Robust tests for log-normal lifetimes under cyclic-stress accelerated tests and interval monitoring
Abstract
Some products are, by nature, designed to operate under stress conditions that repeatedly cycle between two levels, such as batteries undergoing repeated charge and discharge, or components exposed to recurring thermal or pressure cycles. When such products are tested under accelerated conditions, the applied stress is naturally elevated in the same cyclic manner rather than held constant or increased in a single step. Cyclic-stress accelerated life testing (CyALT) reflects this by alternating the applied stress between specified levels. Units are often inspected only at fixed times, so the data consist of interval failure counts rather than exact lifetimes. Hypothesis testing plays a crucial role in this setting. It can assess whether the applied stress significantly affects lifetime, or validate the parameter values used to design the experiment. Classical tests rely on the maximum likelihood estimator, which is highly sensitive to contamination. Since interval probabilities are estimated jointly across stress conditions, a single anomalous failure count can distort the entire parameter vector and severely affect the test's significance level and power. This paper develops Wald-type and Rao-type test statistics for log-normal CyALT lifetimes under interval monitoring, based on the weighted minimum density power divergence estimator. Both tests are derived for simple and composite null hypotheses. A Monte Carlo study shows that classical tests lose control of the significance level rapidly under contamination, while the robust tests stay close to nominal with only a modest loss of power under clean data. An application to air-conditioner evaporator lifetime data further illustrates the proposed tests.
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BibTeX
@misc{jaenada2026robust,
title = {{Robust tests for log-normal lifetimes under cyclic-stress accelerated tests and interval monitoring}},
author = {María Jaenada and Leandro Pardo and Kiran Prajapat},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21434},
eprint = {2609.21434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21434},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Robust tests for log-normal lifetimes under cyclic-stress accelerated tests and interval monitoring
AU - María Jaenada
AU - Leandro Pardo
AU - Kiran Prajapat
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21434
UR - https://arxiv.org/abs/2609.21434
AB - Some products are, by nature, designed to operate under stress conditions that repeatedly cycle between two levels, such as batteries undergoing repeated charge and discharge, or components exposed to recurring thermal or pressure cycles. When such products are tested under accelerated conditions, the applied stress is naturally elevated in the same cyclic manner rather than held constant or increased in a single step. Cyclic-stress accelerated life testing (CyALT) reflects this by alternating the applied stress between specified levels. Units are often inspected only at fixed times, so the data consist of interval failure counts rather than exact lifetimes. Hypothesis testing plays a crucial role in this setting. It can assess whether the applied stress significantly affects lifetime, or validate the parameter values used to design the experiment. Classical tests rely on the maximum likelihood estimator, which is highly sensitive to contamination. Since interval probabilities are estimated jointly across stress conditions, a single anomalous failure count can distort the entire parameter vector and severely affect the test's significance level and power. This paper develops Wald-type and Rao-type test statistics for log-normal CyALT lifetimes under interval monitoring, based on the weighted minimum density power divergence estimator. Both tests are derived for simple and composite null hypotheses. A Monte Carlo study shows that classical tests lose control of the significance level rapidly under contamination, while the robust tests stay close to nominal with only a modest loss of power under clean data. An application to air-conditioner evaporator lifetime data further illustrates the proposed tests.
ER -