Robust Estimation in Step-Stress Experiments under Exponential Lifetime Distributions

TL;DR

This paper introduces robust estimation methods using MDPDEs for step-stress experiments with exponential lifetime data, improving reliability of statistical inference under outliers.

Contribution

It develops a robust estimation approach based on MDPDEs for exponential lifetime models in step-stress tests, including theoretical properties and practical evaluation.

Findings

MDPDEs offer a robust alternative to MLE in step-stress experiments.

Theoretical properties of the estimators are derived under exponential assumptions.

Simulation and real data demonstrate the effectiveness of the proposed method.

Abstract

Many modern products exhibit high reliability, often resulting in long times to failure. Consequently, conducting experiments under normal operating conditions may require an impractically long duration to obtain sufficient failure data for reliable statistical inference. As an alternative, accelerated life tests (ALTs) are employed to induce earlier failures and thereby reduce testing time. In step-stress experiments a stress factor that accelerates product degradation is identified and systematically increased to provoke early failures. The stress level is increased at predetermined time points and maintained constant between these intervals. Failure data observed under increased levels of stress is statistically analyzed, and results are then extrapolate to normal operating conditions. Classical estimation methods such analysis rely on the maximum likelihood estimator (MLE) which is know to be very efficient, but lack robustness in the presence of outlying data. In this work, Minimum Density Power Divergence Estimators (MDPDEs) are proposed as a robust alternative, demonstrating an appealing compromise between efficiency and robustness. The MDPDE based on mixed distributions is developed, and its theoretical properties, including the expression for the asymptotic distribution of the model parameters, are derived under exponential lifetime assumptions. The good performance of the proposed method is evaluated through simulation studies, and its applicability is demonstrated using real data.