A fabrication line used for the manufacture of analog ICs requires tight control on the relative sizes of small geometric features. In a particular case, it is required that transistors on either side of a differential pair differ less than 0.1 µm in their effective gate lengths. If that difference is normally distributed with µ = 0 and σ = 0.05 µm:

(a) Calculate the process capability (Cp) and the fraction of nonconforming product when the process is in control.

(b) Suppose the mean of the process shifts and this shift doubles the fraction of nonconforming product. Calculate the sample size needed to implement a p chart that will detect this shift on the first subsequent sample with 50% certainty.

(c) Design a 3σ and R charts that will detect the previous shift with the same 50% certainty.