In this work, we propose a novel generator called the "extended odd inverse Weibull-generator" to obtain better distribution flexibility. This generator is considered as a generalization of the three well-known families. In comparison to the baseline model, the newly formed family may offer more efficient continuous symmetric and asymmetric models. The statistical features of the proposed family are analyzed, including quantile function, moments, incomplete moments, mean deviation, density function expansion, order statistics and entropy measures. The generated family is used to give a number of well-known models as special cases. We use the Weibull distribution as a baseline model and fully study a five-parameter special member of the extended odd inverse Weibull-G family. In order to evaluate the behavior of the parameter estimates, the point and interval estimation parameters are examined using both Bayesian and non-Bayesian methods. In both symmetric and asymmetric loss functions, Bayes estimates are computed using the Markov Chain-Monte-Carlo method. The effectiveness of the suggested estimators is evaluated using Monte Carlo simulations and certain criterion metrics. Two time between failure data sets are considered in order to apply the extended odd inverse Weibull Weibull distribution. We have demonstrated that, utilizing specific criteria for model selection and goodness of fit test statistics, the suggested model performs better than six other existing models.