Light-emitting diode (LED) lamp has received great attention as a potential replacement for the more commercially available lighting technology, such as incandescence and fluorescence lamps. LED which is the main component of LED lamp has a very long lifetime. This means that no or very few failures are expected during LED lamp testing. Therefore, degradation testing and modelling are needed. Because the complexity of modern lighting system is increasing, it is possible that more than one degradation failures dominate the system reliability. If degradation paths of the system's performance characteristics (PCs) tend to be comonotone there is a likely dependence between the PCs because of the system's common usage history. In this paper, a bivariate constant stress degradation data model is proposed. The model accommodates assumptions of dependency between PCs and allows the use of different marginal degradation distribution functions. Consequently, a better system reliability estimation can be expected from this model than from a model with independent PCs assumption. The proposed model is applied to an actual LED lamps experiment data.