New analytical method for estimating mean life of electric power equipment based on complete and right-censored failure data (original) (raw)
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The two-parameter Weibull distribution is the predominant distribution for lifetime modelling of power equipment. However, the parameter estimation methods reported in the literature require numerical or graphical techniques due to the lack of a closed-form expression for the Weibull shape parameter. Therefore, in this paper, a simple, consistent, closed-form estimator based on maximum likelihood estimate for the Weibull shape parameter is proposed. The new estimator is obtained after proving the existence and uniqueness of the solution of the estimating function. In order to assess the proposed method, two rightcensored data sets of two types of power equipment reported in the literature were used to apply the method for estimating the mean life, standard deviation and survival function. The results obtained were compared with the results from numerical and graphical based estimators. From this comparative analysis, it can be said that the proposed analytical parameter estimation method is more practical and efficient in the sense of closed-form expressions are used to estimate the shape and scale parameters.
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This paper is concerned with using the E-Bayesian method for computing estimates for the parameter and some survival time parameters e.g. reliability (series system and parallel system) and hazard functions of the Weibull distribution based on type-2 censored. The lifetimes of the components follow independent Weibull distributions with known shape parameter are assumed. The estimates are derived based on a conjugate prior for the parameter and squared error loss function. A comparison between the new method and the corresponding Bayes and maximum likelihood techniques are made using the Monte Carlo simulation.
Weibull distribution is a very useful distribution in survival analysis, lifetime analysis, and reliability analysis. Several methods have been proposed to estimate the parameters of different distributions such as the method of moment, maximum likelihood, etc. In this paper, we analyze the 2-parameter Weibull distribution by simulating data on failure times of a product using the Monte Carlo approach and estimating the parameters of the distribution using the maximum likelihood estimation (MLE) and the least-squares method (LS). These methods were also investigated through applications in reliability analysis. The two approaches of estimating the parameters were compared, and the MLE obtained better performance than the least-squares method when the results for the parameters were assessed using the goodness of fit measures. Also, we obtained the asymptotic distribution of the MLE which was asymptotically efficient as the sample size increases. The inverse of the Fisher's information matrix which is the asymptotic variance-covariance matrix was also obtained. I.