The manufacturer wishes to set up a control chart at the final inspection station for a gas water heater. Defects in workmanship and visual quality features are checked in this inspection. For the past 22 working days, 176 water heaters were inspected and a total of 924 nonconformities reported.

(a) What type of control chart would you recommend here, and how would you use it?

(b) Using two water heaters as the inspection unit, calculate the center line and control limits that are consistent with the past 22 days of inspection data.

(c) What is the probability of type I error for the control chart in part (b)?