Robust Estimation in Step-Stress Experiments under Weibull Lifetime Distributions

2026-03-28

AI Summary

This study addresses the challenge of scarce failure data for highly reliable products under normal operating conditions, where step-stress accelerated life testing is commonly employed. Recognizing that conventional maximum likelihood estimation (MLE) is sensitive to outliers in such tests—leading to unreliable inference—this work extends minimum density power divergence estimation (MDPDE) to step-stress models with mixture distributions. Under the assumption of Weibull-distributed lifetimes, the paper establishes the asymptotic theory for parameter estimation. The proposed method maintains high estimation efficiency while substantially enhancing robustness against contaminated data. Comprehensive simulations and a real-data analysis demonstrate that the MDPDE-based approach significantly outperforms MLE in the presence of outliers, achieving both strong robustness and high statistical efficiency.

Abstract

Many modern products are highly reliable, often exhibiting long lifetimes. As a result, conducting experiments under normal operating conditions can be prohibitively time-consuming to collect sufficient failure data for robust statistical inference. Accelerated life tests (ALTs) offer a practical solution by inducing earlier failures, thereby reducing the required testing time. In step-stress experiments, a stress factor that accelerates product degradation is identified and systematically increased at predetermined time points, while remaining constant between intervals. Failure data collected under these elevated stress levels is analyzed, and the results are then extrapolated to normal operating conditions. Traditional estimation methods for such data, such as the maximum likelihood estimator (MLE), are highly efficient under ideal conditions but can be severely affected by outlying or contaminated observations. To address this, we propose the use of Minimum Density Power Divergence Estimators (MDPDEs) as a robust alternative, offering a balanced trade-off between efficiency and resistance to contamination. The MDPDE framework is extended to mixed distributions and its theoretical properties, including the asymptotic distribution of the model parameters, are derived assuming Weibull lifetimes. The effectiveness of the proposed approach is illustrated through extensive simulation studies, and its practical applicability is further demonstrated using real-world data.

Problem

• step-stress
• Weibull lifetime
• robust estimation
• accelerated life testing
• outliers

Innovation

• Minimum Density Power Divergence Estimator
• Step-Stress Accelerated Life Test
• Robust Estimation
• Weibull Lifetime Distribution
• Outlier Resistance