Two new multi-phase reliability growth models from the perspective of time between failures and their applications

Aviation products would go through a multi-phase improvement in reliability performance during the research and development process. In the literature, most of the existing reliability growth models assume a constant failure intensity in each test phase, which inevitably limits the scope of the application. To address this problem, we propose two new models considering time-varying failure intensity in each stage. The proposed models borrow the idea from the accelerated failure-time models. It is assumed that time between failures follow the log-location-scale distribution and the scale parameters in each phase do not change, which forms the basis for integrating the data from all test stages. For the test-find-test scenario, an improvement factor is introduced to construct the relationship between two successive location parameters. Whereas for the test-fix-test scenario, the instantaneous cumulative time between failures is assumed to be consistent with Duane model and derive the formulation of location parameter. Likelihood ratio test is further utilized to test whether the assumption of constant failure intensity in each phase is suitable. Several applications with real reliability growth data show that the assumptions are reasonable and the proposed models outperform the existing models.