Physical Sciences and Mathematics Commons^™

Detection And Estimation Of A Mixture In Power Law Processes For A Repairable System, Ni Wang, Paul Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

The power law process has proved to be a useful tool in characterizing the failure process of repairable systems. This paper presents a procedure for detecting and estimating a mixture of reliable and unreliable (defective) systems. The test of a mixture, based on a simple likelihood ratio, is illustrated with truncated failure data for copy machines. Bootstrap methods are used to gauge the estimation uncertainty, and optimal decisions for system replacement are determined based on the observed likelihood.