A decreasing failure rate model with a novel approach to enhance the artificial neural network's structure for engineering and disease data analysis

The study focuses on key metrics used to examine the characteristics of a lifetime random variable distribution in reliability and survival theory research. In this analysis, metrics including the probability density function time, mean residual lifespan, mean time between failures, hazard rate, and reliability function are essential. The focus of the inquiry is these important parameters in relation to the Burr-Hatke exponential model specifically. The study focuses on key metrics used to examine the characteristics of a lifetime random variable distribution in reliability and survival theory research. In this analysis, metrics including the probability density function time, mean residual lifespan, mean time between failures, hazard rate, and reliability function are essential The focus of the inquiry is these important parameters in relation to the Burr-Hatke exponential model specifically. A key component of the research is a comparison of the outcomes from the artificial intelligence approach and those from conventional literature-based methodologies. This comparison study sheds light on how well the artificial neural network framework performs while evaluating the Burr-Hatke exponential model's technical features. The study allows a comprehensive analysis of the training and prediction capabilities of the growing neural network by calculating multiple performance measures. This comprehensive strategy improves our comprehension of the model's survival traits and reliability, offering significant contributions to the larger field of study. The network structure's mean square error was estimated to be 5.19E-04, and its coefficient of determination value was 0.99987 for the first neural network model. For the second neural network model, the coefficient of determination value was 0.99999 and the mean square error value was 4.58E-06. The outcomes amply revealed the neural network structure's extraordinarily high prediction accuracy and the degree to which the prediction outputs agree with those of the Maximum Likelihood Estimation technique.