Recently I started reading some publications about reliability analysis, and I found that The Weibull analysis is a powerful technique. My question is about estimation the parameters of weibull, which method do you recommend?
I guess "Weibull Distribution" equations has extensively been used in MOSFETs Reliability Degradation Estimation Analysis for NBTI, HCI,TDDB and EM . The equation changes according to every method.
The Weibull Distribution has also been used in Reliability assessment for Power systems and in many other reliability analysis fields.
What are your objectives? Relibaility Degradation Estimation for MOSFETs or for some other application?
In the aim of the wind resource assessment, there are various methods, both numerical and graphic, for estimating the parameters of the Weibull probability distribution function. However, the maximum likelihood method (MLM) has proved to be the most efficient in several studies.
Not especially for MOSFETs, but for other equipment in the industry. For instance identifying the reliability characteristics of WTG.
You first of all need to determine what factors (covariates) affect the reliability and incorporate them into your model: e.g. time to event, average wind speed, number of gusts in an interval, design changes?, maintenance intervals, other design parameters, etc then fit a proportional hazards model to the covariates and then apply a Weibull plot to the hazards. This is available in some packages. However, I tend to do the probability plots by hand (using Chartwell paper) because the data might not be a straight line. Packages assume that the data fits a nice two or three parameter model but real data may have more than one failure mode (two straight lines for two failure modes), curvature (minimum life or inappropriate Weibull distribution) which tell you a lot more about the system being tested.
Weibull is an extreme value distribution. If the physical process is not "weakest link in a chain" then Weibull is not the right distribution to use. Many use it because it fits many curves well, but if it fits everything, it tells you nothing.
Weibull is perhaps the most improperly used distribution in the box of distributions at our disposal. If the physical process is not suitable for an extreme value distribution Weibull should not be used. Remember, you are extrapolating well beyond what is experimentally accessible.
Dear Nihad;
There is many Non-Bayesian (Classical) methods for estimating the Reliability function of Weibull distribution, such as the Maximum likelihood estimator (which has invariant property) and the Uniformly minimum variance unbiased estimator. Also you can use Bayesian method under different loss function as Quadratic loss function or any other loss function (You can use many prior as gamma prior), then, you should use a simulation in Monte Carlo method to compare the different methods that are used to estimate the Reliability function of Weibull distribution with different cases of which sample sizes and replications and different values for each of the shape and the scale parameter of the distribution whose results were evaluated using a statistical measures of mean squares error (MSE) or integral mean squares error (IMSE).
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