When a system consisting of independent components of the same type, some appro-
priate actions may be done as soon as a portion of them have failed. It is, therefore, important to
be able to predict later failure times from earlier ones. One of the well-known failure distributions
commonly used to model component life, is the modified Weibull distribution ( MWD ). In this paper,
two pivotal quantities are proposed to construct prediction intervals for future unobservable lifetimes
based on generalized order statistics (gos) from MWD . Moreover, a pivotal quantity is developed to
reconstruct missing observations at the beginning of experiment. Furthermore, Monte Carlo simula-
tion studies are conducted and numerical computations are carried out to investigate the efficiency of
presented results. Finally, two illustrative examples for real data sets are analyzed