Power divergence approach for one-shot device testing under competing risks

Castilla, Elena; Martín, Nirian

doi:10.1016/j.cam.2022.114676

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…Indeed, the DPD can be defined at β = 0 by taking continuous limits as the KL divergence and thus, the MLE is the more efficient and less robust estimator of the MDPDE family. An important observation is that, since the DPD loss in Equation ( 11) is differentiable in a and the MDPDE is computed as its minimizer, the MDPDE must annul the first derivatives of the loss (11). Therefore, the MDPDE estimating equations are given by…”

Section: The Step-stress Model Under Competing Risksmentioning

confidence: 99%

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Robust inference for nondestructive one‐shot device testing under step‐stress model with exponential lifetimes

Castilla

Jaenada

Pardo

2023

Quality & Reliability Eng

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One‐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 prefixed 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 nondestructive 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 confidence 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 finally for illustrative purpose.

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Section: The Step-stress Model Under Competing Risksmentioning

confidence: 99%

“…The specific algorithm is shown below Algorithm 1: Bootstrap confidence intervals 1. Obtain the MDPDEs defined in (11) based on the observed simple step-stress interval-censored sample of size N .…”

Section: Bootstrap Confidence Intervalsmentioning

confidence: 99%