Studying failure data requires a flexible distribution to interpret the probabilistic behavior of these data. Therefore, the reliability function of the Alpha–Power Fréchet (APF) distribution was used to study the failure data. The Alpha power transformation was applied to the classical Fréchet distribution to develop a more flexible model capable of handling heterogeneous datasets. The probability density function, cumulative distribution function, and the corresponding reliability function for the APF distribution were derived. The maximum likelihood method and the genetic algorithm were used to estimate the reliability function of the Alpha–Power Fréchet distribution. A simulation study was conducted with various sample sizes (ranging from n=15 to n=500) and multiple different parameter combinations to evaluate the performance of both estimators. The comparison was based on the Mean Squared Error (MSE) criterion. The results revealed that the maximum likelihood method (MLE) showed a decrease in MSE values directly proportional to the increase in sample size, confirming its consistency and superior accuracy for large samples. Meanwhile, the genetic algorithm (GA) showed a robust performance that outperformed the maximum likelihood method for small and medium samples, making it a viable alternative in such cases, despite a noted tendency to slightly overestimate the reliability value.
Keywords
Alpha Power Fréchet. Power AlphaReliabilityMaximum LikelihoodGenetic Algorithm.
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