Temperature-dependent variability in lifetime prediction of thermally activated systems

The lifetime of high-temperature systems is often controlled by thermally activated mechanisms such as diffusion. The variability in the lifetime of such systems is analyzed when the operating temperature varies according to a normal (Gaussian) distribution. Linear approximation analysis is employed to obtain simple closed from results for the probability density function (pdf) for the lifetime. The Gaussian variation in temperature is shown to transform to a log-normal distribution for the lifetime. The standard deviation of the log-normal distribution can be predicted from the activation energy, the peak temperature, and the standard deviation of the temperature distribution. Higher activation energy and lower operating temperature increase the variability of the lifetime. This approximate results is compared with the exact transformation. Lifetime experiments with incandescent tungsten lamps are compared to the theoretical prediction.