Consider a process where you are to design a fraction nonconforming control chart with three sigma limits. Assume n = 100, and p = 0.080.

1. What are the three-sigma limits for the p-chart?
2. Calculate the probability of a Type I error. What is the ARL₀ for this process?
3. Construct the O-C curve for this process.
4. Suppose the process fraction nonconforming shifts to p₁ = 0.15.
   1. A. Compute the probability of a Type II error and the ARL₁ for this shift.
   2. B. What is the probability of detecting the shift to p₁ = 0.15 by at most the fourth sample after the shift?