Modeling of lifetime scenarios with non-monotonic failure rates.

The Weibull distribution is an important continuous distribution that is cardinal in reliability analysis and lifetime modeling. On the other hand, it has several limitations for practical applications, such as modeling lifetime scenarios with non-monotonic failure rates. However, accurate modeling of non-monotonic failure rates is essential for achieving more accurate predictions, better risk management, and informed decision-making in various domains where reliability and longevity are critical factors. For this reason, we introduce a new three parameter lifetime distribution-the Modified Kies Weibull distribution (MKWD)-that is able to model lifetime scenarios with non-monotonic failure rates. We analyze the statistical features of the MKWD, such as the quantile function, median, moments, mean, variance, skewness, kurtosis, coefficient of variation, index of dispersion, moment generating function, incomplete moments, conditional moments, Bonferroni, Lorenz, and Zenga curves, and order statistics. Various measures of uncertainty for the MKWD such as Rényi entropy, exponential entropy, Havrda and Charvat entropy, Arimoto entropy, Tsallis entropy, extropy, weighted extropy and residual extropy are computed. We discuss eight different parameter estimation methods and conduct a Monte Carlo simulation study to evaluate the performance of these different estimators. The simulation results show that the maximum likelihood method leads to the best results. The effectiveness of the newly suggested model is demonstrated through the examination of two different sets of real data. Regression analysis utilizing survival times data demonstrates that the MKWD model offers a superior match compared to other current distributions and regression models.