• International Journal of Reliability and Applications
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• 제14권1호
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• pp.27-39
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• 2013

In this article, a new model based on the Rayleigh distribution is introduced. This model is useful and practical in physics, reliability, and life testing. The statistical and reliability properties of this model are presented, including moments, the hazard rate, the reversed hazard rate, and mean residual life functions, among others. In addition, it is shown that the distributions of the new model are ordered regarding the strongest likelihood ratio ordering. Four estimating methods, namely, method of moment, maximum likelihood method, Bayes estimation, and uniformly minimum variance unbiased, are used to estimate the parameters of this model. Simulation is used to calculate the estimates and to study their properties. Finally, the appropriateness of this model for real data sets is shown by using the chi-square goodness of fit test and the Kolmogorov-Smirnov statistic.

• 한국시뮬레이션학회논문지
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• 제10권2호
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• pp.61-74
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• 2001

The reliability evaluation of the large scale network becomes very complicate according to the growing size of network. Moreover if the reliability is not constant but follows probability distribution function, it is almost impossible to compute them in theory. This paper studies the network evaluation methods in order to overcome such difficulties. For this an efficient path set algorithm which seeks the path set connecting the start and terminal nodes efficiently is developed. Also, various variance reduction techniques are applied to compute the system reliability to enhance the simulation performance. As a numerical example, a large scale network is given. The comparisons of the path set algorithm and the variance reduction techniques are discussed.

• 대한산업공학회지
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• 제4권1호
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• pp.29-32
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• 1978

We obtain the minimum variance unbiased estimate of system reliability when a system consists of n components whose life times are assumed to be independent and identically distributed either negative exponential or geometric random variables. For the case of a negative exponential life time, we obtain the minimum variance unbiased estimate of the probability density function of the i-th order statistic.

• Journal of the Korean Data and Information Science Society
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• 제6권2호
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• pp.1-7
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• 1995

This paper considers the reliability estimation of a two-component shared-load system based on Freund model. Maximum likelihood estimator, order restricted maximum likelihood estimator and uniformly minimum variance unbiased estimator of the reliability function for the system are obtained. Performance of three estimators for moderate sample sizes is studied by simulation.

• International Journal of Reliability and Applications
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• 제16권2호
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• pp.123-133
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• 2015

In this paper, the problem of testing exponentiality against net decreasing variance residual lifetime (NDVRL) classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's asymptotic relative efficiency (PARE) is discussed to assess the performance of the test with respect to other tests. Selected critical values are tabulated. Some numerical simulations on the power estimates are presented for proposed test. Finally, numerical examples are presented for the purpose of illustrating our test.

• Journal of the Korean Data and Information Science Society
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• 제22권4호
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• pp.811-817
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• 2011

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.

• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.921-929
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• 2014

A bivariate exponential distribution with a location parameter is proposed as a model for a two-component shared load system with a guarantee time. Some statistical properties of the proposed model are investigated. The maximum likelihood estimators and uniformly minimum variance unbiased estimators of the parameters, mean time to failure, and the reliability function of system are obtained with unknown guarantee time. Simulation studies are given to illustrate the results.

• International Journal of Reliability and Applications
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• 제15권2호
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• pp.125-150
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• 2014

Accelerated life tests (ALTs) are extensively used to determine the reliability of a product in a short period of time. Test units are subject to elevated stresses which yield quick failures. ALT can be carried out using constant-stress, step-stress, progressive-stress, cyclic-stress or random-stress loading and their various combinations. An ALT with linearly increasing stress is ramp-stress test. Much of the previous work on planning ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations where the stress is generally increased. This paper presents an optimal design of ramp soak-stress ALT model which is based on the principle of Thermal cycling. Thermal cycling involves applying high and low temperatures repeatedly over time. The optimal plan consists in finding out relevant experimental variables, namely, stress rates and stress rate change points, by minimizing variance of reliability function with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out.

• International Journal of Reliability and Applications
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• 제17권1호
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• pp.21-49
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• 2016

Many mechanical, electrical and electronic products have more than one performance characteristics (PCs). For example the performance degradation of rubidium discharge lamps can be characterized by the rubidium consumption or the decreasing intensity the lamp. The product may degrade due to all the PCs which may be independent or dependent. This paper deals with the design of optimal bivariate step-stress partially accelerated degradation test (PADT) with degradation paths modelled by gamma process. The dependency between PCs has been modelled through Frank copula function. In partial step-stress loading, the unit is tested at usual stress for some time, and then the stress is accelerated. This helps in preventing over-stressing of the test specimens. Failure occurs when the performance characteristic crosses the critical value the first time. Under the constraint of total experimental cost, the optimal test duration and the optimal number of inspections at each intermediate stress level are obtained using variance optimality criterion.

• Structural Engineering and Mechanics
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• 제86권3호
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• pp.349-359
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• 2023

This paper presents a technique for determining the optimal number of elements in stochastic finite element analysis based on reliability analysis. Using the change-of-variable perturbation stochastic finite element approach, the probability density function of the dynamic responses of stochastic structures is explicitly determined. This method combines the perturbation stochastic finite element method with the change-of-variable technique into a united model. To further examine the relationships between the random fields, discretization of the random field parameters, such as the variance function and the scale of fluctuation, is also performed. Accordingly, the reliability index is calculated based on the explicit probability density function of responses with Gaussian or non-Gaussian random fields in any number of elements corresponding to the random field discretization. The numerical examples illustrate the effectiveness of the proposed method for a one-dimensional cantilever reinforced concrete column and a two-dimensional steel plate shear wall. The benefit of this method is that the probability density function of responses can be obtained explicitly without the use simulation techniques. Any type of random variable with any statistical distribution can be incorporated into the calculations, regardless of the restrictions imposed by the type of statistical distribution of random variables. Consequently, this method can be utilized as a suitable guideline for the efficient implementation of stochastic finite element analysis of structures, regardless of the statistical distribution of random variables.