Drop fragility of the display of a smart mobile phone: weakest link failure or cumulative shock failure?

It is not unusual for portable devices to be damaged when they are accidentally dropped on hard floors. Shock tests are increasingly being used to evaluate the drop impact response of portable devices. However, the underlying failure mechanisms have not been fully theoretically explored. There are two candidate failure mechanisms that can account for the drop impact fragility of the display in a smart mobile phone during a shock test: weakest link failure and cumulative damage failure. The weakest link theory provides a basis on a Weibull distribution and the cumulative damage theory on an inverse Gaussian distribution. This article proposes a discrimination procedure for the two distribution types. The probability of correct selection is computed using asymptotic results on the ratio of the Maximum Likelihood (ML) to discriminate between the two distributions. Expressions are provided that can be used to compute the asymptotic distributions of ML estimators or their functions when there is model mis-specification. The proposed method is applied to real shock test data for smart mobile phone display modules to determine the underlying failure mechanisms.