• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.7-16
• /
• 2014

Erlang-truncated exponential distribution is widely used in the field of queuing system and stochastic processes. This family of distribution include exponential distribution. In this paper we establish some exact expression and recurrence relations satisfied by the quotient moments and conditional quotient moments of the upper record values from the Erlang-truncated exponential distribution. Further a characterization of this distribution based on recurrence relations of quotient moments of record values is presented.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.11 no.4
• /
• pp.460-466
• /
• 2018

With the development of information technology, the scale of computer software system is constantly expanding. Reliability and cost of software development have a great impact on software quality. In this study, based on the software failure interval time data, a comparative analysis was performed on the characteristics of the software development cost model based on the lifetime distribution following the Type-2 Gumbel and Erlang distribution in the NHPP model. As a result, the trends of the cost curves for the Go-Okumoto model and the proposed Erlang model and the Type-2 Gumble model both decreased in the initial stage and gradually increased in the latter half of the failure time. Also, Comparing the Erlang model with the Type-2 Gumble model, we found that the Erlang model is faster and more cost-effective at launch. Through this study, Software operators should remove possible defects from the testing phase rather than the operational phase to reduce defects after the software release date, it is expected to be able to study the prior information needed to understand the characteristic of software development cost.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.28 no.4
• /
• pp.145-153
• /
• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.

• Journal of Industrial Convergence
• /
• v.18 no.3
• /
• pp.19-25
• /
• 2020

In the software development process, software reliability evaluation is a very important issue. In particular, finding the optimal development model that satisfies high reliability is the more important task for software developers. For this, in this study, Pareto and Erlang life distributions were applied to the finite failure NHPP model to evaluate the reliability attributes. For this purpose, parametric estimation is applied to the maximum likelihood estimation method, and nonlinear equations are calculated using the bisection method. As a result, the Erlang model showed better performance than the Pareto model in the evaluation of the strength function and the mean value function. Also, as a result of inputting future mission time and evaluating reliability, the Erlang model showed an effectively high trend together with the Pareto model, while the Goel-Okumoto basic model showed a decreasing trend. In conclusion, the Erlang model is the best model among the proposed models. Through this study, it is expected that software developers will be able to use it as a basic guideline for exploring and evaluating the optimal software reliability model.

• Journal of Information Technology Applications and Management
• /
• v.24 no.2
• /
• pp.71-80
• /
• 2017

Software reliability is one of the most elementary and important problems in software development In order to find the software failure occurrence, the instantaneous failure rate function in the Poisson process can have a constant, incremental or decreasing tendency independently of the failure time. In this study, we compared the reliability performance of the software reliability model using the parameters of Pareto life distribution with the intensity decreasing pattern and the shape parameter of Erlang life distribution with the intensity increasing and decreasing pattern in the software product testing. In order to identify the software failure environment, the parametric estimation was applied to the maximum likelihood estimation method. Therefore, in this paper, we compare and evaluate software reliability by applying software failure time data. The reliability of the Erlang and Pareto life models is shown to be higher than that of the Pareto lifetime distribution model when the shape parameter is higher and the Erlang model is more reliable when the shape parameter is higher. Through this study, the software design department will be able to help the software design by applying various life distribution and shape parameters, and providing basic knowledge using software failure analysis.

• Journal of applied mathematics & informatics
• /
• v.41 no.2
• /
• pp.449-468
• /
• 2023

This paper deals in the study of the estimation of the parameters of Erlang distribution based on rank set sampling and some of its modifications. Here we considered Maximum Likelihood (ML) and the Bayesian technique to estimate the shape and scale parameter of Erlang distribution based on RSS and its some modifications such as ERSS, MRSS, and MRSSu. The derivation for unknown parameters of Erlang distribution is well presented using normal approximation to the asymptotic distribution of ML estimators. But due to the complexity involves in the integral, the Bayes estimator of unknown parameters is obtained using MCMC method. Further, we compared the MSE of estimation in different sampling schemes with different set sizes and cycle size. A real-life data application is also given to illustrate the efficiency of the proposed scheme.

• The Korean Journal of Applied Statistics
• /
• v.18 no.1
• /
• pp.57-66
• /
• 2005

In this paper, we propose a method to evaluate the solutions of the renewal equations related to SPRT for Erlang distribution. In SPRT, the Average Sample Number(ASN) and type I or type II error probabilities are shown in Fredholm type integral equations. The integral equations are generally solved by the approximation method using Gaussian quadrature. For Erlang distribution, it has been known that the exact solutions of the equations exist. We propose the algorithm to solve the equations.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.10 no.1
• /
• pp.7-14
• /
• 2006

The finite failure NHPP models proposed in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, we propose the Erlang reliability model, which can capture the increasing nature of the failure occurrence rate per fault. Equations to estimate the parameters of the Erlang finite failure NHPP model based on failure data collected in the form of inter-failure times are developed. For the sake of proposing shape parameter of the Erlang distribution, we used to the goodness-of-fit test of distribution. Data set, where the underlying failure process could not be adequately described by the existing models, which motivated the development of the Erlang model. Analysis of the failure data set which led us to the Erlang model, using arithmetic and Laplace trend tests, goodness-of-fit test, bias tests is presented.

• Journal of Korean Society of Transportation
• /
• v.21 no.4
• /
• pp.103-111
• /
• 2003

This study proposes methodology deterimining a basic pedestrian crossing capacity that plays a critical role in the installation of pedestrian signal at the crosswalks. The methodology is based on the pattern of vehicle arrived at the crosswalks. Erlang distribuion is used as headway distribution that can cover the various levels of flow rate. Models using Erlang distribution are represented by Erlang parameter (K) of 1, 2, or 3 at 2-, 4-, or 6-lane roadway in both directions. In addition, this study considered the only type of road with a pedestrian refuge area in the median that is used to wait for the allowable gap provided by the flow of another direction. As a result, the pedestrian capacity decreases as flow rate increases and Erlang parameter increases for the road with the pedestrian refuge. This study develops the models to determine the pedestrian capacity under a variety of flow rates and the outcomes of this study could be used as the criteria for the determination of the installation of pedestrian signal or for the provision of pedestrian refuge in the median of road.

• International Journal of Reliability and Applications
• /
• v.1 no.1
• /
• pp.49-64
• /
• 2000

We consider a system whose inherent life follows an Erlang distribution, which is subject to two heterogeneous random shocks. Minor shocks arrive according to a renewal process and each causes the system to fail independently with a certain probability. A major shock whose interarrival times follow an Erlang distribution causes the system to fail with probability one. The Laplace transform of the distribution of the time to system failure is derived in a functional form of the Laplace transform of the interarrival time distribution of minor shocks. An algorithm is given for the computation of the moments of the time to system failure.