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.
A new method to evaluate mean life of power system equipment
IET Conference Publications, 2009
Traditional statistical reliability analysis relies on failure data for a population of devices. If a complete data set is available (i.e., failure ages are known for each device within the population), statistical reliability analysis can provide predictions, such as mean-time-to-failure for a particular device, percentages of devices that will fail at a particular time or before a particular age, a statistical distribution of failure ages, and other statistical measures of device failures. However, a typical population includes devices that have not yet failed, termed "suspensions". In reliability analysis, such populations are often denoted as "right censored populations". In this paper, we propose a new method to evaluate mean life of power system equipment with limited end-of-life failure data. The method is based on the generalized exponential distribution. This method can be used as an alternative to methods based on normal and Weibull distribution models.
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An important topic in the manufacturing industries is the assessing of the lifetime performance. In this paper, it is supposed the lifetimes of products are independent and have a common Weibull distribution with a known shape parameter. The lifetime performance index (C L) proposed by Montgomery (1985) [1], is used for evaluating the performance of a process with respect to a lower specification limit (L). The maximum likelihood estimate of C L is obtained on the basis of the progressive first-failure censored data. This estimate is then used for developing a confidence interval for C L. The behavior of the confidence interval for the parameter C L given a significance level is investigated and also two illustrative examples and a sensitivity analysis are given. For the exponential distribution as a special case of Weibull distribution, a comparison study for various estimates of C L based on mean squared error (MSE) and Pitman measure of closeness (PMC) criteria is done.
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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.
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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...
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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...
A generalized modified Weibull distribution for lifetime modeling
Computational Statistics & Data Analysis, 2008
A four parameter generalization of the Weibull distribution capable of modeling a bathtubshaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution.
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.
Reliability estimation in a Weibull lifetime distribution with zero-failure field data
Quality and Reliability Engineering International, 2010
The estimation of product reliability has attracted worldwide attention during the past several decades. The estimation procedure usually begins with parameter estimation based on test data. When there is no failure occurring in tests, traditional approaches like Maximum Likelihood Estimation (MLE) cannot be applied to estimate parameters. When product lifetime follows a Weibull distribution, to cope with this problem, we propose the modified MLE (MMLE) for estimating the parameters, based on the zero-failure data. In this paper, we also consider the prior reliability estimate from a similar product and make use of it by incorporating it with the MMLE to construct the shrinkage preliminary test estimator (SPTE). We present the calculation method of the shrinkage factor in the SPTE, by referring to the comparison of critical quality characteristics related to product reliability, between the current batch of products and the similar (or earlier version) batch of products. Restrictions for the shrinkage factor to ensure the performance of SPTE are also discussed. The example demonstrates that the proposed SPTE of the product reliability is an effective methodology to estimate the product reliability and improve the estimation performance of the MMLE, when only zero-failure data are available.
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.