A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Eight models for forecasting the maximum speed of aeroplanes are presented and their performances are critically evaluated.

Nahi [2] considered the optimal linear estimation with uncertain observations. In his model, the binary random variables characterizing uncertainty of signals in the observation were statistically independent. This correspondence considers the same model but with the binary random variables correlated.

The optimal control of unreliable dynamic systems where the mode (working or failed) is continuously inspected or monitored has received attention in the past. We consider the problem where instead of continuous inspection we have either no inspection or inspection at discrete time instants. The optimal feedback control is derived for the case where the system has no renewable capabilities. The case where a fixed number of renewals are allowed is briefly discussed.