Papers by Hanan M O H A M E D Aly
Journal of Statistics and Management Systems, 2020
In this paper, the expectation-maximization (EM) algorithm and adaptive type-II progressive censo... more In this paper, the expectation-maximization (EM) algorithm and adaptive type-II progressive censoring (A-II-PC) scheme are discussed for the first time under ramp-stress accelerated life testing (RS-ALT) experiment based on extended Weibull (EW) distribution. Under the assumptions of cumulative exposure (CE) model and inverse power law relationship, the maximum likelihood estimators (MLEs) of the unknown parameters and acceleration factors are obtained using the EM algorithm, then compared with the scoring algorithm. Furthermore, the observed information matrix based on the missing value principle is computed and used to construct the asymptotic confidence intervals for the parameters and acceleration factors. Bootstrap techniques are also considered in the interval estimation. Moreover, a numerical example is presented to illustrate the application of both the scoring and EM algorithms. Finally, a Monte Carlo simulation study is carried out to assess the performance of the suggested algorithms.
Journal of Data Science
Analyzing time to event data arises in a number of fields such as Biology and Engineering. A comm... more Analyzing time to event data arises in a number of fields such as Biology and Engineering. A common feature of this data is that, the exact failure time for all units may not be observable. Accordingly, several types of censoring were presented. Progressive censoring allows units to be randomly removed before the terminal point of the experiment. Marshall-Olkin bivariate lifetime distribution was first introduced in 1967 using the exponential distribution. Recently, bivariate Marshall-Olkin Kumaraswamy lifetime distribution was derived. This paper derives the likelihood function under progressive type-I censoring for the bivariate Marshall-Olkin family in general and applies it on the bivariate Kumaraswamy lifetime distribution. Maximum likelihood estimators of model parameters were derived. Simulation study and a real data set are presented to illustrate the proposed procedure. Absolute bias, mean square error, asymptotic confidence intervals, confidence width and coverage probability are obtained. Simulation results indicate that the mean square error is smaller and confidence width is narrower and more precise when number of removals gets smaller. Also, increasing the terminal point of the experiment results in reducing the mean square error and confidence width.
International Journal of Reliability, Quality and Safety Engineering, 2021
A copula approach decomposes the joint distribution of random variables into marginal distributio... more A copula approach decomposes the joint distribution of random variables into marginal distributions of individual variables and the copula form that links the marginals together. When a researcher is dealing with a modeling problem, he is confronted with obtaining the best possible fit for the observed dependence structure. One possibility is to construct a new ideal copula that can describe the observed dependence. Finding a flexible multi-dimensional copula for modeling dependence is still quite challenging. In this paper, we will construct a new multi-dimensional Archimedean copula function that is characterized by a generator with two parameters which allows for more flexibility in modeling dependence. Moreover, we will apply the new constructed copula on step stress accelerated life testing with dependent competing risks under type II censoring. The point estimates of the unknown parameters are obtained using the maximum likelihood method. Also, the approximate and the parametr...
Abstract: Accelerated life testing (ALT) has gained greater importance because of dealing with hi... more Abstract: Accelerated life testing (ALT) has gained greater importance because of dealing with high reliability units. As a result, there is a big need to use a goodness of fit (GOF) technique for testing the underlying lifetime distribution. But there is a difficulty due to the existence of several stress levels with different samples of units at each level. Then, the choice of a certain GOF technique is based on its capability to combine the failure times from all stress levels to reach a conclusion about the adequacy of a certain lifetime distribution at each stress level. In this paper, the extended Neyman’s smooth test (ENST) is chosen. It is then modified in order to be used in validating the distributional assumption of accelerated failure time (AFT) model. This modified method is called; the adapted extended Neyman’s smooth test (AENST). It is applied to test for both Weibull and exponential distributions in case of constant stress under complete sampling. To check the perfo...
International Journal of Contemporary Mathematical Sciences, 2013
This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Typ... more This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Type-II censoring scheme. Failure times are assumed to distribute as the three-parameter Generalized Logistic (GL) distribution. The inverse power law model is used to represent the relationship between the stress and the scale parameter of a test unit. Bayes estimates are obtained using Markov Chain Monte Carlo (MCMC) simulation algorithm based on Gibbs sampling. Then, confidence intervals, and predicted values of the scale parameter and the reliability function under usual conditions are obtained. Numerical illustration and an illustrative example are addressed for illustrating the theoretical results. WinBUGS software package is used for implementing Markov Chain Monte Carlo (MCMC) simulation and Gibbs sampling.
Pakistan Journal of Statistics and Operation Research, 2016
This paper suggests the use of the conditional probability integral transformation (CPIT) method ... more This paper suggests the use of the conditional probability integral transformation (CPIT) method as a goodness of fit (GOF) technique in the field of accelerated life testing (ALT), specifically for validating the underlying distributional assumption in accelerated failure time (AFT) models. The CPIT method is based on transforming the data into independent and identically distributed (i.i.d) Uniform (0, 1) random variables and then applying a certain GOF technique to test the uniformity of the transformed random variables. In this paper, the CPIT method is used to validate each of the exponential and lognormal distributions' assumptions in an AFT model under constant stress and complete sampling. The performance of this method is investigated via a simulation study. Moreover, a real life example is presented to illustrate the application of it. Concluding comments about the good performance of the CPIT method are made.
Quality and Reliability Engineering International, 2015
ABSTRACT The Accelerated Life Testing (ALT) has been used for a long time in several fields to ob... more ABSTRACT The Accelerated Life Testing (ALT) has been used for a long time in several fields to obtain information on the reliability of product components and materials under operating conditions in a much shorter time. One of the main purposes of applying ALT is to estimate the failure time functions and reliability performance under normal conditions. This paper concentrates on the estimation procedures under ALT and how to select the best estimation method that gives accurate estimates for the reliability function. For this purpose, different estimation methods are used, such as maximum likelihood, least squares (LS), weighted LS, and probability weighted moment. Moreover, the reliability function under usual conditions is predicted. The estimation procedures are applied under the family of the exponentiated distributions in general, and for the exponentiated inverted Weibull (EIW) as a special case. Numerical analysis including simulated data and a real life data set is conducted to compare the performances between these four methods. It is found that the ML method gives the best results among other estimation methods. Finally, a comparison between the EIW and the Inverted Weibull (IW) distributions based on a real life data set is made using a likelihood ratio test. It is observed that the EIW distribution can provide better fitting than the IW in case of ALT.
Recently a new distribution, named a bivariate generalized linear failure rate distribution has b... more Recently a new distribution, named a bivariate generalized linear failure rate distribution has been introduced by Sarhan et al. (2011). In this paper, we obtained the moment generating function for the bivariate generalized linear failure rate distribution and the maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix in case of left random censoring. A numerical example is carried out to discuss the properties of the estimators.
This paper presents estimation and derivation of optimum test plan for time step stress accelerat... more This paper presents estimation and derivation of optimum test plan for time step stress accelerated life test (SSALT). The maximum likelihood (ML) method is applied to estimate the unknown parameters of the generalized logistic distribution, to construct the asymptomatic confidence intervals, and to predict the value of the scale parameter and the reliability function under the usual conditions. The scale parameter of the lifetime distribution is assumed to be an inverse power law function of the stress level. Moreover, we consider minimizing the determinant of Fisher information matrix to obtain the optimum time of changing stress point, and also the optimum censoring time. Finally, numerical simulation is introduced.
Communications in Statistics - Simulation and Computation
Abstract The copula approach is a way to describe the dependence structure between variables. Thi... more Abstract The copula approach is a way to describe the dependence structure between variables. This could be done through splitting the analysis of the joint distribution of a multivariate random vector into two parts: the analysis of the marginals and the analysis of a copula which describes the dependence structure. An important field of reliability in which the copula approach could be applied, is the accelerated life testing (ALT). When a test unit fails under ALT, there are often more than one fatal cause for the failure. In this paper, we consider the simple step-stress ALT (SSALT) under type II censoring when the lifetime distribution of the different risks are dependent. The dependence structure between the competing risks is described using the copula approach. The point estimates of the unknown parameters are obtained using the maximum likelihood method. Also, the interval estimates for the unknown parameters are constructed using the asymptotic distributions and the parametric bootstrap method. Numerical analysis including simulated data and a real life data set is conducted to study the performance of the estimates.
The optimal designs and statistical inference of accelerated life tests under type-I are studied ... more The optimal designs and statistical inference of accelerated life tests under type-I are studied for constant stress-accelerated life tests (CSALTs). It is assumed that the lifetime at design stress has generalized logistic distribution. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The maximum likelihood (ML) estimators of the model parameters, Fisher information matrix, the asymptomatic variance-covariance matrix, the confidence bounds, the predictive value of the scale parameter, and the reliability function under the usual conditions are obtained under type-I censoring. Moreover, the optimal design of the accelerated life tests is studied according to the D-optimality criterion to specify the optimal censoring time. Finally, the numerical studies are introduced to illustrate the proposed procedures.
Communications in Statistics - Simulation and Computation, 1998
... ESTIMATION OF THE PARAMETERS OF PARETO DISTRIBUTION AND THE RELIABILITY FUNCTION USING ACCELE... more ... ESTIMATION OF THE PARAMETERS OF PARETO DISTRIBUTION AND THE RELIABILITY FUNCTION USING ACCELERATED LIFE TESTING WITH CENSORING Abdel-Ghaly, AA Attia, AF Aly, HM Dept. ... Page 2. ABDEL-GHALY, ATTIA, AND ALY 1. INTRODUCTION ...
This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Typ... more This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Type-II censoring scheme. Failure times are assumed to distribute as the three-parameter Generalized Logistic (GL) distribution. The inverse power law model is used to represent the relationship between the stress and the scale parameter of a test unit. Bayes estimates are obtained using Markov Chain Monte Carlo (MCMC) simulation algorithm based on Gibbs sampling. Then, confidence intervals, and predicted values of the scale parameter and the reliability function under usual conditions are obtained. Numerical illustration and an illustrative example are addressed for illustrating the theoretical results. WinBUGS software package is used for implementing Markov Chain Monte Carlo (MCMC) simulation and Gibbs sampling.
Accelerated life testing (ALT) has gained greater importance because of dealing with high reliabi... more Accelerated life testing (ALT) has gained greater importance because of dealing with high reliability units. As a result, there is a big need to use a goodness of fit (GOF) technique for testing the underlying lifetime distribution. But there is a difficulty due to the existence of several stress levels with different samples of units at each level. Then, the choice of a certain GOF technique is based on its capability to combine the failure times from all stress levels to reach a conclusion about the adequacy of a certain lifetime distribution at each stress level. In this paper, the extended Neyman's smooth test (ENST) is chosen. It is then modified in order to be used in validating the distributional assumption of accelerated failure time (AFT) model. This modified method is called; the adapted extended Neyman's smooth test (AENST). It is applied to test for both Weibull and exponential distributions in case of constant stress under complete sampling. To check the performance of the AENST, a comparison is made with the conditional probability integral transformation test (CPITT) via a simulation study. Moreover, a real data set is provided to illustrate the application of the introduced AENST. The results revealed that the AENST is a powerful test comparing with the CPITT. Thus, the AENST is recommended for testing the AFT models.
This paper suggests the use of the conditional probability integral transformation (CPIT) method ... more This paper suggests the use of the conditional probability integral transformation (CPIT) method as a goodness of fit (GOF) technique in the field of accelerated life testing (ALT), specifically for validating the underlying distributional assumption in accelerated failure time (AFT) models. The CPIT method is based on transforming the data into independent and identically distributed (i.i.d) Uniform (0, 1) random variables and then applying a certain GOF technique to test the uniformity of the transformed random variables. In this paper, the CPIT method is used to validate each of the exponential and lognormal distributions' assumptions in an AFT model under constant stress and complete sampling. The performance of this method is investigated via a simulation study. Moreover, a real life example is presented to illustrate the application of it. Concluding comments about the good performance of the CPIT method are made.
The Accelerated Life Testing (ALT) has been used for a long time in several fields to obtain info... more The Accelerated Life Testing (ALT) has been used for a long time in several fields to obtain information on the reliability of product components and materials under operating conditions in a much shorter time. One of the main purposes of applying ALT is to estimate the failure time functions and reliability performance under normal conditions. This paper concentrates on the estimation procedures under ALT and how to select the best estimation method that gives accurate estimates for the reliability function. For this purpose, different estimation methods are used, such as maximum likelihood, least squares (LS), weighted LS, and probability weighted moment. Moreover, the reliability function under usual conditions is predicted. The estimation procedures are applied under the family of the exponentiated distributions in general, and for the exponentiated inverted Weibull (EIW) as a special case. Numerical analysis including simulated data and a real life data set is conducted to compare the performances between these four methods. It is found that the ML method gives the best results among other estimation methods. Finally, a comparison between the EIW and the Inverted Weibull (IW) distributions based on a real life data set is made using a likelihood ratio test. It is observed that the EIW distribution can provide better fitting than the IW in case of ALT.
This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Typ... more This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Type-II censoring scheme. Failure times are assumed to distribute as the three-parameter Generalized Logistic (GL) distribution. The inverse power law model is used to represent the relationship between the stress and the scale parameter of a test unit. Bayes estimates are obtained using Markov Chain Monte Carlo (MCMC) simulation algorithm based on Gibbs sampling. Then, confidence intervals, and predicted values of the scale parameter and the reliability function under usual conditions are obtained. Numerical illustration and an illustrative example are addressed for illustrating the theoretical results. WinBUGS software package is used for implementing Markov Chain Monte Carlo (MCMC) simulation and Gibbs sampling .
This paper presents estimation and derivation of optimum test plan for time step stress accelerat... more This paper presents estimation and derivation of optimum test plan for time step stress accelerated life test (SSALT). The maximum likelihood (ML) method is applied to estimate the unknown parameters of the generalized logistic distribution, to construct the asymptomatic confidence intervals, and to predict the value of the scale parameter and the reliability function under the usual conditions. The scale parameter of the lifetime distribution is assumed to be an inverse power law function of the stress level. Moreover, we consider minimizing the determinant of Fisher information matrix to obtain the optimum time of changing stress point, and also the optimum censoring time. Finally, numerical simulation is introduced.
Recently a new distribution, named a bivariate generalized linear failure rate distribution has b... more Recently a new distribution, named a bivariate generalized linear failure rate distribution has been introduced by Sarhan et al. (2011). In this paper, we get the maximum likelihood estimators for the unknown parameters of bivariate generalized linear failure rate distribution and their approximate variance-covariance matrix in case of type II censored samples based on concomitants of order statistics. Moreover, these estimators are obtained assuming hybrid random censored samples when censored times follow either exponential or Weibull distribution. Numerical examples are carried out to check the properties of the estimators.
Recently a new distribution, named a bivariate generalized linear failure rate distribution has b... more Recently a new distribution, named a bivariate generalized linear failure rate distribution has been introduced by Sarhan et al. (2011). In this paper, we obtained the moment generating function for the bivariate generalized linear failure rate distribution and the maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix in case of left random censoring. A numerical example is carried out to discuss the properties of the estimators.
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Papers by Hanan M O H A M E D Aly