Reliability evaluation for Weibull distribution under multiply type-I censoring

The multiply type-D dagger censoring represented that all units in life test were terminated at different times. For estimations of Weibull parameters, it was easy to compute the maximum likelihood estimation (MLE) and least-squares estimation (LSE) while it was hard to build confidence intervals (CI). The concept of generalized confidence interval (GCI) was introduced to build CIs of parameters under multiply type-I censoring. Further, GCI based on LSE and GCI based on MLE were proposed. It is mathematically proved that the former is exact and the latter is approximate. Besides, a Monte Carlo simulation study and an illustrative example also turn out that the GCI method based on LSE yields rather satisfactory results by comparison with the ones based on MLE. It should be clear that the GCI method is a sensible choice to evaluate reliability under multiply type-I censoring.