Meeker introduced the concept of limited failure population (LFP) while studying integrated circuits, where most devices exhibit a near-zero probability of failure throughout their technological life, while a small subset contains latent defects that manifest only after prolonged operation. In this article, we extend the LFP framework to the context of one-shot device testing, wherein devices get destroyed or must be rebuilt after testing. We propose a model that incorporates a relationship between defect probability and a set of covariates and develop an expectation–maximization algorithm for estimating the model parameters. The effectiveness of the proposed method is then assessed through a Monte Carlo simulation study, assuming the lifespan of defective devices follow a log-location-scale distribution. Finally, the developed methods are applied to three real datasets.

Robust estimators and Wald-type tests are developed for the multinomial logistic regression based on$\phi $-divergence measures. We compute the influence function of the proposed estimators and tests and discuss some consequences. Their robustness is illustrated by an extensive simulation study and two real examples.

In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) with non-random covariates. While the classical methods are based on the maximum likelihood estimator (MLE), it is well known its lack of robustness to small deviations from the assumed conditions. In this paper, and based on the Rényi’s pseudodistance (RP), we introduce a new family of estimators in case our information about the unknown parameter is given for i.n.i.d.o.. This family of estimators, let us say minimum RP estimators (as they are obtained by minimizing the RP between the assumed distribution and the empirical distribution of the data), contains the MLE as a particular case and can be applied, among others, to the MLRM with non-random covariates. Based on these estimators, we introduce Wald-type tests for testing simple and composite null hypotheses, as an extension of the classical MLE-based Wald test. Influence functions for the estimators and Wald-type tests are also obtained and analysed. Finally, a simulation study is developed in order to asses the performance of the proposed methods and some real-life data are analysed for illustrative purpose.

In this article, we develop robust estimators and tests for one-shot device testing under proportional hazards assumption based on divergence measures. Through a detailed Monte–Carlo simulation study and a numerical example, the developed inferential procedures are shown to be more robust against data contamination than the classical procedures, based on maximum likelihood estimators.

Classical inferential methods for one-shot device testing data from an accelerated life-test are based on maximum likelihood estimators (MLEs) of model parameters. However, the lack of robustness of MLE is well-known. In this article, we develop robust estimators for one-shot device testing by assuming a Weibull distribution as a lifetime model. Wald-type tests based on these estimators are also developed. Their robustness properties are evaluated both theoretically and empirically, through an extensive simulation study. Finally, the methods of inference proposed are applied to three numerical examples. Results obtained from both Monte Carlo simulations and numerical studies show the proposed estimators to be a robust alternative to MLEs.

This paper develops a new family of estimators, the minimum density power divergence estimators (MDPDEs), for the parameters of the one-shot device model as well as a new family of test statistics, Z-type test statistics based on MDPDEs, for testing the corresponding model parameters. The family of MDPDEs contains as a particular case the maximum likelihood estimator (MLE) considered in Balakrishnan and Ling (2012). Through a simulation study, it is shown that some MDPDEs have a better behavior than the MLE in terms of robustness. At the same time, it can be seen that some Z-type tests based on MDPDEs have a better behavior than the classical Z-test statistic in terms of robustness, as well.