## 1 Introduction  
Since the development of multi-layer organic light-emitting diodes (OLEDs) in 1987 [1], the device performance has been improved tremendously over the past decades. Owing to the merits of organic materials and improvements of their efficiencies, the application of OLEDs is widespread and anticipated to be expanded even further [2, 3]. Despite the advantages compared with inorganic counterparts, however, the utilization of OLEDs is sometimes limited by their reliabilities. Especially, OLEDs are vulnerable to environments such as water vapor and oxygen [4]. Hence, remedies to enhance the storage lifetime shortened by the external factors have been pursued intensely and a significant progress has been made [5]. With the strict standards, the encapsulation of OLEDs has now become quite reliable for harsh environments. Thus, the degradation during the device operation requires more attention to improve the device reliability further.  
In general, the monitoring of luminance reduction is used to evaluate how fast the device degrades [6]. The degradation curve is empirically fitted with a stretched exponential decay function [7]. The device lifetime, which is defined, for example, as the elapsed time when the luminance is decreased to the half of its initial value, follows the power law depending on the aging current [6]. This method can be applied universally as there is no assumption involved for the test. However, physical foundation on the properties of the luminance decay is not considered sufficient. Moreover, the dominant cause of the device degradation cannot be determined from this empirical evaluation.  
The chemical analyses to clarify the OLED degradations have also been used popularly [8, 9]. These methods examine the chemical products after the acceleration test. By investigating the chemical products inside the device, one can guess a chemical reaction involved during the device operation. However, these analyses require destructive prob-ings after which the device does not function any longer. Also, they take additional time as the OLED devices contain many different kinds of chemicals from the deposition of multi-layer structures.  
Taken together, the methods described above can give a clue why the device has degraded. However, characterization and understanding of the performance degradation from the device point of view is necessary and beneficial in industry. The device analyses and modeling based on the physical mechanisms can give more insights into how the device degrades than the conventional chemical reaction or decomposition suggests. For this purpose, introducing quantitative factors from the electrical and optical properties of OLEDs [10, 11] is essential in evaluating how the device degradation progresses. From the analyses, the direction for further enhancing the device performance can also be determined, which leads to save resources and time.  
In this paper, we analyze the transient behavior of the OLED device characteristics under electrical stress, where both the current and luminance at a given voltage initially increase before the degradation occurs. The quantitative factors are used to characterize how the device behaves under electrical stress and a model that can explain this observation is presented.