• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.9 no.2
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• pp.133-140
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• 2016

Software reliability in the software development process is an important issue. Software process improvement helps in finishing with reliable software product. Infinite failure NHPP software reliability models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, we were proposed the reliability model with the exponential and inverse exponential distribution, which made out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on mean square error (MSE) and coefficient of determination($R^2$), for the sake of efficient model, were employed. Analysis of failure, using real data set for the sake of proposing the exponential and inverse exponential distribution, was employed. This analysis of failure data compared with the exponential and inverse exponential distribution property. In order to insurance for the reliability of data, Laplace trend test was employed. In this study, the inverse exponential distribution model is also efficient in terms of reliability because it (the coefficient of determination is 80% or more) in the field of the conventional model can be used as an alternative could be confirmed. From this paper, the software developers have to consider life distribution by prior knowledge of the software to identify failure modes which can be able to help.

• The Journal of the Korea institute of electronic communication sciences
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• v.18 no.5
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• pp.935-944
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• 2023

In this study, the Inverse-type (: Inverse-Exponential, Inverse-Rayleigh) life distribution, which is known to be suitable for reliability research, was applied to a software development cost model based on finite failure NHPP(: Nonhomogeneous Poisson Process), and then the attributes that determine the model's performance were analyzed. Additionally, to evaluate the efficiency of the model, it was compared with the Goel-Okumoto basic model. The performance of the model was analyzed using failure time data, and MLE (: Maximum Likelihood Estimation) was applied to calculate the parameters. In conclusion, first, as a result of analyzing m(t), which determines the development cost, the Inverse-Exponential model was efficient due to its small error in the true value. Second, as a result of analyzing the release time along with the development cost, the Inverse-Rayleigh model was confirmed to be the best. Third, as a result of comprehensive evaluation of the attributes (m(t), cost, and release time) of the proposed model, the Inverse-Rayleigh model had the best performance. Therefore, if software developers can effectively utilize this research data in the early process, they will be able to proactively explore and analyze attributes that affect cost.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.93-109
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• 2007

In this paper we study a number of new exponentiated distributions. The survival function, failure rate and moments of the distributions have been derived using certain special functions. The behavior of the failure rate has also been studied.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.4
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• pp.641-648
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• 2022

In this study, the performance of the NHPP software reliability model with exponential distribution (Exponential Basic, Inverse Exponential, Lindley, Rayleigh) characteristics was comparatively analyzed, and based on this, the optimal reliability model was also presented. To analyze the software failure phenomenon, the failure time data collected during system operation was used, and the parameter estimation was solved by applying the maximum likelihood estimation method (MLE). Through various comparative analysis (mean square error analysis, true value predictive power analysis of average value function, strength function evaluation, and reliability evaluation applied with mission time), it was found that the Lindley model was an efficient model with the best performance. Through this study, the reliability performance of the distribution with the characteristic of the exponential form, which has no existing research case, was newly identified, and through this, basic design data that software developers could use in the initial stage can be presented.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.647-661
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• 2024

This study aims to determine the optimal solution to transportation problems. We proposed a novel approach for tackling the initial basic feasible solution. This is a critical step toward achieving an optimal or near-optimal solution. The transportation issue is an issue of distributing goods from several sources to several destinations. The literature demonstrates many ways to improve IBFS. In this work, to solve the IBFS, we suggested a new method based on the statistical formula called cumulative distribution function (CDF) in exponential distribution, and inverse contra-harmonic mean (ICHM). The spreadsheet converts transportation cost values into exponential cost cell values. The stepping-stone method is used to identify an optimum solution. The results are compared with other existing methodologies, the suggested method incorporates balanced, and unbalanced, maximizing the profits, random values, and case studies which produce more effective outcomes.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.425-435
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• 2016

In this paper, we analyze the inverse statistics of rainfall for 12 regions from 1973 to 2014. We obtain a probability density function f(x) of daily rainfall x, and $f({\tau}_{\rho})$ of the first passage time ${\tau}_{\rho}$ for a given ${\rho}$. Lastly, we derive the relation between ${\rho}$ and ${\tau}_{mean}({\rho})$, i.e., the averaged value of ${\tau}_{\rho}$. The analyses result in the x and ${\tau}_{\rho}$ have stretched exponential distributions. Also, ${\tau}_{mean}({\rho})$ has the form of a stretched exponential function. We derive the shape parameter ${\beta}$ of the distribution, and analyze the characteristics of 12 regional rainfalls.

• Journal of Korean Society for Quality Management
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• v.25 no.2
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• pp.1-14
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• 1997

This paper considers maximum likelihood (ML) estimation of lifetime distribution under stress bounded ramp tests in which the stress is increased linearly from used condition stress to the stress u, pp.r bound. The following assumptions are used: exponential lifetime distribution under a constant stress, an inverse power law relationship between stress and mean of exponential lifetime distribution, and a cumulative exposure model for the effect of changing stress. Likelihood equations for the parameters involved in the model and asymptotic distribution of the estimators are obtained, and a numerical example is given.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.531-542
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• 2015

In this survey, we use the normal linear model to demonstrate the use of the linear Bayes method. The superiorities of linear Bayes estimator (LBE) over the classical UMVUE and MLE are established in terms of the mean squared error matrix (MSEM) criterion. Compared with the usual Bayes estimator (obtained by the MCMC method) the proposed LBE is simple and easy to use with numerical results presented to illustrate its performance. We also examine the applications of linear Bayes method to some other distributions including two-parameter exponential family, uniform distribution and inverse Gaussian distribution, and finally make some remarks.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.479-496
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• 2016

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.