Inference for exponential mean parameter under progressive Type-II censoring from imprecise lifetime

Progressively Type-II censored sampling is an important method of obtaining data in lifetime studies. Statistical analysis of lifetime distributions under this censoring scheme is based on precise lifetime data. However, in real situations all observations and measurements of progressive Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. In this paper, we consider the estimation of exponential mean parameter under progressive 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 unknown mean parameter. In addition, a new numerical method for parameter estimation based on fuzzy data is provided. Using the parametric bootstrap method, we then discuss the construction of confidence intervals for the mean parameter. Monte Carlo simulations are performed to investigate the performance of all the different proposed methods. Finally, an illustrative example is also included.