The distribution of failures is crucial in reliability engineering, and the applicability of a single distribution is limited. In complex systems, a mixture distribution is more appropriate. This article introduces the 3CAW distribution, which provides a more flexible failure rate function, especially a bathtub-shaped failure rate with a long constant region, which is suitable for more complex systems. This article discusses the use of maximum likelihood estimation to estimate the unknown parameters of the 3CAW distribution, and calculate reliability and failure rate as reliability indicators. The cross-entropy method is used to find the global optimum of the logarithmic likelihood function and compare it with single distributions such as the Weibull distribution. The results show that although the model is complex, it has the highest logarithmic likelihood function value and the highest fitting accuracy. The cross-entropy method reduces the difficulty of parameter estimation, making it worth further promotion in engineering practice.