Advanced Reliability Analysis with Applications of Hjorth Constant-Stress Normal-Operating Setting Using Newly Progressive Censored Data

Modern high-reliability products fail rarely, so researchers rely on accelerated life testing to obtain failure information within practical time limits. This study presents a useful framework integrating constant-stress accelerated life tests with an improved adaptive progressive Type-II censoring plan to estimate the reliability function under normal operating conditions of the Hjorth model. The Hjorth model is chosen because its hazard rate can be constant, increasing, decreasing, or bathtub-shaped, which reduces errors due to incorrect hazard assumptions. Stress affects lifetime through a log-linear relationship applied to the scale and the shape parameter. We derive the full likelihood for the proposed censoring plan across several stress levels, obtain maximum likelihood estimates with confidence intervals based on the observed information matrix, and develop a Bayesian analysis with informative prior distributions and sampling by Markov chain Monte Carlo technique. We then estimate reliability at normal operating conditions together with its interval estimates by both approaches. Extensive Monte Carlo simulations demonstrate the superior accuracy of the Bayesian estimators, especially when the number of observed failures is small or censoring is heavy, while maintaining interval coverage close to the nominal level. The practical utility of the proposed methodology is demonstrated through its application to real-world accelerated lifetime data sets. Applications to real-world data sets show that the proposed model fits the data well and yields reliable estimates of reliability at normal operating conditions.OPEN ACCESS Received: 26/07/2025 Accepted: 28/10/2025 Published: 23/01/2026