Robust divergence-based tests of hypotheses for simple step-stress accelerated life-testing under Gamma lifetime distributions

• Challenges in statistical analysis of highly reliable devices : Reliability tests under real-use conditions may require impractically long durations for highly reliable devices and typically involve censoring. As an alternative, Accelerated Life-Tests (ALTs) are used for reliability inference. • Need for robust statistical methods : Lifetime data often have outlying observations. Beyond point estimation, a robust analysis requires robust inferential methods, including hypothesis testing, to fully evaluate the product’s reliability behavior. • Divergence-based test statistics : This paper presents two families of robust test statistics based on the density power divergence for analyzing ALT data under step-stress conditions and Gamma lifetime distributions. Many modern devices are highly reliable, with long lifetimes before their failure. Conducting reliability tests under actual use conditions may require therefore impractically long experimental times to gather sufficient data for developing accurate inference. To address this, Accelerated Life Tests (ALTs) are often used in industrial experiments to induce product degradation and eventual failure more quickly by increasing certain environmental stress factors. Data collected under such increased stress conditions are analyzed, and results are then extrapolated to normal operating conditions. These tests typically involve a small number of devices and so pose significant challenges, such as interval-censoring. As a result, the outcomes are particularly sensitive to outliers in the data. Additionally, a comprehensive analysis requires more than just point estimation; inferential methods such as confidence intervals and hypothesis testing are essential to fully assess the reliability behaviour of the product. This paper presents robust statistical methods based on minimum divergence estimators for analyzing ALT data of highly reliable devices under step-stress conditions and Gamma lifetime distributions. Robust test statistics generalizing the Rao test and divergence-based tests for testing linear null hypothesis are then developed. These hypotheses include in particular tests for the significance of the identified stress factors and for the validity of the assumption of exponential lifetimes.