A new block censoring scheme: comparative assessment of likelihood and spacings methods for Weibull distribution with an application to cancer data

In reliability experiments conducted across multiple groups, prolonged test durations and heterogeneity among groups can substantially reduce efficiency and affect statistical inference. This study has proposed a new censoring design that combines block experimentation with an improved adaptive progressive Type-Ⅱ hybrid termination rule to ensure controlled test duration while maintaining sufficient failure information. The proposed framework generalizes several existing censoring schemes and allows independent groups to operate under flexible stopping conditions. Assuming Weibull lifetimes with a common shape parameter and group-specific scale parameters, parameter estimation and reliability characteristics were obtained using maximum likelihood and maximum product of spacings methods. Both point and interval estimators were developed. To quantify heterogeneity across groups, a new measure based on confidence interval overlap, called the coverage similarity index, was introduced. Simulation results showed that the maximum product of spacings method generally provides more accurate estimation for scale-related quantities and reliability measures, while maximum likelihood performs slightly better for the shape parameter and mean time to failure. The proposed methodology was illustrated using cancer survival data from ovary, breast, and kidney groups, where meaningful heterogeneity was detected. The findings confirm the practical value of the proposed design and highlight the importance of accounting for group-level variation in reliability and survival analysis.