• 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.

• Journal of the Korean Ceramic Society
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• v.34 no.9
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• pp.927-934
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• 1997

Static and cyclic fatigue tests were carried out for alumina specimen to study the statistical analyses (normal, lognormal and Weibull distribution) of fatigue lifetime data and nominal initial crack length data. Fatigue lifetime data followed Weibull distribution better than normal or lognormal distribution, for the shape parameter of the notched specimen was larger than that of the unnotched specimen. The nominal initial crack length data obtained from fatigue lifetime followed the lognormal and Weibull distribution better than normal distribution, for the coefficient of variation of the unnotched specimen was larger than that of the notched specimen, and shape parameter of unnotched specimen was smaller than that of the notched specimen.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.1
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• pp.52-60
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• 2007

Estimating parameters of the lifetime distribution is investigated when field failure data are not completelyreported. To take into account the reality and the accuracy of the estimates in such a case, the failure reportingprobability is incorporated in estimating parameters, Firstly, method of maximum likelihood estimate (MLE) isused to estimate parameters of the lifetime distribution when failure reporting probability is known, Secondly,Expectation and Maximization (EM) algorithm is used to estimate the failure reporting probability and parame-ters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both cases,procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simula-tion results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

• Journal of Applied Reliability
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• v.17 no.4
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• pp.332-342
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• 2017

Purpose: In this study, the lifetime distribution of a k-out-of-n system with heterogeneous components is suggested as Markov model, and the time-to-failure (TTF) distribution of each component is considered as phase-type distribution (PHD). Furthermore, based on the model, a redundancy allocation problem with a mix of components (RAPMC) is proposed. Methods: The lifetime distribution model for the system is formulated by the structured Markov chain. From the model, the various information on the system lifetime can be ascertained by the matrix-analytic (or-geometric) method. Conclusion: By the generalization of TTF distribution (PHD) and the consideration of heterogeneous components, the lifetime distribution model can delineate many real systems and be exploited for developing system operation policies such as preventive maintenance, warranty. Moreover, the effectiveness of the proposed RAPMC is verified by numerical experiments. That is, under the equivalent design conditions, it presented a system with higher reliability than RAP without component mixing (RAPCM).

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.7
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• pp.2302-2324
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• 2014

Cluster-based wireless sensor network (WSN) can significantly reduce the energy consumption by data aggregation and has been widely used in WSN applications. However, due to the intrinsic many-to-one traffic pattern in WSN, the network lifetime is generally deteriorated by the unbalanced energy consumption in a cluster-based WSN. Therefore, energy efficiency and network lifetime improvement are two crucial and challenging issues in cluster-based WSNs. In this paper, we propose a Non-Uniform Node Distribution (NUND) scheme to improve the energy efficiency and network lifetime in cluster-based WSNs. Specifically, we first propose an analytic model to analyze the energy consumption and the network lifetime of the cluster-based WSNs. Based on the analysis results, we propose a node distribution algorithm to maximize the network lifetime with a fixed number of sensor nodes in cluster-based WSNs. Extensive simulations demonstrate that the theoretical analysis results determined by the proposed analytic model are consistent with the simulation results, and the NUND can significantly improve the energy efficiency and network lifetime.

• Journal of Korean Society for Quality Management
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• v.38 no.4
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• pp.504-511
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• 2010

A fuze detonator comprising star shells is an important device so that its failure usually leads to failure of the shells. In this paper, accelerated degradation tests of RD1333 (lead azide) using temperature stress were performed, and then degradation data of explosive power for the detonator were analyzed to predict the storage lifetime of detonator. Degradation data analysis to estimate the storage lifetime is based on a distribution-based degradation process. Statistical distribution parameters of explosive power degradation measures at each time were estimated for each temperature level, and then reliability of the detonator for each accelerated temperature level was estimated using both time-varying distribution parameters and critical level of explosive power. Arrhenius model was applied to estimate storage lifetime of the detonator under the field temperature condition. Accelerated distribution-based degradation analysis to estimate storage lifetime is explained in detail, and estimation results are compared to field data of storage lifetime in this paper.

• Journal of Korean Society for Quality Management
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• v.41 no.1
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• pp.135-148
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• 2013

Purpose: This paper presents a method to evaluate the stockpile reliability of propelling charge for performance and storage safety with storage time. Methods: We consider a performance failure level is the amount of muzzle velocity drop which is the maximum allowed standard deviation multiplied by 6. The lifetime for performance is estimated by non-linear regression analysis. The state failure level is assumed that the content of stabilizer is below 0.2%. Because the degradation of stabilizer with storage time has both distribution of state and distribution of lifetime, it must be evaluated by stochastic process method such as gamma process. Results: It is estimated that the lifetime for performance is 59 years. The state distribution at each storage time can be shown from probability density function of degradation. It is estimated that the average lifetime as $B_{50}$ life is 33 years from cumulative failure distribution function curve. Conclusion: The lifetime for storage safety is shorter than for performance and we must consider both the lifetime for storage safety and the lifetime performance because of variation of degradation rate.

• Journal of Korean Society for Quality Management
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• v.16 no.2
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• pp.56-67
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• 1988

It is wellknown that the left truncated exponential distribution with positivity constraint on the location parameter is appropriate as a lifetime distribution model, In this paper, some Bayes estimators of the parameters and reliability for the left truncated exponential lifetime distribution when an unidentified-failure outlier is included and it is excluded in the exchangeable outlier model are proposed, and the performances of these proposed Bayes estimators are also discussed.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.363-383
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• 2016

The Weibull family of lifetime distributions play a fundamental role in reliability engineering and life testing problems. This paper investigates the potential usefulness of transmuted new generalized Weibull (TNGW) distribution for modeling lifetime data. This distribution is an important competitive model that contains twenty-three lifetime distributions as special cases. We can obtain the TNGW distribution using the quadratic rank transmutation map (QRTM) technique. We derive the analytical shapes of the density and hazard functions for graphical illustrations. In addition, we explore some mathematical properties of the TNGW model including expressions for the quantile function, moments, entropies, mean deviation, Bonferroni and Lorenz curves and the moments of order statistics. The method of maximum likelihood is used to estimate the model parameters. Finally the applicability of the TNGW model is presented using nicotine in cigarettes data for illustration.

• Journal of Applied Reliability
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• v.13 no.3
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• pp.191-206
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• 2013

Application areas for Lifetime Performance Index(LPI), a kind of process capability index to be frequently used as a means of measuring process performance are illustrated with examples. Statistical properties for maximum likelihood and unbiased estimators of LPI are evaluated and discussed under Weibull distribution with known shape parameter. Furthermore, guidelines for selecting an estimator of LPI are also presented.