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Computer Modeling in Engineering & Sciences 2023年第3期134卷 1943-1956页

作者： Alhanouf Alburaikan Hamiden Abd El-Wahed Khalifa Pavan Kumar SeyedaliMirjalili Ibrahim Mekawy Department of Mathematics College of Science and ArtsQassim UniversityAl-Badaya51951Saudi Arabia Department of Operations Research Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt Division of Mathematics School of Advanced Science and LanguagesVIT Bhopal UniversitySehore466114India Centre for Artificial Intelligence Research and Optimization Torrens University AustraliaBrisbane4006Australia Department of Mathematics College of Science and ArtsQassim UniversityAr Rass6688Saudi Arabia YFL(Yonsei Frontier Lab) Yonsei UniversitySeoul03722Korea

In this article,mathematical modeling for the evaluation of reliability is studied using two *** of the methods,is developed based on possibility *** performance of the reliability of the system is of prime *** view of this,the outcomes for the failure are required to evaluate with utmost *** possibility theory,the reliability information data determined from decision-making experts are *** samemethod is also related to the survival possibilities as against the survival *** other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy *** this method,a decision-making expert is not sure of his/her estimates of the reliability *** experiments are performed to illustrate the efficiency of the suggested methods in this *** the end,the paper is concluded with some future research directions to be explored for the proposed approach.

关键词： reliability function probabilistic function piecewise quadratic fuzzy numbers survival possibility failure rate possibility distribution state function closed interval approximation

The New Mixed Generalized Erlang Distribution

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Applied Mathematics 2023年第8期14卷 497-511页

作者： Therrar Kadri Yara Ghannam Department of Mathematics Lebanese International University Beirut Lebanon

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

关键词： Generalized Erlang Distribution Mixed Distribution Probability Density function Cumulative Distribution function Moment Generating function Hazard Rate function reliability function Moment of Order k

Bayesian Estimation and Prediction for the Maxwell Failure Distribution Based on Type II Censored Data

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Open Journal of Statistics 2016年第1期6卷 49-60页

作者： Anwar M. Hossain Gabriel Huerta Department of Mathematics New Mexico Tech Socorro NM USA Department of Mathematics and Statistics University of New Mexico Albuquerque NM USA

We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and to compare the performances of the different methods.

关键词： Bayes Estimator HPD Interval Maxwell Distribution MLE Prediction reliability function

The Marshall-Olkin Right Truncated Fréchet-Inverted Weibull Distribution: Its Properties and Applications

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Open Journal of Modelling and Simulation 2021年第1期9卷 74-89页

作者： Nora Nader M. A. El-Damcese B. S. El-Desouky Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt Department of Mathematies Faculty of Science Tanta University Tanta Egypt

In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.

关键词： Marshall and Olkin Moment Generating function Density function Order Statistics reliability function Inverse Weibull Distribution Maximum Likelihood