Testing the Adequacy of a Semi-Markov Process

• Activity Number: 140
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Richard Seymour* and Christine Schubert Kabban and Gilbert Peterson and Richard Warr
• Companies: and Air Force Institute of Technology and Air Force Institute of Technology and Air Force Institute of Technology
• Keywords: Semi-Markov Process ; Goodness of Fit

Abstract

Semi-Markov processes, which are commonly used for multi-state modeling, lack an effective test to determine if the process accurately models the sample data. To overcome this shortcoming, we present a test that assesses the goodness of fit for a semi-Markov process. This goodness of fit test utilizes the covariance structure of the model to determine whether or not the model could have generated the sample data by comparing the observed to the expected values of the transitions. This test requires expectations generated by Laplace transformations and a simulated model covariance matrix. The final test statistic follows a non-central Chi-squared distribution. Simulation testing demonstrates that the test can differentiate between similar hypothesized models for a given observed data set. Because this test was developed for the generalized class of models, it can be directly applied to continuous-time Markov chains in addition to any of the more specific models that exist in this class.