Person: Castilla González, Elena María
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First Name
Elena María
Last Name
Castilla González
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Estadística e Investigación Operativa
Area
Estadística e Investigación Operativa
Identifiers
6 results
Search Results
Now showing 1 - 6 of 6
Item Robust inference for non-destructive one-shot device testing under step-stress model with exponential lifetimes(2022) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Jaenada Malagón, María; Pardo Llorente, LeandroOne-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step-stress tests allow the experimenter to increase the stress levels at pre-fixed times gradually during the life-testing experiment. The cumulative exposure model is commonly assumed for step-stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and conffidence intervals for different lifetime characteristic such as reliability, distribution quantiles and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real-life data sets are analyzed ffinally for illustrative purpose.Item Robust Inference for One-Shot Device Testing Data Under Weibull Lifetime Model(IEEE Transactions on Reliability, 2020) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Martín Apaolaza, Nirian; Pardo Llorente, LeandroClassical 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.Item Robust inference for one‐shot device testing data under exponential lifetime model with multiple stresses(Quality and Reliability Engineering International, 2020) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Martín Apaolaza, Nirian; Pardo Llorente, LeandroIntroduced robust density-based estimators in the context of one-shot devices with exponential lifetimes under a single stress factor. However, it is usual to have several stress factors in industrial experiments involving one-shot devices. In this paper, the weighted minimum density power divergence estimators (WMDPDEs) are developed as a natural extension of the classical maximum likelihood estimators (MLEs) for one-shot device testing data under exponential lifetime model with multiple stresses. Based on these estimators, Wald-type test statistics are also developed. Through a simulation study, it is shown that some WMDPDEs have a better performance than the MLE in relation to robustness. Two examples with multiple stresses show the usefulness of the model and, in particular, of the proposed estimators, both in engineering and medicine.Item Divergence-based robust inference under proportional hazards model for one-shot device life-test(IEEE Transactions on Reliability, 2021) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Martín, N; Pardo Llorente, LeandroIn this paper, 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 than the classical procedures, based on maximum likelihood estimators.Item Optimal designs of constant‐stress accelerated life‐tests for one‐shot devices with model misspecification analysis(Quality and Reliability Engineering International, 2021) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Ling, Man HoThe design of constant-stress accelerated life-test (CSALT) is important in reliability estimation. In reliability studies, practitioners usually rely on underlying distribution to design CSALTs. However, model misspecification analysis of optimal designs has not been examined extensively. This paper considers one-shot device testing data by assuming gamma, Weibull, lognormal and Birnbaum–Saunders (BS) lifetime distributions, which are popular lifetime distributions in reliability studies. We then investigate the effect of model misspecification between these lifetime distributions in the design of optimal CSALTs, in which the asymptotic variance of the estimate of reliability of the device at a specific mission time is minimized subject to a prefixed budget and a termination time of the life-test. The inspection frequency, number of inspections at each stress level, and allocation of the test devices are determined in optimal design for one-shot device testing. Finally, a numerical example involving a grease-based magnetorheological fluids (G-MRF) data set is used to illustrate the developed methods. Results suggest the assumption of lifetime distribution as Weibull or lognormal to be more robust to model misspecification, while the assumption of gamma lifetime distribution seems to be the most non-robust (or most sensitive) one.Item Power divergence approach for one-shot device testing under competing risks(Journal of Computational and Applied Mathematics, 2022) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Martín Apaolaza, Nirian; Pardo Llorente, LeandroMost work on one-shot devices assume that there is only one possible cause of device failure. However, in practice, it is often the case that the products under study can experience any one of various possible causes of failure. Robust estimators and Wald-type tests are developed here for the case of one-shot devices under competing risks. An extensive simulation study illustrates the robustness of these divergence-based estimators and test procedures based on them. A data-driven procedure is proposed for choosing the optimal estimator for any given data set which is then applied to an example in the context of survival analysis.