Power Law Selection Model for Repairable Systems

Abstract

A repairable system, under minimal repair, is usually modeled according to a Non-Homogeneous Poisson Process (NHPP) assuming a Power Law intensity function. A traditional approach considers iid NHPPs in order to conduct a statistical analysis based on a sample of systems. However, systems might be heterogeneous due to unmeasured variables such as age, suppliers, and so on. In order to verify this assumption a frequentist approach is proposed in this article. Some possible model scenarios considering different systems heterogeneity are compared using likelihood ratio tests and information criteria. Real data sets illustrate the proposed methodology.

Keywords:

• Information criteria
• Minimal repair
• Poisson process
• Recurrent events

Mathematics Subject Classification:

• Primary 62M86
• Secondary 62F86

Acknowledgments

The research of the first author was partially supported by CAPES and CNPq grants. The research of the second author was partially supported by CAPES, CNPq, and FAPIMIG grants. The research of the third author was partially supported by CAPES, CNPq, and FINATEC grants.

Notes

Degrees of freedom for χ² distribution presented in parenthesis.

Degrees of freedom for χ² distribution presented in parenthesis