Gaussian parametric failure-rate model with application to quartz-crystal device aging

A model for predicting parametric failure rate for a time-dependent normal (Gaussian) distribution is obtained in closed form. The model can be applied to any device parameter that can be modeled by a normal distribution when the parameter time-dependence is known. The model is applied to the aging law of quartz surface-acoustic-wave (SAW) devices. The parametric failure rate of a 295.6 MHz SAW filter was obtained at 75°C based on data for 80 SAW filters. The frequency and phase parameters of the population were characterized over time using an accelerated test. The example illustrates how the mean and standard deviation can be characterized over time for the parametric distribution. Then using these results for the representative lot, the model predicts the population´s parametric failure rate at use conditions. This application shows that when a characteristic parameter for a population device being investigated is normally distributed and ages in log(time), then the failure rate has a lognormal form in time, and that a sample standard deviation for time-dependent parameters is also time dependent