The Pentel Microchip Company has started production of its new microchip. The first phase in this production is the wafer fabrication process. Because of the great difficulty in fabricating acceptable wafers, many of these tiny wafers must be rejected because they are defective. Therefore, management places great emphasis on continually improving the wafer fabrication process to increase its production yield (the percentage of wafers fabricated in the current lot that are of acceptable quality for producing microchips).
So far, the production yields of the respective lots have been 15, 21, 24, 32, 37, 41, 40, 47, 51, and 53 percent. Use exponential smoothing with trend to forecast the production yield of the next lot. Begin with initial estimates of 10 percent for the expected value and 5 percent for the trend. Use smoothing constants of α = 0.2 and β = 0.2.