scholarly journals Appendix B: Erlang Distribution Program

2003 ◽  
pp. 833-834
Keyword(s):  
Erlang Distribution

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies and heterogeneous components: Erlang time-to-failure distribution

2020 ◽  
pp. 1748006X2095257
Author(s):  
Meisam Sadeghi ◽  
Emad Roghanian ◽  
Hamid Shahriari ◽  
Hassan Sadeghi
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
System Reliability ◽  
Parallel Systems ◽  
Closed Form Expression ◽  
Erlang Distribution ◽  
Time To Failure ◽  
Form Expression ◽  
Integrodifference Equation ◽  
Cold Standby

The redundancy allocation problem (RAP) of non-repairable series-parallel systems considering cold standby components and imperfect switching mechanism has been traditionally formulated with the objective of maximizing a lower bound on system reliability instead of exact system reliability. This objective function has been considered due to the difficulty of determining a closed-form expression for the system reliability equation. But, the solution that maximizes the lower bound for system reliability does not necessarily maximize exact system reliability and thus, the obtained system reliability may be far from the optimal reliability. This article attempts to overcome the mentioned drawback. Under the assumption that component time-to-failure is distributed according to an Erlang distribution and switch time-to-failure is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. A semi-analytical expression is also derived for the reliability equation of a subsystem with mixed redundancy strategy. The accuracy and the correctness of the derived equations are validated analytically. Using these equations, the RAP of non-repairable series-parallel systems with a choice of redundancy strategies is formulated. The proposed mathematical model maximizes exact system reliability at mission time given system design constraints. Unlike most of the previous formulations, the possibility of using heterogeneous components in each subsystem is provided so that the active components can be of one type and the standby ones of the other. The results of an illustrative example demonstrate the high performance of the proposed model in determining optimal design configuration and increasing system reliability.

scholarly journals Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution

2016 ◽  
Vol 4 (1) ◽  
pp. 62 ◽  
Author(s):  
Hesham Reyad ◽  
Adil Younis ◽  
Amal Alkhedir
Keyword(s):  
Loss Function ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Likelihood Function ◽  
Hierarchical Bayes ◽  
Erlang Distribution ◽  
Quadratic Loss ◽  
Hierarchical Bayesian ◽  
Empirical Bayesian ◽  
Symmetric Loss

This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and four different asymmetric loss functions [Precautionary loss function (PLF), entropy loss function (ELF), Degroot loss function (DLF) and quadratic loss function (QLF)]. The properties of the QE-Bayesian estimates are introduced and the relations between the QE-Bayes and quasi-hierarchical Bayes estimates are discussed. Comparisons among all estimators are performed in terms of mean square error (MSE) via Monte Carlo simulation.

scholarly journals Comparing Multicomponent Erlang Distribution and Lévy Distribution of Particle Transverse Momentums

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hua-Rong Wei ◽  
Ya-Hui Chen ◽  
Li-Na Gao ◽  
Fu-Hu Liu
Keyword(s):  
Hadron Collider ◽  
Center Of Mass ◽  
Heavy Ion ◽  
Erlang Distribution ◽  
Relativistic Heavy Ion Collider ◽  
Final State ◽  
Heavy Particles ◽  
Proton Proton ◽  
Lévy Distribution ◽  
Levy Distribution

The transverse momentum spectrums of final-state products produced in nucleus-nucleus and proton-proton collisions at different center-of-mass energies are analyzed by using a multicomponent Erlang distribution and the Lévy distribution. The results calculated by the two models are found in most cases to be in agreement with experimental data from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The multicomponent Erlang distribution that resulted from a multisource thermal model seems to give a better description as compared with the Lévy distribution. The temperature parameters of interacting system corresponding to different types of final-state products are obtained. Light particles correspond to a low temperature emission, and heavy particles correspond to a high temperature emission. Extracted temperature from central collisions is higher than that from peripheral collisions.

Sign in / Sign up

Export Citation Format

Share Document