Abstract
Statistical analysis of lifetime distributions under Type-II censoring scheme is based on precise lifetime data. However, in real situations all observations and measurements of Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. This paper deals with the estimation of exponential mean parameter under 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 use Newton-Raphson algorithm as well as EM algorithm to determine the maximum likelihood estimate (MLE) of parameter. We also obtain the estimate, via moment method and Bayesian procedure, of the unknown parameter. In addition, a new numerical method for parameter estimation is provided. Monte Carlo simulations are performed to investigate performance of the different methods. Finally, an example is presented in order to illustrate the methods of inference discussed here.
Highlights
In life testing and reliability studies, the experimenter may not always obtain complete information on failure times for all experimental units
Their research results for estimating parameters of different lifetime distributions under Type-II censoring are limited to precise data
The problem of estimation of exponential mean parameter based on the censored data has been studied extensively, traditionally it is assumed that the data available are performed in exact numbers
Summary
In life testing and reliability studies, the experimenter may not always obtain complete information on failure times for all experimental units. Data obtained from such experiments are called censored data. One of the most common censoring scheme is Type-II (failure) censoring, where the life testing experiment will be terminated upon the r-th (r is pre-fixed) failure. The lifetime observations may be reported as imprecise quantities such as: ’about 1000h’, ’approximately 1400h’, ’almost between 1000h and 1200h’, ’essentially less than 1200h’, and so on. This imprecision is different from variability and errors. We need suitable statistical methodology to handle these data as well
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