Abstract
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.
Highlights
In many life testing experiments, the experimenter may not observe the lifetimes of all inspected units in the life test
The Rayleigh distribution is a special case of the Weibull distribution, which provides a population model useful in several areas of statistics, including life testing and reliability which age with time as its failure rate is a linear function of time
The maximum likelihood estimation of the parameter of Rayleigh distribution based on censored data has been studied extensively, traditionally it is assumed that the data available are performed in exact numbers
Summary
In many life testing experiments, the experimenter may not observe the lifetimes of all inspected units in the life test. The scheme of doubly type-II censored sampling is an important method of obtaining data in life testing experiments. Kim and Song (2010) considered the problem of estimating parameters and reliability function of the generalized exponential distribution, based on type II doubly censored sample using Bayesian viewpoints. Our objective is to devise the method for parameter estimation regarding a life-test from which the doubly type-II censored data are reported in the form of fuzzy numbers.
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