Suppose that “the process going out of control” corresponds to a shift of the mean from  to    with probability .25,   2 with probability .25,    with probability .25, and   2 with probability .25. What modifications in the model are required? In particular, if we write the shift in the form   , show how to compute 1 and 2 that would correspond to values of   1 and   2, respectively.

If the out-of-control costs were now represented by a3 when   1 and a4 when   2, determine an expression for the average annual operating costs. (Assume all other costs and system parameters remain the same.)