Using the genetic algorithm to improve the survival function estimates of the Frechet-Weibull exponential distribution mixed model with a practical application.

Abstract

In this research, one of the most important failure models widely used in reliability studies and life tests when the population is heterogeneous, which is the Frechet-Weibull mixed exponential distribution, was studied. This model was discussed in some detail in terms of its importance, uses, properties and formulation, and then focusing on some estimation methods. The survival function for the most mixed distributions, where two important methods were used to estimate the survival function, namely the maximum likelihood method, and it was compared with the moment’s method. To improve the capabilities of these two methods, a genetic algorithm was used and these methods were applied to real data related to the deaths of children with leukemia for the year 2022, and both methods were proven. The survival function behaves in a decreasing manner with increasing survival times for a patient for all methods, being a monotonically decreasing function, and this matches the theoretical properties. Finally, we hope that this model will have more comprehensive applications in different fields, estimation methods, and other intelligence algorithms .