You are a Quality Control consultant. You design control systems such in order to minimize the overall expected cost per hour. This afternoon you are planning to meet with two clients regarding their processes, but you have accidentally mixed up their files. You have the output for each. One scheme has an optimal n = 5, h = 1, and k = 2.3. The other scheme has an optimal n = 5, h = 1, and k = 3.2. Below is a description of the main characteristics of your two clients’ processes. Determine which scheme goes with each client. You must explain your reasoning to receive any credit.
Client A: The cost of operating in an out of control state is $1000 per hour because you have to scrap most of your production, while the cost of investigating a false alarm is $100 per hour.
Client B: The cost of operating in an out of control state is $20 per hour, and the cost of investigating a false alarm is $200 per hour because you have to stop the entire process anytime there is an out of control signal.