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In this paper, we discuss linear inference for the lifetime distribution of components based on a Type-II censored lifetime data of reliability systems with known signatures. We derive the best linear unbiased estimators (BLUE) for the parameter(s) in general scale and location-scale parameter families. The exact computational formulas of the BLUE and their variances and covariance are provided. Selected tables of the coefficients of BLUE are presented for the exponential and extreme value distributions. Using these, best linear unbiased predictors of future system failure times are discussed. Finally, two examples are provided to illustrate all the methods of inference developed here.