Reliability inference of the quadratic hazard rate model under step-stress partially accelerated life testing with progressive Type-Ⅱ censoring

Step-stress partially accelerated life testing (SSPALT) provides an effective framework for obtaining timely reliability information when products operate under varying stress levels. In this paper, statistical inference and applications of the quadratic hazard rate distribution are developed under SSPALT with progressive Type-Ⅱ censoring and binomial removals. This censoring scheme offers flexibility in balancing the experimental cost and statistical efficiency while accommodating practical testing constraints. Maximum likelihood and Bayesian estimation are derived for the model parameters and the acceleration factor. Computational implementations are carried out using the Markov chain Monte Carlo method. Reliability analyses, including survival and hazard rate functions, are carried out to support practical reliability assessment and decision-making. Asymptotic confidence intervals and credible intervals are constructed to quantify the estimation uncertainty. The performance of the proposed estimators is evaluated through Monte Carlo simulations under different experimental settings. The methodology is illustrated using three real data sets from solar lighting equipment, nanocrystalline devices, and micro-unmanned aerial vehicles. The results emphasize the flexibility and accurate inference for accelerated reliability testing, making it suitable for a wide range of applications.