Mango Airways has twelve scheduled flight per day from Cape Town to Durban. As part of their process improvement programme they have decided to conduct an investigation into the turnaround time at Cape Town airport. The turnaround time specified is 15 minutes. The data recorded below was obtained during a typical 15 day period. The turnaround time is assumed to be normally distributed. Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X1 7 8 7 5 9 9 2 8 9 9 10 13 10 12 12 X2 8 7 8 7 -3 -2 7 10 12 13 6 8 15 14 15 X3 6 5 5 8 6 -1 4 12 15 10 9 12 10 15 16 X4 -2 2 2 0 4 5 5 15 8 11 12 12 8 10 17 X5 0 -2 0 0 0 8 0 13 9 7 13 10 12 11 20 1.1. Calculate the process mean and standard deviation 1.2. Determine the upper and lower control limits for x and R control charts. 1.3. Determine the upper and lower control limits for x and S control charts. 1.4. Set up x and R control charts on this process. Is this process in control? Explain. 1.5. Set up and S control charts on this process. Is this process in control? Explain. 1.6. Calculate and interpret the process capability index for this process. (2) 1.7. A penalty charge of R 15,000.00 is payable by the airline for late departures. Calculate the penalty that Mango will pay per annum in penalties. (8) [31 marks] Mango Airways has twelve scheduled flight per day from Cape Town to Durban. As part of their process improvement programme they have decided to conduct an investigation into the turnaround time at Cape Town airport. The turnaround time specified is 15 minutes. The data recorded below was obtained during a typical 15 day period. The turnaround time is assumed to be normally distributed. Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X1 7 8 7 5 9 9 2 8 9 9 10 13 10 12 12 X2 8 7 8 7 -3 -2 7 10 12 13 6 8 15 14 15 X3 6 5 5 8 6 -1 4 12 15 10 9 12 10 15 16 X4 -2 2 2 0 4 5 5 15 8 11 12 12 8 10 17 X5 0 -2 0 0 0 8 0 13 9 7 13 10 12 11 20 1.1. Calculate the process mean and standard deviation 1.2. Determine the upper and lower control limits for x and R control charts. 1.3. Determine the upper and lower control limits for x and S control charts. 1.4. Set up x and R control charts on this process. Is this process in control? Explain. 1.5. Set up and S control charts on this process. Is this process in control? Explain. 1.6. Calculate and interpret the process capability index for this process. (2) 1.7. A penalty charge of R 15,000.00 is payable by the airline for late departures. Calculate the penalty that Mango will pay per annum in penalties. (8) [31 marks]