On Crevecoeur's bathtub-shaped failure rate model

Crevecoeur (1993) developed a three-parameter bathtub-shaped failure rate model that enjoys nice mathematical properties and justification from engineering perspectives. In this paper, we derive the explicit formulas for the maximum likelihood estimation (MLE) of parameters for his model applied to both non-censored data and right-censored data. Meanwhile, explicit formulas for the MLE of parameters of Xie-Tang-Goh's model (Xie et al., 2002) are given for both types of data in the paper. The results from using these two models are compared to some real data sets both in terms of AIC values and in terms of how well the intensity is fitted. We also investigate the MLE-based statistical inference including parameter confidence intervals and parameter significance test for both models. Finally, aiming at reliability-related decision-making and predicting the evolution behavior of a system, we report the relations of the reliability characteristics during the improvement phase to those of the steady service phase. A theory of system improvement limit is presented based on Crevecoeur's failure rate model.