Robust inference for cyclic-stress accelerated life tests under interval monitoring with lognormal lifetimes

2026-06-04

AI Summary

This study addresses the challenges posed by interval-censored data and the sensitivity of conventional maximum likelihood estimation to outliers in cyclic accelerated life testing (CyALT). Under the assumption that product lifetimes follow a log-normal distribution, the authors propose a robust inference method based on the weighted minimum density power divergence estimator (WMDPDE). The proposed approach achieves both high statistical efficiency and strong resistance to contamination. Notably, this work establishes the asymptotic theory and influence function of WMDPDE within the CyALT framework for the first time. Simulation studies demonstrate that WMDPDE substantially outperforms traditional methods in the presence of outliers while retaining high efficiency under clean data conditions. The practical applicability and robustness of the method are further confirmed through analysis of real-world air conditioner reliability data.

Abstract

Highly reliable products are often tested under accelerated conditions to provoke failures within a feasible timeframe. For products whose service life involves repeated alternation between two stress levels, such as automotive air-conditioners, batteries, and aerospace components, cyclic-stress accelerated life testing (CyALT) provides a more realistic loading profile than conventional accelerated tests. In practice, failures are often recorded only at scheduled inspection times, leading to interval-censored counts rather than exact lifetimes. Moreover, traditional maximum likelihood estimation is sensitive to data contamination, which is a genuine concern in small-sample industrial experiments. This paper develops robust inferential procedures for CyALT models with lognormal lifetimes under interval monitoring. Robust estimators are obtained by minimizing a weighted density power divergence (WDPD), leading to the weighted minimum density power divergence estimator (WMDPDE). We establish the asymptotic distribution of the WMDPDE, derive influence function expressions to characterize the robustness, and present asymptotic and bootstrap confidence intervals for important lifetime characteristics. A simulation study confirms that the WMDPDE provides substantial protection against outliers while retaining high efficiency under clean data. The methodology is illustrated through the analysis of an air-conditioner reliability dataset, demonstrating the practical advantages of robust inference in the CyALT framework.

Problem

• cyclic-stress accelerated life test
• interval censoring
• lognormal lifetime
• robust inference
• data contamination

Innovation

• cyclic-stress accelerated life testing
• interval censoring
• robust estimation
• weighted minimum density power divergence
• lognormal lifetime