Comparing three estimators of fuzzy reliability for one scale parameter Rayleigh distribution

This paper deals with comparing three different estimators of fuzzy reliability estimator of one scale parameter Rayleigh distribution were first of all the one scale parameter Rayleigh is defined. Afterwards, the cumulative distribution function is derived, as well as the reliability function is also found. The parameters θ is estimated by three different methods, which are maximum likelihood, and moments, as well as the third method of estimation which is called percentile method or Least Square method, where the estimator (\hat{\vartheta}_{pec}) obtained from Minimizing the total sum of the square between given C DF, and one non-parametric estimator like \hat{F}(ti,\theta)=\frac{i}{n+۱} after the estimator of (\theta), which (\hat{\theta}) is obtained. We work on comparing different fuzzy reliability estimators and all the results are explained besides different sets of taking four sample sizes (n= ۲۰, ۴۰, ۶۰, and ۸۰).

Keywords:

Fuzzy Reliability Estimator (FRE) , Least Square Estimators (LSE) , Maximum Likelihood Estimator (MLE) , Moments estimator (MOM) , Rayleigh distribution