A Markov chain model for predicting the reliability of multi-build software

Abstract

In previous work we developed a method to model software testing data, including both failure events and correct behavior, as a finite-state, discrete-parameter, recurrent Markov chain. We then showed how direct computation on the Markov chain could yield various reliability related test measures. Use of the Markov chain allows us to avoid common assumptions about failure rate distributions and allows both the operational profile and test coverage of behavior to be explicitly and automatically incorporated into reliability computation. Current practice in Markov chain based testing and reliability analysis uses only the testing (and failure) activity on the most recent software build to estimate reliability. In this paper we extend the model to allow use of testing data on prior builds to cover the real-world scenario in which the release build is constructed only after a succession of repairs to buggy pre-release builds. Our goal is to enable reliability prediction for future builds using any or all testing data for prior builds. The technique we present uses multiple linear regression and exponential smoothing to merge multi-build test data (modeled as separate Markov chains) into a single Markov chain which acts as a predictor of the next build of testing activity. At the end of the testing cycle, the predicted Markov chain represents field use. It is from this chain that reliability predictions are made.