Interval estimation of the generalized half-normal constant-stress accelerated life testing under Type-II censoring

The generalized half-normal distribution is an important life distribution that can model non-monotonic failure rates. This paper considers the generalized half-normal (GHN) constant-stress accelerated life test model under Type-II censoring, where the scale parameter of the GHN distribution is assumed to be the exponential function of stress. We derive maximum likelihood estimators and asymptotic confidence intervals (ACIs) for the model parameters. Since commonly used ACIs do not perform well in the case of small and moderate sample sizes, we use the generalized pivotal quantity (GPQ) method to derive the interval estimation of the model parameters. Using the random variable transformation method, we construct the GPQs of the parameters. Then, based on the proposed GPQs, we derive the generalized confidence intervals (GCIs) for the model parameters and the commonly used reliability metrics. The performance of the proposed GCIs is evaluated through Monte Carlo simulations and a real data example, both of which demonstrate their robustness and precision, particularly under small sample sizes.