The Gamma constant-stress accelerated degradation model is a natural model for monotonous degradation processes. However, unit heterogeneity often exists in practice, necessitating a more realistic model. This study develops a Gamma process with random effects to accurately capture accelerated degradation data for reliability analysis, encompassing both point and interval estimation. First, the Expectation-Maximization (EM) algorithm is developed to obtain point estimates of the proposed model. Since these estimates are sensitive to initial values, potentially impacting the outcomes, an improved EM algorithm is proposed, which iteratively refines the estimation quality by executing two different M-steps, thereby enhancing overall estimation accuracy. Secondly, given the complexity of the model and the constraint of small sample sizes and limited stress levels, a three-step interval estimation method is devised. This method segregates the parameters into three distinct parts and addresses them individually using the generalized pivotal quantity method, which simplifies the parameter interval estimation process and enhances the estimation accuracy. Finally, simulation studies and a real example of O-rings are presented to demonstrate the effectiveness of the proposed method.

Superior thermal quenching and degradation of phosphors are required for long lifetime lighting devices, such as light-emitting diodes, which can be realized through composition modification. Here, Al-N bonds in AlON: Eu²⁺ phosphors are substituted by higher bond order of Si-C. Photoluminescence (PL) results show thermal quenching (at 150 °C) and thermal degradation (after 600 °C treatment in air) are improved by 5% and 8% with a small decrease of PL intensity in 5% SiC doped AlON: Eu²⁺ phosphor. To explain these observations, first-principles computational study was performed to understand the Si and C configuration in AlON:Eu²⁺. The calculations reveal that Si and C elements are not randomly distributed in AlON lattice. It was found that Si prefers occupying tetrahedral sites (Td-Si) and the insertion of C in Td-Si is always energetically favorable, which results in the formation of SiC₄ and SiNC₃ clusters. Thus, the Al-N substitution by Si-C induces a stronger local structure, which accounts for the emission redshift and better thermal stability.