Performance analysis of classical and fuzzy series components system of reliability estimation of New X-Lindley distribution simulation with comparative

This paper deal with analysis of classical and fuzzy series components systems of reliability shortly respectively R_s and R_Fs, based on estimation of these systems for New X –Lindley (NXL) distribution using eight different techniques. The techniques used include maximum likelihood estimation (MLE), weighted least squared (WLS), Approximate least squared (ALS), precise moments Method (PMM), percentile estimation (PE), and three shrinkage (Sh1, Sh2, and Sh3) techniques. Monte Carlo simulation is applied to test the performance of these techniques in estimating classical and fuzzy series distribution systems and analyze their accuracy according to criteria as mean absolute percentage error (MAPE), mean square error (MSE), and bias. The proofs of these distribution systems are presented, and then the extent of the impact of fuzziness in series components systems data on the estimation results is evaluated. This study founded that the performance of estimation techniques varied dependent on sample size, with MLE, Sh2, and Sh3 being the most accurate according to the evaluation criteria used. The results also showed that some traditional techniques, as WLS and ALS, suffer from greater bias when using fuzzy data, highlighting the impact of fuzzy estimation on the results of statistical models.