A generalized equivalent temperature model in a time-varying environment

Accelerated test is an efficient method to collect information of products by measuring performance data directly over time from the test at high stress while the collected data are used to extrapolate the information through a physically reasonable statistical model to obtain the estimate of life or long-term performance at lower stress, normal use or storage condition [12]. The frequently used stresses include use rate, voltage, humidity, pressure, especially temperature [13, 16, 23]. Long-term reliability of gold (Au) and copper (Cu) ball bonds in fineline ball grid array package under storage condition 30°C was estimated by high temperature storage bake test at elevated temperatures of 150°C, 175°C and 200°C [8]. Wang predicted the storage life of aerospace electromagnetic relay under storage temperature 25°C -32°C based on auto-regressive and moving average model and wavelet transform model [21]. Anisotropic magnetoresistive read sensors were exposed to elevated temperatures to estimate end-of-life conditions under normal operating temperatures [5]. Huang predicted the life of tantalum capacitors under working temperature which was specified as 35°C [4]. Vakulov studied the properties changing in storage condition by accelerating ageing test on the example of rubbers К-14-1 and К-14-2 [18]. From the examples above, a common phenomenon is observed that the temperature in storage condition or normal operating is often assumed as a constant temperature [7](e.g. 25°C,30°C), or a temperature interval. However, the temperature in real storage or operating condition often varies with the season and region. For some long-life products, a minor temperature difference may lead to a major difference in the result of life assessment. As a result, it is important to consider the impact of the changing temperature appropriately. Particularly, it is of interest to wonder whether there is a temperature under which the life or performance of the product is equal to the life or performance at real storage or operating temperature. This issue consists of the primary goal of this paper, proposing an equivalent temperature model. In literature, a substantial number of degradation models have been developed to model the accelerated degradation data [10]. In general, these existing models can be divided into linear and nonlinear Li Sun Xiao-Hui Gu Pu SonG Yi Di