Sequential ALT plans for systems with mixture of units

Statistics-based failure models utilize the failure data to evaluate the unit's reliability but fail to consider the physics of failure process of a unit. On the other hand, physics of failure models consider the failure mechanism and evaluate the reliability based on the design and life cycle of the unit but they ignore the uncertainty in the modeling process. In this paper, we develop a physics-statistics-based failure model to investigate a system which is composed of units with different characteristics and develop sequential non-destructive tests (under either normal or accelerated conditions) to estimate its reliability. Moreover, by applying the physics-statistics-based failure model which relates the failure time directly to the applied stresses, we optimally design a sequence of non-destructive tests with accelerated stresses. As the number of units in the system becomes large, we selected samples to conduct such reliability testing. The optimal design of the test is affected by the system's status and previous test plans. The designed ALT plans can also be applied to predict the reliability of the system at the end of the tests.