Upside-Down Bathtub-Shaped Log-Normal Failure Intensity Model for Repairable Systems

Purpose: This study proposes a log-normal failure intensity model for repairable systems exhibiting upside-down bathtub-shaped failure intensity functions. The maximum likelihood estimation method for estimating the model parameters is presented.<br/>Methods: The proposed log-normal model is formulated using the hazard function of the log-normal distribution. The failure occurrence process of the repairable system is assumed to follow a non-homogeneous Poisson process (NHPP).<br/>Results: A case study of Weapon System A is conducted to demonstrate that the proposed log-normal model is effective in explaining the failure intensity behavior of Weapon System A. A comparative study with other existing upside-down bathtub-shaped failure intensity models, based on the mean squared error (MSE) criterion, indicates that the proposed log-normal failure intensity model provides an appropriate representation of the failure intensity of Weapon System A.<br/>Conclusion: The proposed log-normal failure intensity model is suitable for modeling repairable systems with upside-down bathtub-shaped failure intensity characteristics.