Jaech [2] considers point and interval estimation of the shape parameter in the Weibull distribution based on two failures per lot from one or more lots. This paper provides similar procedures for two or more failures per lot. Point estimation procedures for the scale parameter and for reliability are also provided, and interval estimation is considered for the two failures per lot case. Some comparisons of the estimators with maximum likelihood estimators and a comparison of the relative expected experiment time for censored sampling compared to complete sampling are also included.