This study aims to investigate the estimation of the parameters of the inverse exponential Rayleigh distribution using the Maximum Likelihood Estimation (MLE) and Ranked Set Sampling (RSS) methods, on account of their importance in modeling across lifespan and reliability data. The model is used on empirical data representing the fracture stress of carbon fibers for both single and saturated fibers, in order to determine the accuracy of the estimation methods in given applications. In addition, the classical model is expanded to a fuzzy model to focus on inherent uncertainty in real-world applications. This is realized by designing fuzzy numbers using Shih-skewed membership functions, which offer greater flexibility in illustrating asymmetry in the data. Yager algorithms are used to transform fuzzy values into crisp and clear estimates. At the end, the key distributional functions, consisting of the probability density function, cumulative distribution function, survival function, and hazard function, are derived and analyzed under both classical and fuzzy approaches. Finally, the accuracy of the estimation methods is tested with the Mean Squared Error (MSE), where the result suggests that the RSS method excels the MLE method, in particular when paired with fuzzy techniques, yielding more precise estimation in the face of uncertainty.
Shalan et al. (Fri,) studied this question.
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