Aging-related failure rate obtained from bathtub curve data

The bathtub curve (BTC) can be viewed as an experimental reliability “passport” of a population of mass produced devices. This curve considers and reflects the combined effect of two irreversible processes: statistics-related mass-production process and reliability-physics-related degradation (aging) process. The statistics-related process results in a decreasing failure rate with time. The reliability-physics-related process leads to an increasing failure rate. This circumstance explains particularly why the steady-state portion of a BTC is characterized by a more or less constant failure rate. The statistical process can be evaluated theoretically, using a rather simple predictive model. Owing to that and assuming that the two processes are statistically independent one can assess the failure rates associated with the aging process from the BTC data by simply subtracting the predicted ordinates of the statistical process from the experimentally determined BTC ordinates. The cases when the statistical failure rate is distributed in accordance with the Rayleigh law or is normally distributed are used as illustrations of the suggested methodology. In either case it is assumed that effective burn-in has been carried out by the manufacturer, so that the BTC does not contain the infant mortality portion. The developed models can be employed when there is a need to better understand the relative roles of the statistics-related and physics-of-failure-related processes in reliability evaluations of the aerospace electronic and photonic products. The models can be used also beyond the field of aerospace engineering, and even beyond the area of electronics-and-photonics engineering, when there is a need to separate the roles of the two processes in question. One of the challenges in the future work is to determine the probability distributions of actual statistical failure rates for particular electronic, photonic or MEMS products and applications.