To mitigate the seriousness of robustness problem, weighted minimum density power divergence estimator, which is a natural extension of the maximum likelihood estimator, can be used as a robust estimator, as it has a better behavior than the maximum likelihood estimator in case of departures from the assumed model. This chapter presents the framework for the development of robust estimators for exponential, gamma, and Weibull lifetime distributions for one-shot devices. Wald-type tests based on them are also presented for one-shot device testing data collected from constant-stress accelerated life-tests. Extensive simulation studies are carried out to examine the behavior of the weighted minimum density power divergence estimators of model parameters and the robustness of Wald-type tests with 𝛿 = 0.05 level of significance for various sample sizes, different values of tuning parameter and different lifetime distributions. The chapter considers the glass capacitors data with R code.