Comparing different estimators of parameters and reliability of one distribution of failure

Abstract EN

This research deals with estimating the parameters and reliability function of the well known distribution, which represents the distribution of time to failure, called Weibull distribution, denoted by WEI (λ , θ) (λ is called the shape parameter and θ is the scale parameter).

The method of estimation are Maximum likelihood to obtain (θMLE), Minimax estimator (d*1), and the proposed Bayes estimator (d*2).

The comparison between these estimators was done through simulation experiment for three sample size (n = 25, 50, 100), and it is also applied on real life data which represent the time to failure of (30) independent machines from State Company for Cotton Industries.

From the results we fond that the best estimator for scale parameter (θ) is the Minimax estimator (d*1) compared with likelihood (θMLE) and Bayes estimator (d*2), which works on minimizing the maximum expected risk function.