Multi-phase reliability growth test planning for repairable products sold with a two-dimensional warranty

For products sold with a two-dimensional warranty policy, the warranty servicing cost can be reduced through reliability growth during development. This paper investigates a multi-phase reliability growth test program for repairable products with independent competing failure modes. Considering a test-find-test scheme, an accelerated reliability growth model is developed, allowing different failure modes having distinct accelerated relationships. Taking usage heterogeneity and mode-specific failure learning effect into account, the reliability growth is achieved through periodic fixes on a phase-by-phase basis. From the manufacturer's perspective, the main objective is to achieve the optimal trade-off between the warranty cost and the reliability growth test cost by determining the optimal test program that minimizes the expected total cost per product sold, ensuring that the pre-specified reliability growth requirement is met. Assuming the tri-Weibull product failure distribution, we illustrate the proposed optimization model numerically and study the effect of relevant parameters on the optimal reliability growth test program. The results show that the proposed approach yields significant cost reduction and reliability improvement for the examples studied in this paper, especially when the manufacturer possesses high failure learning ability, and the product has expensive repair cost per a warranty failure and extensive warranty coverage.