Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes

Many highly reliable products usually have complex structure, with their reliability being evaluated by two or more performance characteristics. In certain physical situations, the degradation of these performance characteristics would be always positive and strictly increasing. In such a case, the gamma process is usually considered as a degradation process due to its independent and non-negative increments properties. In this paper, we suppose that a product has two dependent performance characteristics and that their degradation can be modeled by gamma processes. For such a bivariate degradation involving two performance characteristics, we propose to use a bivariate Birnbaum–Saunders distribution and its marginal distributions to approximate the reliability function. Inferential method for the corresponding model parameters is then developed. Finally, for an illustration of the proposed model and method, a numerical example about fatigue cracks is discussed and some computational results are presented.