• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.53-70
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• 2008

In this paper, we discuss the plethora of uses for the software package R, and focus specifically on its helpful applications in reliability data analyses. Examples are presented; including the R coding protocol, R code, and plots for various statistical as well as reliability analyses. We explore Kaplan-Meier estimates and maximum likelihood estimation for distributions including the Weibull. Finally, we discuss future applications of R, and usages of quantile regression in reliability.

• Journal of the Korean Data and Information Science Society
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• v.2
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• pp.23-39
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• 1991

The maximum likelihood estimators and Bayes estimators of the parameters and reliability function for the two-parameter Weibull distribution under the type-II progressively censoring schemes are derived when a shape parameter is known and unknown, respectively. Efficiencies for above estimators are also compared each other in terms of the mean square errors, and Bayes risk sensitivities of the Bayes estimators are investigated.

• Communications for Statistical Applications and Methods
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• v.29 no.6
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• pp.665-677
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• 2022

This paper proposes a new estimation method based on the maximum product of spacings for estimating unknown parameters of the three-parameter Weibull distribution under a generalized Type-II progressive hybrid censoring scheme which guarantees a constant number of observations and an appropriate experiment duration. The proposed approach is appropriate for a situation where the maximum likelihood estimation is invalid, especially, when the shape parameter is less than unity. Furthermore, it presents the enhanced performance in terms of the bias through the Monte Carlo simulation. In particular, the superiority of this approach is revealed even under the condition where the maximum likelihood estimation satisfies the classical asymptotic properties. Finally, to illustrate the practical application of the proposed approach, the real data analysis is conducted, and the superiority of the proposed method is demonstrated through a simple goodness-of-fit test.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.201-206
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• 2003

This study is test for STS304 specimen using bending and torsion state. Rounded specimen and notched specimen including fracture surface investigation was comparatively experimented, fatigue life according to degree of surface finishing was examined. Fatigue fracture probability of notched canilever specimens were predicted by P-S-N curve, median rank and Weibull distribution. And at the relation with the rotational speed and stress, the fatigue life of the test specimen was higher at high speed than low speed If summarize STS304 torsion result of fatigue test, is as following. Fatigue life prediction was available by Weibull statistics distribution, and 50% breakdown probability correlation equation was appeared as following.

• Journal of Power System Engineering
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• v.21 no.5
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• pp.79-85
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• 2017

Vickers hardness is an important material in the design and reliability is required. Therefore, these values are very important as the basic data for design, manufacture and development, and the identification of quantitative probability distribution characteristics such as mean and dispersion is a very important parameter in design. In this study, Vickers hardness was measured after artificially heat-treated in the temperature range 753K, where chrome depletion near the grain boundary occurred for three kinds of stainless steels, and the Vickers hardness were evaluated. From the results, Vickers hardness increased with increasing heat treatment temperature. In Weibull distribution for Vickers hardness, the dispersion of STS310S at 813K and 873K was small, and the dispersion of STS316L at 753K, 933K and 993K was small. Also, STS347H exhibited the lowest dispersion at 753K in three kinds of stainless steels. The scale parameter increased with increasing heat treatment temperature in three kinds of stainless steels.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.39-48
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• 2009

Fisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference which derives to the posterior distribution using a noninformative prior distribution and is an example of metric functions in geometry. The more parameters for estimating in a distribution are, the more complicate derivation of the Fisher information matrix for the distribution is. In this paper, we derive to the Fisher information matrix for 3-parameters Weibull distribution which is used in reliability theory using Mathematica programs.

• Journal of Korean Society for Quality Management
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• v.9 no.1
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• pp.3-11
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• 1981

A stress-strength model is formulated for s of k systems consisting of identical components. We consider minimum variance unbiased (MVU) estimation of system reliability for data consisting of a random sample from the stress distribution and one from the strength distribution when the two distirubtions are Weibull with unknown scale parameters and same known shape parameter. The asymptotic distribution of MVU estimate of system reliability in the model is obtained by using the standard asymptotic properties of the maximum likelihood estimate of system reliability and establishing their equivalence. Uniformly most accurate unbiased confidence intervals are also obtained for system reliability. Empirical comparison of the two estimates for small samples is studies by Monte Carlo simulation.

• Wind and Structures
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• v.19 no.4
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• pp.371-387
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• 2014

Probability plotting positions are popular and used as the basis for distribution fitting and for inspecting the quality of the fit because of its simplicity. The plotting positions that lead to excellent approximation to the mean of the order statistics should be used if the objective of the fitting is to estimate quantiles. Since the mean depends on the sample size and is not amenable for simple to use closed form solution, many plotting positions have been presented in the literature, including a new plotting position that is derived based on the weighted least-squares method. In this study, the accuracy of using the new plotting position to fit the Gumbel distribution for estimating quantiles is assessed. Also, plotting positions derived by fitting the mean of the order statistics for all ranks is proposed, and an approximation to the covariance of the order statistics for the Gumbel (and Weibull) variate is given. Relative bias and root-mean-square-error of the estimated quantiles by using the proposed plotting position are shown. The use of the proposed plotting position to estimate the quantiles of annual maximum wind speed is illustrated.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.325-337
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• 2017

In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponential-Poisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.

• Journal of Communications and Networks
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• v.11 no.3
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• pp.240-247
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• 2009

The results of performance analysis by adopting the channel scenarios characterized as Weibull fading for an multicarrierdirect sequence-coded division multiple access (MC-DS-CDMA) system are proposed in this investigation. On the other hand, an approximate simple expression with the criterion of bit error rate (BER) versus signal-to-noise ratio (SNR) method is derived for an MC-DS-CDMA system combining with maximal ratio combining (MRC) diversity based on the moment generating function (MGF) formula of Weibull statistics, and it associates with an alternative expression of Gaussian Q-function. Besides, the other point of view on the BER performance evaluation of an MC-DS-CDMA system is not only the assumption of both single-user and multi-user cases applied, but the phenomena of partial band interference (PBI) is also included. Moreover, in order to validate the accuracy in the derived formulas, some of the system parameters, such as Weibull fading parameter (${\beta}$), user number (K), spreading chip number (N), branch number (L), and the PBI (JSR) values, etc., are compared with each other in the numerical results. To the best of author's knowledge, it is a brand new idea which proposes the evaluation of the system performance for an MC-DS-CDMA system over the point of view with Weibull fading channel.