On Estimation of Rayleigh Scale Parameter under Doubly Type-II Censoring from Imprecise Data

The scheme of doubly type-II censored sampling is an important method of obtaining data in lifetime studies. Statistical analysis of life time distributions under this censoring scheme is based on precise lifetime data. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. This paper deals with the prob lem of estimating the scale parameter of Rayleigh distribution under doubly type-II censoring scheme when the lifetime observations are fuzzy and are assumed to be related to underlying crisp realization of a random sample. We propose a new method to determine the maximum likelihood estimate of the parameter of interest. The asymptotic variance of the ML estimate is then derived by using the missing information principle. Their performance is then assessed through Monte Carlo simulations. Finally, an illustrative example with real data concerning 25 ball bearings in a life test is presented.