New analytical method for estimating mean life of electric power equipment based on complete and right-censored failure data (original) (raw)

An analytical method to estimate the Weibull parameters for assessing the mean life of power equipment

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.

A New Four-Parameter Weibull Distribution with Application to Failure Time Data

FUDMA JOURNAL OF SCIENCES, 2020

A lifetime model called Transmuted Exponential-Weibull Distribution was proposed in this research. Several statistical properties were derived and presented in an explicit form. Maximum likelihood technique is employed for the estimation of model parameters, and a simulation study was performed to examine the behavior of various estimates under different sample sizes and initial parameter values. Through using real-life datasets, it was empirically shown that the new model provides sufficient fits relative to other existing models.

Statistical analysis of lifetime data using new modified Weibull distributions

2014

The Weibull distribution is a popular and widely used distribution in reliability and in lifetime data analysis. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. Many modifications of the Weibull distribution have achieved the above purpose. On the other hand, the number of parameters has increased, the forms of the survival and hazard functions have become more complicated and the estimation problems have risen.This thesis provides an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution, which could serve as an important reference and encourage further modifications of the Weibull distribution. Four different modifications of the Weibull distribution are proposed to address some of the above problems using different techniques. First model, with five parameters, is constructed by considering a two-component serial system with one component following a Weibull...

Parameters Estimation of the Modified Weibull Distribution

2009

AbstractRecently, Sarhan and Zaindin (2008) introduced a generalization ofthe Weibull distribution and named it as modiļ¬ed Weibull distribution.In this paper, we deal with the problem of estimating the parametersof this distribution based on Type II censored data. The maximumlikelihood and least square techniques are used. For illustrative purpose,the results obtained are applied on sets of real data. Also, simulation isused to study the properties of the estimators derived. Keywords: Maximum likelihood, least square, linear failure rate, Rayleigh,exponential distribution 1 Introduction The exponential, Rayleigh, linear failure rate and Weibull distributions arethe most commonly used distributions in reliability and life testing, Lawless(2003). These distributions have several desirable properties and nice physicalinterpretations. Unfortunately the exponential distribution only has constantfailure rate and the Rayleigh distribution has increasing failure rate. The lin-ear failure ra...

E-Bayesian estimation of system reliability with Weibull distribution of components based on type-2 censoring

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.

Parameter estimation of the Weibull Distribution; Comparison of the Least-Squares Method and the Maximum Likelihood estimation

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.