Optimal design of systems subject to two kinds of failure

The problem of achieving optimal system size is treated for k-out-of-n systems, assuming that failure may take either one of two forms. Under the assumption that components are independent and identically-distributed and the two kinds of system failures can have different costs, the optimal system size n which maximizes the mean system profit is determined. The effect of the system parameters on the optimal system size n is studied. A numerical example is given to illustrate the results.<<ETX>>