Pooling interval-monitored step-stress accelerated life tests for reliability prediction: A failure-rate-based meta-analysis for the proportional hazards family
Abstract
Reliability qualification often relies on several step-stress accelerated life tests conducted in separate campaigns, laboratories, or test rigs, each with its own stress profile, sample size, and inspection schedule, and with units inspected only periodically so that only failure counts between inspections are recorded. Existing meta-analysis methods combine several step-stress experiments but require exactly observed failure times. Methods for interval-inspected step-stress data, on the other hand, have been developed only for a single experiment. This paper develops a failure-rate-based meta-analysis framework for multiple interval-inspected step-stress experiments within the proportional hazards family, linking the experiments through a common underlying lifetime model and a log-linear stress-life relationship. Maximum likelihood estimators and confidence intervals are derived for the model parameters and for engineering quantities of interest at normal operating conditions, including mission reliability, mean time to failure, and lifetime quantiles such as the 0.10 quantile (B10 life). For the LED data, pooling the two tests reduced the RMSE of the estimated reliability at 5 hours by about 20% and that of the 0.10 quantile by about 66%, compared with the better single test. A misspecification study shows that the median is robust to the choice of lifetime distribution (relative bias below 6%), whereas tail quantiles can have a relative bias of up to 34% that does not vanish as the sample size increases, which is critical for warranty decisions. The methodology is illustrated with simulated data and with two step-stress tests of light-emitting diodes.
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BibTeX
@misc{palit2026pooling,
title = {{Pooling interval-monitored step-stress accelerated life tests for reliability prediction: A failure-rate-based meta-analysis for the proportional hazards family}},
author = {Pranoy Palit and Ayan Pal and Kiran Prajapat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34231},
eprint = {2610.34231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34231},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Pooling interval-monitored step-stress accelerated life tests for reliability prediction: A failure-rate-based meta-analysis for the proportional hazards family
AU - Pranoy Palit
AU - Ayan Pal
AU - Kiran Prajapat
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34231
UR - https://arxiv.org/abs/2610.34231
AB - Reliability qualification often relies on several step-stress accelerated life tests conducted in separate campaigns, laboratories, or test rigs, each with its own stress profile, sample size, and inspection schedule, and with units inspected only periodically so that only failure counts between inspections are recorded. Existing meta-analysis methods combine several step-stress experiments but require exactly observed failure times. Methods for interval-inspected step-stress data, on the other hand, have been developed only for a single experiment. This paper develops a failure-rate-based meta-analysis framework for multiple interval-inspected step-stress experiments within the proportional hazards family, linking the experiments through a common underlying lifetime model and a log-linear stress-life relationship. Maximum likelihood estimators and confidence intervals are derived for the model parameters and for engineering quantities of interest at normal operating conditions, including mission reliability, mean time to failure, and lifetime quantiles such as the 0.10 quantile (B10 life). For the LED data, pooling the two tests reduced the RMSE of the estimated reliability at 5 hours by about 20% and that of the 0.10 quantile by about 66%, compared with the better single test. A misspecification study shows that the median is robust to the choice of lifetime distribution (relative bias below 6%), whereas tail quantiles can have a relative bias of up to 34% that does not vanish as the sample size increases, which is critical for warranty decisions. The methodology is illustrated with simulated data and with two step-stress tests of light-emitting diodes.
ER -