Robust Estimation in Step-Stress Experiments under Weibull Lifetime Distributions

TL;DR

This paper introduces a robust estimation method using MDPDEs for step-stress experiments with Weibull lifetimes, improving reliability analysis under contaminated data conditions.

Contribution

It extends MDPDEs to mixed distributions in step-stress Weibull models, providing theoretical properties and demonstrating practical robustness through simulations and real data.

Findings

MDPDEs offer robustness against outliers in Weibull-based step-stress experiments.

Theoretical derivations include the asymptotic distribution of estimators.

Simulation studies confirm improved performance over traditional MLEs.

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.