Weighted Erlang-Truncated Exponential Distribution: System Reliability Optimization, Structural Properties, and Simulation

In this paper, we have presented a novel extension of the Erlang-Truncated Exponential distribution (ETE), called Weighted Erland-Truncated Exponential distribution (WETE), and inspected its statistical properties and application to the system reliability. We calculated the parameters estimation and the Fishers information matrix, which are important for estimating various system component reliabilities. To validate the effectiveness of WETE distribution, the performance comparisons were made using real-life data sets from earthquakes, engineering, and medical sciences. The WETE distribution provides a better fit than other existing distributions. In the context of system reliability, the probability of a system or component functioning well is shown. We have used simulations to predict a system's performance under different conditions. The results show that the maximum likelihood estimator's performance improves consistency with large sample sizes in the WETE distribution. Finally, we have discussed the application of WETE in reliability optimization problems. The optimal allocation of reliabilities components is determined using the Lagrange multiplier technique. The effectiveness of reliability optimization is evident in improved system performance. This paper also studied the structural properties of WETE, such as the likelihood ratio test, Renyi and Tsallis entropies, order statistics, and Bonferroni and Lorenz curves.