Lifetime data with time and failure censoring arises frequently in the controlled lifetime study. The Fisher information matrix I^M(θ) of this data is more complex than that of the typeⅠcensored data. For Location-Scale distribution families, we prove that the asymptotic Fisher information I^M(θ) equals typeⅠcensored Fisher information matrix. The results can be extended to Log Location-Scale family, such as Weibull and Lognormal distributions.