Classical and Bayesian estimations of improved Weibull-Weibull distribution for complete and censored failure times data

In this article, we demonstrate how to enhance the Weibull-Weibull (WW) distribution introduced in the earlier literature into a better form for fitting monotone and non-monotone failure rate data, especially the bathtub-shaped failure rate data with or without a flat region. The model is referred to as an improved WW distribution. The model's flexibility enables it to describe lifetime data with various failure rate functions, including increasing, decreasing, U or V-shaped, and bathtub-shaped with a comparatively low and long-flat segment. We provide a thorough Bayesian analysis of the modified model for complete and right-censored data. Additionally, we developed maximum likelihood estimators for the model's parameters for both complete and right-censored data. The Bayesian credible and asymptotic confidence intervals of the estimators are defined, and simulation results validate the estimators' consistency. To illustrate the applications of the improved distribution with the WW and other generalized distributions, we apply one censored and one uncensored failure times data, each with bathtub-shaped failure rates. The numerical results demonstrate that the improved WW model outperforms the WW distribution and other existing models, as indicated by goodness-of-fit statistics and supported by the fitted models' survival and failure rate curves and P-P plots.