Weibull distribution model, using... more This paper discusses statistical inference in connection with a Weibull distribution model, using Type-II progressively censored data with random scheme. We used the maximum likelihood procedure to derive both point and interval estimates of the unknown parameters included in the model. The expected termination point to complete the censoring test is computed and analyzed under different censoring schemes. A numerical study is presented to illustrate the application of the theoretical results presented.
International Journal of Reliability and Applications, 2009
A new bivariate linear failure rate distribution is introduced through a shock model. It is prove... more A new bivariate linear failure rate distribution is introduced through a shock model. It is proved that the marginal distributions of this new bivariate distribution are linear failure rate distributions. The joint moment generating function of the bivariate distribution is derived. Mixtures of bivariate linear failure rate distributions are also discussed. Application to a real data is given.
Journal of Mathematical Sciences and Modelling, 2019
A new discrete two-parameter bathtub hazard distribution is proposed by Sarhan \cite{Sarhan-2017}... more A new discrete two-parameter bathtub hazard distribution is proposed by Sarhan \cite{Sarhan-2017}. This paper uses Bayes method to estimate the two unknown parameters and the reliability measures of this distribution. The joint posterior distribution of the model parameters cannot be obtained in a convenient form. Therefore, numerical techniques are needed. We apply four Bayesian numerical methods to get random draws from the joint posterior distribution to be used to estimate the model parameters and its reliability measures without deriving the actual joint posterior distribution. It is assumed here that the two model parameters are priori independent random variables with beta and gamma distributions. Two scenarios for the hyperparameters are applied to compare their contributions on the Bayesian inferences. Two real data sets are re-analyzed using the Bayesian techniques applied here. A simulation study is performed to investigate the properties of the methods applied.
Journal of Mathematical Sciences and Modelling, 2019
This paper introduces a new bivariate distribution named the bivariate generalized Rayleigh distr... more This paper introduces a new bivariate distribution named the bivariate generalized Rayleigh distribution (BVGR). The proposed distribution is of type of Marshall-Olkin (MO) distribution. The BVGR distribution has generalized Rayleigh marginal distributions. The joint cumulative distribution function, the joint survival function, the joint probability density function and the joint hazard rate function of the proposed distribution are obtained in closed forms. Statistical properties of the BVGR distribution are investigated. The maximum likelihood and Bayes methods are applied to estimate the unknown parameters. Both maximum likelihood and Bayes estimates are not obtained analytically. Therefore, numerical algorithms are required to report on the model parameters and its reliability characteristics. Markov Chain Monte Carlo (MCMC) algorithm is applied for the Bayesian method. A real data set is analyzed using the proposed distribution and compared it with existing distributions. It...
International Journal of Reliability and Applications, Jun 1, 2013
ABSTRACT The availability equivalence factors of a general repairable series-parallel system is d... more ABSTRACT The availability equivalence factors of a general repairable series-parallel system is discussed in this paper based on the availability function of the system. The system components are assumed to be repairable and independent but not identical. The life and repair times of the system components are exponentially distributed with different parameters. Two types of availability equivalent factors of the system are derived. The results derived in this paper generalizes those given in the literature. A case study is introduced to illustrate how the idea of this work can be applied.
International Journal of Statistics and Economics, Jan 20, 2008
Recently, Sarhan and Kundu (2007) introduced a new distribution named generalized linear failure ... more Recently, Sarhan and Kundu (2007) introduced a new distribution named generalized linear failure rate distribution. This paper deals with the problem of estimating the parameters of this distribution in the case where the data is grouped and censored. We use both the maximum likelihood and Bayes techniques. The results obtained are illustrated on a set of real data.
In this paper, we introduce a new generalization of the Weibull distribution. This new distributi... more In this paper, we introduce a new generalization of the Weibull distribution. This new distribution generalizes several distributions, among them are the modified Weibull, the generalized linear failure rate and the exponentiated Weibull distributions. The properties of this distribution are investigated. The maximum likelihood estimates of the four unknown parameters indexed to this new distribution are obtained. A set of real data is used to explain how this new distribution can fit a real data better than some other known distributions.
This paper discusses statistical inference in connection with a Weibull distribution model, using... more This paper discusses statistical inference in connection with a Weibull distribution model, using Type-II progressively censored data with random scheme. We used the maximum likelihood procedure to derive both point and interval estimates of the unknown parameters included in the model. The expected termination point to complete the censoring test is computed and analyzed under different censoring schemes. A numerical study is presented to illustrate the application of the theoretical results presented.
International Journal of Reliability and Applications, 2009
A new bivariate linear failure rate distribution is introduced through a shock model. It is prove... more A new bivariate linear failure rate distribution is introduced through a shock model. It is proved that the marginal distributions of this new bivariate distribution are linear failure rate distributions. The joint moment generating function of the bivariate distribution is derived. Mixtures of bivariate linear failure rate distributions are also discussed. Application to a real data is given.
Journal of Mathematical Sciences and Modelling, 2019
A new discrete two-parameter bathtub hazard distribution is proposed by Sarhan \cite{Sarhan-2017}... more A new discrete two-parameter bathtub hazard distribution is proposed by Sarhan \cite{Sarhan-2017}. This paper uses Bayes method to estimate the two unknown parameters and the reliability measures of this distribution. The joint posterior distribution of the model parameters cannot be obtained in a convenient form. Therefore, numerical techniques are needed. We apply four Bayesian numerical methods to get random draws from the joint posterior distribution to be used to estimate the model parameters and its reliability measures without deriving the actual joint posterior distribution. It is assumed here that the two model parameters are priori independent random variables with beta and gamma distributions. Two scenarios for the hyperparameters are applied to compare their contributions on the Bayesian inferences. Two real data sets are re-analyzed using the Bayesian techniques applied here. A simulation study is performed to investigate the properties of the methods applied.
Journal of Mathematical Sciences and Modelling, 2019
This paper introduces a new bivariate distribution named the bivariate generalized Rayleigh distr... more This paper introduces a new bivariate distribution named the bivariate generalized Rayleigh distribution (BVGR). The proposed distribution is of type of Marshall-Olkin (MO) distribution. The BVGR distribution has generalized Rayleigh marginal distributions. The joint cumulative distribution function, the joint survival function, the joint probability density function and the joint hazard rate function of the proposed distribution are obtained in closed forms. Statistical properties of the BVGR distribution are investigated. The maximum likelihood and Bayes methods are applied to estimate the unknown parameters. Both maximum likelihood and Bayes estimates are not obtained analytically. Therefore, numerical algorithms are required to report on the model parameters and its reliability characteristics. Markov Chain Monte Carlo (MCMC) algorithm is applied for the Bayesian method. A real data set is analyzed using the proposed distribution and compared it with existing distributions. It...
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Papers by Ammar Sarhan