On the Development of Fuzzy Estimators for Life Time Distributions based on Censored Fuzzy Life Times

Abstract

Lifetime analyses comprise the techniques dealing with observations obtained from the occurrence of a specified event(s). In most of the situations dealing with lifetime observations, some units are recorded as censored observations. Dealing with censored observations makes these techniques unique. Countless standard statistical tools are available for inference based on censored lifetime observations. These classical techniques consider lifetime observations as precise numbers and ignore the uncertainty of single observations. Whereas in practical applications it is not possible to measure life times as precise numbers, they are always more or less nonprecise. The imprecision in measurements can be covered by neutrosophic set. Fuzzy estimators for life time distributions potentially use neutrosophic system to model and analyze the inherent uncertainties and neutalities present in the data and the parameter estimates. This study aimed to obtain estimators for the Weibull parameters and two exponential parameters based on the up-to-date fuzzy number approach, a special case for neutrosophic set. The suggested estimators incorporate fuzziness in addition to random variation, which makes these estimators more realistic. The same techniques need to be extended to fuzzy and neutrosophic sets.