A one-shot device is a unit that operates only once, after which it is either destroyed or needs to be rebuilt. For this type of device, the operational status can only be assessed at a specific inspection time, determining whether failure occurred before or after it. Consequently, lifetimes are subject to left- or right-censoring. One-shot devices are usually highly reliables. To analyze the reliability of such products, an accelerated life test (ALT) plan is typically employed by subjecting the devices to increased levels of stress factors, thus allowing life characteristics observed under high-stress conditions to be extrapolated to normal operating conditions. By accelerating the degradation process, ALT significantly reduces both the time required for testing and the associated experimental costs. Recently, robust inferential methods have gained considerable interest in statistical analysis. Among them, weighted minimum density power divergence estimators (WMDPDEs) are widely recognized for their robust statistical properties with small loss of efficiency. In this work, robust WMDPDE and associated statistical tests are developed under a log-logistic lifetime distribution with multiple stresses. Explicit expressions for the estimating equations and asymptotic distribution of the estimators are obtained. Further, a Monte Carlo simulation study is presented to evaluate the performance of the WMDPDE in practical applications.

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.

Uncertainty is defined in a new manner, as a function of discrete probability distributions satisfying a simple and intuitively appealing weak monotonicity condition. It is shown that every uncertainty is Schur-concave and conversely, every Schur-concave function of distributions is an uncertainty. General properties of uncertainties are systematically studied. Many characteristics of distributions introduced previously in statistical physics, mathematical statistics, econometrics and information theory are shown to be particular examples of uncertainties. New examples are introduced, and traditional as well as some new methods for obtaining uncertainties are discussed. The information defined by decrease of uncertainty resulting from an observation is investigated and related to previous concepts of information. Further, statistical inference about uncertainties is investigated, based on independent observations of system states. In particular, asymptotic distributions of maximum likelihood estimates of uncertainties and uncertainty-related functions are derived, and asymptotically /spl alpha/-level Neyman-Pearson tests of hypotheses about these system characteristics are presented.

In order to define a measure of the information processed by a fuzzy event and by a partition of fuzzy events, the `information energy' provided by a fuzzy event and a partition of fuzzy events is considered. This measure integrates the statistical uncertainty resulting from the occurrence of events and the uncertainty of meaning of events that is expressed by the membership function. The functional information energy if formally similar to the Onicescu's information energy, which used an analogy to kinetic energy from mechanisms, although it is conceptually different.