A corona virus infectious disease (COVID – 19) is spreading quickly throughout the globe. An exhaustive data available for this infectious disease on confirmed cases, active cases, recovered cases and fatal cases and relation between them will give us some information for future statistical analysis and modelling. In this research paper, the focus is on Modelling and forecasting the COVID – 19 cases for India and Karnataka. With this view an auto regressive model has been developed for the confirmed and fatal cases which are validated for the period of data which has not been used for modelling. While comparing to the other existing models this gives preferable results.

Optimization of a redundancy allocation problem designed specifically for systems with k-out-of-n subsystems has been the motive of this work. The main motive is to select the components and redundancy levels to maximize system reliability given system-level constraints. With cost and weight as constraints as 3 out of 5 subsystems has been optimized in the present study for maximizing the reliability of a mechanical system. Component reliabilities in every stage are treated as unknowns in this model. Evolutionary and Generalised Reduced Gradient method (GRG nonlinear Solver) in Excel has been applied here to determine the component reliabilities, stage reliabilities to maximize system reliability. A comparative study has been done using the methodology in the present paper with the methods already used by the other authors for the similar systems.