The article introduces new estimators and test statistics for testing one-shot devices under the exponential distribution. These new methods, called minimum density power divergence estimators (MDPDEs) and Z-type test statistics, are shown to be more robust than traditional methods like maximum likelihood estimators (MLE) and classical Z-tests. The simulation study demonstrates that some MDPDEs perform better than MLEs in terms of robustness, and some Z-type tests based on MDPDEs outperform classical Z-tests in terms of robustness as well.