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This paper develops a new family of estimators, the minimum density powerdivergence estimators (MDPDEs), for the parameters of the one-shot device modelas well as a new family of test statistics, Z-type test statistics based onMDPDEs, for testing the corresponding model parameters. The family of MDPDEscontains as a particular case the maximum likelihood estimator (MLE) consideredin Balakrishnan and Ling (2012). Through a simulation study, it is shown thatsome MDPDEs have a better behavior than the MLE in relation to robustness. Atthe same time, it can be seen that some Z-type tests based on MDPDEs have abetter behavior than the classical Z-test statistic also in terms ofrobustness.

Robust Estimators and Test-Statistics for One-Shot Device Testing Under the Exponential Distribution