Prediction and reconstruction of future and missing unobservable modified Weibull lifetime based on generalized order statistics

When a system consisting of independent components of the same type, some appropriate 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 simulation 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.