A new bounded intensity function for repairable systems

Abstract

Lifetime failure data might have a bathtub-shaped failure rate. In this study, we propose a new model based on a mixture of bounded Burr XII distribution and 2-parameter Engelhardt-Bain process, to describe a failure process including a decreasing intensity phase, an increasing phase, and an accommodation phase for repairable systems. The estimates of the model parameters are easily obtained using the maximum likelihood estimation method. Through numerical example, the results show that our proposed model outperforms other existing models, such as superposed power law process and bounded bathtub intensity process with regard to Akaike Information Criterion value.

Keywords:

• bathtub-shaped failure rate
• bounded intensity function
• maximum likelihood estimation
• repairable system

Acknowledgements

The authors are grateful for financial support from the National Science Council in Taiwan under the Grant NSC-101-2221-E011-050-MY3.